**High-Frequency Deep Sclerotomy, A Minimal Invasive Ab Interno Glaucoma Procedure Combined with Cataract Surgery: Physical Properties and Clinical Outcome**

#### **Bojan Pajic 1,2,3,4,\*, Zeljka Cvejic 2, Kaweh Mansouri 5,6, Mirko Resan <sup>4</sup> and Reto Allemann <sup>1</sup>**


Received: 25 November 2019; Accepted: 23 December 2019; Published: 27 December 2019

**Abstract:** Background: The efficiency and safety of primary open-angle glaucoma with high-frequency deep sclerotomy (HFDS) combined with cataract surgery has to be investigated. Methods: Right after cataract surgery, HFDS was performed ab interno in 205 consecutive patients with open angle glaucoma. HFDS was performed with a custom-made high-frequency disSection 19 G probe (abee tip 0.3 × 1 mm, Oertli Switzerland). The bipolar current with a frequency of 500 kHz is applied. The nasal sclera was penetrated repetitively six times through the trabecular meshwork and consecutively through Schlemm's canal. Every time, a pocket of 0.3 mm high and 0.6 mm width was created. Results: Mean preoperative intraocular pressure (IOP) was 24.5 ± 2.1 mmHg (range 21 to 48 mmHg). After 48 months, the follow up average IOP was 15.0 ± 1.7 mmHg (range 10 to 20 mmHg). Postoperative IOP has been significantly reduced compared to preoperative IOP for all studied cases (*p* < 0.001). After 48 months, the target IOP less than 21 mmHg reached in 84.9%. No serious complications were observed during the surgical procedure itself and in the postoperative period. Conclusions: HFDS is a minimally invasive procedure. It is a safe and efficacious surgical technique for lowering IOP combined with cataract surgery.

**Keywords:** glaucoma; ab interno; minimally invasive glaucoma surgery; cataract surgery; high-frequency deep sclerotomy; intraocular pressure

#### **1. Introduction**

It is well known that glaucoma comes first in cases of irreversible vision loss and is the second leading cause of blindness worldwide [1]. Nowadays in developed countries, less than 50% of people are unaware of their diagnosis, mainly because of the asymptomatic nature of chronic glaucoma [2].

Trabeculectomy remains the gold standard for glaucoma surgery despite high rates of complications [3–5]. Choroidal effusions, hypotony, shallow anterior chambers, and hyphema are known as early postoperative complications [6–8]. Late complications are often bleb-related, including leakage, blebitis, and endophthalmitis. These complications are more common if antimetabolites like 5-Fluorouracil and Mitomycin C are used [9].

Outflow resistance is caused primarily by the juxtacanilicular trabecular meshwork and, especially, by the inner wall of the Schlemm's canal. This fact is used for the concept of the trabecular meshwork bypass [10]. It is presumed that 35% of the outflow resistance arises in the inner wall of the Schlemm's canal [11].

In addition to the procedures already mentioned, we focus in this work on an enhanced Schlemms canal (SC), which can be addressed both internally and externally. According to the current classification, the ab interno methods include trabectome, iStent, Hydrus, the results presented in this work, and high-frequency deep sclerotomy (HFDS) [12]. The trabectome was introduced in 2004 and has an electroablation of an arc of trabecular meshwork where direct access to the collector channels is given. The intraocular pressure (IOP) reduction of up to 40% is stated in the literature for this ab interno method [13,14]. Another approach for a micro-invasive glaucoma surgery (MIGS) from interno is the iStent. With this device, the aqueous humor is drained directly into the Schlemm's canal, thus avoiding the resistance of the trabecular meshwork [15]. Another representative of the ab interno procedure of the Schemm's canal microstent is the so-called hydrus. It is an 8 mm long crescent-shaped open structure that the bend and sludge canal adapts. It is introduced into the Schlemm's canal by a clear corneal incision [16]. The HFDS is an internally operative glaucoma method that was introduced in 1999. Initially, this surgical procedure was known as sclerothalamotomy ab interno (STT ab interno), and its name was only changed to HFDS in 2012. The aim of the new nomenclature was to describe the procedure more precisely. Regarding the procedure, there were no differences between STT ab interno and HFDS [17–20].

The aim of all MIGS is that, in addition to being effective, they can be carried out simply, quickly and inexpensively with the longest possible effect. The aim of this study is to show the clinical 4-year investigations of this trans-trabecular surgery using the Schlemm's canal as an outflow pathway combined with cataract surgery.

#### **2. Materials and Methods**

In this single center study from December 2012 till December 2016, 223 patients with insuffiently controlled primary open-angle glaucoma under maximal tolerated topical therapy without history of prior ocular surgery with significant cataract were included. Exlcusion criteria were monophthalmia, angle closure with or without glaucoma, missing willingness to attend follow-up examinations with randomization or any psychiatric disorder, and any condition that affects the optical system (severe alteration of cornea, anterior chamber, or retina). During the observation period of 48 months, 18 patients did not finish the follow up due to several reasons, so finally 205 patients were included in the study. HFDS was performed combined with cataract surgery, with cataract surgery first being performed. Both procedures were always performed by the same surgeon. A complete ophthalmological examination was carried out in each patient prior to surgery. Further ophthalmologic follow-up examinations were carried out postoperatively on days 1, 2, and 3, after 1 and 4 weeks, and then every 3 months until 48 months. Gonioscopy with a three-mirror goniolens was performed after 4 weeks to check the persistence of the sclerotomy. Tobramycin/dexamethasone and pilocarpin 2% eye drops were applied 3 times daily for 1 month. The tenets of the Declaration for Helsinki were followed in this study. The cantonal ethics committee of Aargau approved the study. According to the ethics committee, patient consent is not required for this retrospective study.

#### *High-Frequency Diathermic Probe*

The high-frequency diathermic probe (abee® Glaucoma Tip, Oertli Instrumente AG, Berneck, Switzerland) consists of an inner and outer coaxial electrode. Both electrodes are isolated, while the inner one is made by platinum.

The dimensions of platinum probe tips are 1 mm in length, 0.3 mm high, and 0.6 mm wide. The platinum probe tip is bent posteriorly at an angle of 150◦. The probe external diameter is 0.9 mm. Electrical current is modulated at MF (~500 kHz) frequency. The temperature of approximately 130 ◦C

at the tip of the probe is generated by alternating current, while target tissue temperature ranges from 90◦ to 100◦. The tissue is heated by radio frequency-induced intracellular oscillation of ionized molecules, which leads to elevation of intracellular temperature. The very high temperatures cause breakdown of tissue molecules. Inhomogeneous electric field with high voltage and selective current flow conduct to electric arcs (Figure 1).

**Figure 1.** Inhomogeneous electric field, high voltage, and electric arc.

Bearing in mind that the vaporization or cutting process is the best accomplished with relatively low voltage, the coagulation is performed by arcing modulated high-voltage current to tissue. The electric arcs create cell bursts through the evaporation of cell content. By modulating the voltage, it is possible to cut and at the same time make locale coagulation. There is a galvanic separation between the power source and the surgery hand piece (Figure 2).

**Figure 2.** High-frequency (HF) generator.

First, the electrodes are placed away from the tissue, and then the gap between two electrodes is ionized. Due to ionization process, an electric arc discharge develops. In this approach, tissue burning is more superficial because the current is spread over the tissue area more than over the tip of electrode. The experimental set-up provides high-frequency power dissipation in the vicinity of the tip. This was demonstrated in the histological analysis by showing that there is more of a cutting effect in the tissue than coagulation, because there is no tissue nor cell denaturation in the cutting channel and surrounding tissue (Figure 3).

**Figure 3.** Histological analysis of a high-frequency deep sclerotomy (HFDS) cut (HE staining, human eye).

Two clear corneal incisions were used: one of 1.2-mm temporale or temporo-superior for introducing the abee tip and the other nasal with 0.8-mm created for cataract surgery. In the study, miochol (Acetylcholine chlorid 20 mg) was given intracamerally for the miosis. Anterior chamber was filled with a cohesive ophthalmic viscosurgical device (OVD). The standard high-frequency probe (Figure 4) as described above is consecutively inserted through the temporal paracentesis using a four mirror gonioscopic lens, until the probe is properly placed opposite nasally to the iridocorneal structure.

**Figure 4.** Abee® (HFDS) tip.

Then, six pockets were created consecutively in a row with approximately one tip length space between them. Recently, a new diathermic probe design was developed and used for all patients in the study. For all patients, six pockets were done. With the new abee tip design, three accesses to the anterior chamber are possible, i.e., temporal, superotemporal, or superonasal. The pockets can thus be placed nasally, nasally inferior, or nasally temporal. Consequent retreatments can be done easily. The external diameter is 0.9 mm. Oertli devices were used for the study, i.e., the Pharos and Catarhex 3, with the same setting.

The electric specifications of the probe remained unchanged. Pockets were created with the probe 1 mm through the trabecular meshwork, into Schlemm canal. The target was the insertion of a pocket of 1 mm into the sclera. The target deep sclerotomy pocket is approximatively 0.3 mm thick and 0.6 mm wide, resulting in a resorption surface area of 3.6 mm2 (Figure 5a).

**Figure 5.** (**a**) OCT image of the anterior chamber: Overview after HFDS procedure with a newly created pocket in the chamber angle (Visante OCT, Zeiss, Oberkochen, Germany). (**b**) OCT image of the anterior chamber of a normal angle anterior before HFDS surgery.

For comparison, it is shown a normal anterior chamber and angle anterior (Figure 5b).

The tip's dimensions and ab interno approach make it compatible with the stipulations of minimally invasive glaucoma surgery.

Statistical analysis: statistical calculation was done with SPSS Program Version 22. Two-tailed student t-test was used for statistical evaluation of parametric data. Significance was set at a *p* value of <0.05.

#### **3. Results**

Mean age of patients with open-angle glaucoma was 76.8 ± 11.1 years (range: 35–88 years). 103 patients (50.2%) were female, and 102 patients (49.8%) male. One eye of each patient was included. During the whole period of 48 months, no repeat-surgery was needed in any included patient.

Mean preoperative IOP in the study population of 205 patients was 24.5 ± 4.3 mmHg (range 18 to 48 mmHg). Decimalised Snellen visual acuity (VA) increased from 0.46 ± 0.27 preoperative to 0.68 ± 0.27 postoperative. For all patients, the follow-up was 48 months. After 10 days, a slight increase of IOP was detected but was not statistically significant. Mean IOP after 48 months was 15.0 ± 1.7 mmHg (range 10 to 20 mmHg). The IOP drop was statistically significant (*p* < 0.001) at all measured postoperative intervals (Figure 6).

**Figure 6.** Intraocular pressure (IOP) follow-up of operated eyes during 48 months.

At month 48 after surgery, 54.7% of patients had an IOP < 15 mmHg, 77% had an IOP < 18 mmHg, and 84.9% had an IOP < 21 mmHg. Qualified success rate, defined as an IOP lower than 22 mmHg with medication, was 100% for all patients at 48 months (Figure 7).

**Figure 7.** Qualified success rate after 48 months of follow-up.

The average preoperative administration of pressure-reducing number of antihypertensive eye agents was 2.6 ± 1.0. Following surgery, this value was decreased to 0.47 ± 0.59 after 1 month, 0.40 ± 0.54 after 3 months, 0.28 ± 0.62 after 6 months, 0.31 ± 0.49 after 12 months, 0.38 ± 0.57 after 24 months, 0.42 ± 0.83 after 36 months, and 0.48 ± 0.97 after 48 months (Figure 8).

**Figure 8.** Progression of pressure-reducing eye agents pre-and postoperative during the 48 months, showing a marked and sustained postoperative reduction in numbers of agents needed.

There were no significant visual field changes (Octopus 900, Haag Streit, Switzerland) from baseline with a mean defect MD 7.06 ± 6.54 and loss of variance LV 26.4 ± 23.92. At 48 months, these values were MD 8.43 ± 2.11 and LV 24.1 ± 24.92 (*p* = 0.22 for MD, *p* = 0.58 for LV).

The mean excavation preoperative was 0.63 ± 0.22 and after 48 months 0.65 ± 0.21, which is not statistically significant (*p* = 0.36).

Temporary IOP elevation higher than 21 mmHg was observed in 18 of 205 eyes (8.7%). Four eyes (2%) showed transient fibrin formation. Fibrin was treated by topical dexamethasone and disappeared one day later.

#### **4. Discussion**

The present study has shown sustained IOP—lowering effect over 48 months using Schlemm's canal as an outflow pathway with a novel MIGS procedure. Looking into the past, the only possibility of glaucoma treatment was conservative medical management and more invasive glaucoma surgery. The advance MIGS procedure was intended to fill the existing gap regarding treatment. Early studies [19] have demonstrated its ability to lower IOP with minimal risk for mild to moderate glaucoma.

The HFDS ab interno method intends the creation of a direct channel between the anterior chamber and the Schlemm canal. Persistence of the sclerotomy has been investigated with a three-mirror goniolens 4 weeks after the procedures. The abee tip creates a deep sclerotomy with subsequent access of aqueous outflow to the scleral layer. Both aspects may facilitate a bypass effect of aqueous outflow. In an earlier study with deep sclerotomy ab interno, a significant IOP peak could be seen ten days postoperatively [17]. As shown in our study, with introduction of postoperative pilocarpine 2% eye drops application for the first 4 weeks, the high IOP peak amplitude could be avoided. This may have also been the case because the procedures were done combined with cataract surgery.

In general, MIGS procedures share five important features: ab interno approach, potential minimal trauma, ability to lower IOP, a high level of safety, and faster visual recovery. Hence, advantages of HFDS ab interno method, compared with trabeculectomy and perforating and nonperforating deep sclerectomy, seem to have a low rate of postoperative complications and a stable level of reduced IOP. Hypotension, a frequent finding in trabeculectomy, which is less frequently found in nonperforating deep sclerectomy, was not seen in the present population. The most frequent early complications in trabeculectomy are hyphaema (24.6%), shallow anterior chamber (23.9%), hypotony (24.3%), wound leak (17.8%), and choroidal detachment (14.1%). The most frequent late complications are iris incarceration (5.1%) and encapsulated bleb (3.4%) [21]. After HFDS, a transient IOP elevation was seen in 18 of 205 eyes (8.7%), on average occurring 10 days postoperatively. Four of 205 eyes (2%) had transient fibrin formation. Therefore, compared with penetrating or nonpenetrating techniques, HFDS seems to be a safe surgical technique [22–25].

An earlier study with deep sclerotomy ab interno had a complete success rate of 83% after 48 months [17,19] for open angle glaucoma. The present study shows that the success rate of 84.9% was similar. The slight improvement could be due to the fact that the procedures was carried out in combination with cataract surgery. It was particularly striking that the postoperative IOP range was significantly lower in the combined procedure. This effect could be explained by the additional reduction due to the cataract surgery, but also by the postoperative application of pilocarpine 2% during the first 4 weeks. If the postoperative IOP profile is analyzed, after 24 months there is a loss of the additional IOP-lowering effect from the cataract surgery will be apparent.

Advantages of HFDS include its comparative simplicity and short duration of the surgical procedure itself. Additionally, unlike ab externo filtering techniques, the technique avoids stimulation of episcleral and conjunctival tissues leading to fibroblast activation. Additionally, by comparing the histological alterations of HFDS with trabectome, another MIGS procedure, it has been shown that with trabectome tissue was damaged near the incision [26]. As trabectome was validated mainly in the pediatric population associated with long-term IOP control, recently a dual-blade device was developed for adult use but showing also smaller but still detectable damage to the tissue [27].

#### **5. Conclusions**

Although the number of six surgical pockets chosen was arbitrary, our results suggest that it may be sufficient to provide good long-term IOP-lowering efficacy and safety. With the introduction of the new abee-tip design, it is possible to perform surgical retreatment in the nasal and inferior quadrants

of the trabecular meshwork. HFDS is a safe and minimally invasive method for glaucoma surgery with good long-term results. More studies are needed to confirm our findings in different populations and types of glaucoma.

**Author Contributions:** B.P. provided the treatment indication, developed the study design, acquired clinical data, and contributed to writing the paper. Z.C. contributed substantially to the development of the study design and substantially contributed to writing the paper. K.M. performed data analyses and substantially contributed advising regarding the paper contents. M.R. performed data anlysis and substantially contributed the study design. R.A. performed data analysis and contributed to writing the paper. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## *Article* **Laser Vision Correction for Regular Myopia and Supracor Presbyopia: A Comparison Study**

**Bojan Pajic 1,2,3,4, Zeljka Cvejic 2, Horace Massa 3, Brigitte Pajic-Eggspuehler 1, Mirko Resan <sup>4</sup> and Harald P. Studer 1,5,\***


Received: 29 December 2019; Accepted: 22 January 2020; Published: 27 January 2020

**Abstract:** A study to compare femto-presbyLASIK to standard myopia femto-LASIK refractive surgical correction with a total of 45 candidates was performed. The goal was to identify a more specific set of indications for presbyopia LASIK treatments. The results showed thoroughly good uncorrected visual acuity for myopia (decimal: 1.01 ± 0.15) as well as for presbyLASIK (decimal: 0.78 ± 0.17) corrections. Astigmatism was comparable in both groups and did not change significantly from preoperative (0.98D ± 0.53 SD) to postoperative (1.01D ± 0.50 SD). Our study results suggest, that presbyLASIK treatment is as safe and effective as regular LASIK myopia correction and can hence be recommended to treat presbyopia.

**Keywords:** supracor; myopia; presbyopia; presbyLASIK; refractive surgery; follow-up; clinical results; lasik; excimer laser

#### **1. Introduction**

Laser Assisted In-Situ Keratomileusis (LASIK) has become the most prevalent refractive surgical procedure for myopic and hyperopic corrections (about 1.2 million procedures a year in the US)—over the last two decades. Patient satisfaction is generally found to be very high between 92 and 98 percent [1,2]. Modern excimer laser systems can restore 20/20 uncorrected visual acuity (UCVA) in myopic eyes up to—10D and hyperopic up to +6D, feature tissue saving procedures [3], provide patient-specific, wavefront and/or topography guided ablation patterns, and can treat astigmatism with elliptically shaped patterns.

The concept of multifocal PresbyLASIK is a relatively new yet attractive surgical procedure for the correction of presbyopia. It involves two steps: (1) the correction of the ametropic state for distance vision, and (2) the multifocality addition for near vision. As most commonly reported in literature, multifocality is usually implemented by combining a central corneal curvature addition for near vision correction with a paracentral corneal curvature, adjusted to correct distance vision [4–9].

The downside of multifocal LASIK treatments is that they always represent a compromise between distance—and near vision correction, as they create unwanted aberrations—especially spherical aberrations in the central pupillary region. For this reason, modern PresbyLASIK treatment algorithms are wavefront-guided to minimize unwanted aberrations. Compared to treating presbyopia with the well-established multifocal intra ocular lens (IOL) implantation, PresbyLASIK has the advantage of being less invasive because the ocular globe does not need to be opened for treatment. However, the planning of PresbyLASIK procedures is much more demanding and requires experience in the interpretation of the preoperative corneal topography, wavefront analysis and the Zernike coefficients, which all have significant impact on the surgery result. Hence, it is not enough to simply apply the common LASIK indications to PresbyLASIK as well. Presumably, the lack of specific indications—along with missing to consider refraction and wavefront analysis parameters, might well be the reason for the not all encouraging LASIK presbyopia treatment results presented in literature [10,11].

In this study we present our PresbyLASIK results and compare them to a control group of regular LASIK myopia correction cases. Further, we propose an updated set of more specific indications for the PresbyLASIK treatment.

#### **2. Materials and Methods**

Our study population included two groups of eyes, 40 eyes of 20 study patients (female: 14, male: 6, age: 30 ± 9 years) were treated with regular myopic LASIK correction, and 50 eyes of 25 study patients (female: 14, male: 11, age: 52 ± 3.8 years) were treated for presbyopia with the PresbyLASIK Supracor treatment (B&L Technolas, Munich, Germany). All surgery procedures were performed by an experienced surgeon (BP) at the Eye Clinic ORASIS between January 2014 and February 2015.

The LDV femtosecond laser (Ziemer Ophthalmology, Port, Switzerland) was used to make the LASIK flaps, whereby the hinge was superior in all cases. The flap diameter depended on the corneal curvature and was between 8.5 and 9.0 mm. The Munnerlyn formula [12] along with the B&L-Technolas proprietary transition zone algorithm was used to calculate the ablation patterns for the regular myopia corrections. In a two-step approach a 2.0 mm laser spot diameter was first used to apply the basic correction, followed by the fine-tuning step with a 1.0 mm laser spot. An eye tracker system was active during all interventions. The cyclorotation is automatically compensated which is especially important for cases where astigmatism correction was included. Whenever the angle kappa was smaller or equal 6◦ the laser spot was placed in the pupil center, otherwise it was placed at the point of the arithmetic mean between the pupil center and the Purkinje reflex. After the laser correction, the flap was carefully placed back onto the stromal bed, making sure no visible wrinkles are left.

The same approach as for the myopia ablation patterns is also employed to calculate the Supracor PresbyLASIK ablation patterns, however, the target refraction is chosen such that the dominant eye was at 0.0D and the follow-eye was at −0.5D. The goal of a first application phase is to obtain a perfect mono-focal correction, and only in the second phase the central cornea is steepened by the multifocal curvature addition in the 3.0 to 6.0 mm zone. Considering that such an ablation could potentially induced spherical aberration, the Supracor procedure was performed wavefront-guided for all cases.

Corneal shape was assessed one week before and then 3 months after the LASIK treatment, with the Galilei G4 tomographer (Ziemer Ophthalmic Systems, Port, Switzerland). Thereby, each individual measurement was repeated three times in a row. So, only one measurement with the median astigmatism cylinder value is selected for further data evaluation.

The statistical methods used in this study were straightforward calculations of average and standard deviation, as described in any textbook of statistics. Excel software package (Microsoft, Redmond, WA, USA) was used to import and process data, as well as, to obtain the functional dependence of the selected parameters and their visualization. Two-tailed Student *t*-test was used for calculating the parametric datas and for the nonparametric test the Wilcoxon signed rank test was used. The level of significance was set at *p* < 0.05.

#### **3. Results**

All study data were carefully analyzed and are presented in the following. Manifest refraction of the whole study population was sph: −1.99D ± 3.48 (SD), cyl: −0.80D ± 0.79 (SD) before, and sph: −0.03D ± 0.27 (SD), cyl: −0.18D ± 0.32 (SD) after the surgery. While the myopia group had a manifest

refraction of sph: −3.53D ± 2.48 (SD), cyl: −0.93D ± 0.84 (SD) before, and sph: +0.05D ± 0.19 (SD), cyl: −0.09D ± 0.27 (SD) after the surgery, the presbyopia group had a manifest refraction of sph: −1.02D ± 3.78 (SD), cyl:−0.72D ± 0.75 (SD) before, and sph: −0.09D ± 0.31 (SD), cyl: −0.24D ± 0.34 (SD) after the surgery.

#### *3.1. Uncorrected Visual Acuity*

Uncorrected visual acuity (UCVA) was assessed before (decimal scale: 0.31 ± 0.24) and after the treatment (decimal scale: 0.88 ± 0.20) for the whole study population. In the myopia group UCVA was 0.19 ± 0.16 preoperatively, and 1.01 ± 0.15 postoperatively. In the presbyopia group UCVA was 0.38 ± 0.25 preoperatively, and 0.78 ± 0.17 postoperatively. A statistically significant improvement was observed in both groups (*p* < 0.0001). In 4 eyes (4.3%, two in myopia and two in presbyopia group), UCVA remained unchanged, and for two eyes (2.2%, all in the presbyopia group) UCVA was slightly worse than before the treatment. For all other eyes (93.5%), UCVA improved (see Table 1). The failure to achieve the target refraction and UCVA could be corrected with a re-treatment.

**Table 1.** Uncorrected visual acuity after regular myopia and Supracor presbyopia treatment.


While the multifocal presbyopia treatments showed a small trend (R2 = 0.01) towards greater corrections having a lower postoperative UCVA, this trend could not be observed (R<sup>2</sup> = 1 <sup>×</sup> 10<sup>−</sup>5) for the myopic corrections (see Figure 1).

#### *3.2. Residual Stromal Bed and Percentage Tissue Altered*

The average residual stromal bed thickness for all cases was 385 μm ± 49 (SD), with a minimum of 285 μm, and a maximum of 510 μm. The recently published and already widely accepted new criterion for LASIK safety, the percentage tissue altered (PTA) value [13] was 32.0% ± 3.0 (SD), with a minimum of 22% and a maximum of 47%.

**Figure 1.** *Cont*.

**Figure 1.** Trend analysis for presbyopia treatments (**b**) showed a mild correlation (R<sup>2</sup> = 0.01 with slope 0.005) that greater dioptric corrections resulted in lower uncorrected visual acuity (UCVA). No such correlation (R2 = 1E-05 with slope < 0.001) between dioptric correction and resulting UCVA could be observed in the myopia (**a**) results, though.

#### *3.3. Astigmatism Change*

Corneal astigmatism, assessed with the Galilei G4, showed very little difference (*p* > 0.6), between preoperative (0.98D ± 0.53 SD) and postoperative measurements (1.01D ± 0.50 SD) over the whole study population. Likewise, the myopia group had preoperative astigmatism of 1.17D ± 0.63 (SD), which changed to postoperative astigmatism of 0.78D ± 0.74 (SD) *p* > 0.02. The presbyopia group had preoperative astigmatism of 1.02D ± 0.42 (SD), which changed to postoperative astigmatism of 0.96D ± 0.58 (SD) *p* > 0.02. Also, Figure 2 shows double-angle polar plots of pre-, and post-operative astigmatism measurements for both groups, myopia and presbyopia, and suggests only small changes in astigmatism from pre—to postoperative measurements. However, the Alpins method [14] vector analysis (including the astigmatism orientation) showed that astigmatism changed significantly, by 0.78D ± 0.74 (SD) for myopia and by 0.96D ± 0.58 (SD) for presbyopia, respectively. The intended astigmatic change (planned astigmatic LASIK ablations) was 0.94D ± 0.84 (SD) for myopia group and 0.65D ± 0.41 (SD) for presbyopia group.

**Figure 2.** Double-angle polar plots comparing (**a**) pre- to (**b**) postoperative astigmatism. Myopia results are shown as circles and presbyopia results are shown as solid squares. No obvious differences between myopia and presbyopia correction were visible.

#### *3.4. Corneal Curvature Change*

The planned shape change of the anterior corneal surface was compared to the measured corneal surface average corneal curvature–AvgK (postoperative Galilei minus preoperative Galilei). In an ideally case, in Figure 3, all data points would lie on a diagonal line (y = 1.0x + 0.0, with an R<sup>2</sup> = 1.0). The top plot (b) in Figure 3 shows that the above graph (b) in Figure 3 shows that the presbyopia corrections showed a better match between the planned and achieved spherical correction (y = 0.67x <sup>−</sup> 0.09, R<sup>2</sup> = 0.93) compared to the myopia correction (see graph (a) in Figure 3) (y = 0.45x <sup>−</sup> 1.22, R2 = 0.47).

**Figure 3.** Comparing planned to achieved shape change of anterior corneal surface. Presbyopia treatments (**b**) showed a better match (R2 = 0.93 and slope 0.67) than (**a**) myopia (R<sup>2</sup> = 0.45 and slope 0.47).

#### **4. Discussion**

In this study, femto-LASIK refractive surgical treatments were performed in two groups of study populations. While one of the groups received a standard myopia treatment, the second group was treated with a specific multifocal presbyLASIK algorithm to treat presbyopia. Study data, such as uncorrected visual acuity (UCVA), were carefully analyzed and presented as study results.

In almost all the cases (>93%), UCVA was improved after the surgery, with respect to the baseline assessment before the treatment. Thereby, the standard femto-LASIK myopia treatment showed slightly better results than the presbyLASIK treatment, where outcome UCVA was lower. This most likely arises from the fact that the subjective tolerance to eye surgical treatments including multifocal optics is greater than in monofocal treatments. Even a small deviation of 0.5D from the target value can be disturbing for the patient. Accordingly, there was a small but significant trend in recent results, where higher correction of presbyLASIK lead to lower postoperative UCVA. No similar trend was observed in the standard myopia treatment cases, where even high corrections of up to −10.5D had perfect vision with UCVA result of decimal 1.0.

The completely positive UCVA outcome was achieved, although the results suggest that astigmatism was drastically undertreated. Even though the laser was programmed with astigmatism correcting ablation patterns for all cases with treatable preoperative astigmatism, significant postoperative corneal astigmatism was observed in the topography measurements of both study groups. This observation is not supported by estimates of apparent refraction, where the cylinder of astigmatism decreased from −0.80D ± 0.79 (SD) to −0.18 D ± 0.33 (SD) (*p* < 0.00001). Thus, it could be assumed that the topography measurements were not accurate enough, but we did not have additional data to examine this in more details.

After surgical treatment, the mechanical strength of the cornea depends only on the residual stroma. It is well known that when the residual stroma is too thin to handle IOP, both its anterior and posterior surface will bulge forward as in ectasia. Nowadays, residual stroma thickness (RST) is accepted to be at least 250 μm. Conventionally, thickness less than 480 is considered abnormal, while some surgeons consider preoperative corneal thickness less than 500 μm unsuitable for LASIK. While planning the treatments, 250 μm of the RST was suggested as it accounts for 50% of 500 μm, which is the minimum corneal thickness recommended for LASIK. Also, high percentage of tissue altered (PTA) is the most common cause of ectasia after LASIK in patients with normal preoperative corneal topography. According to Santiago et al. [13], high values of PTA, especially higher than 40% is important factor in the development post-Lasik ectasia with normal preoperative corneal topography. For that reasonPTA should be taken as one of the screening parameter for refractive surgery candidates. In addition to this criterion, we have aimed at a postoperative thickness of 300 μm residual cornea stroma or more for all cases to allow re-treatment if necessary. None of the eyes in this study developed postoperative ectasia.

The observation, that postoperative central corneal curvature was steeper than planned comes from the fact that the algorithm used for the multifocality add-on causes a central steepening within the 3.0 mm zone. This is because the central zone is intended to be used for near vision. The 3.0 to 6.0 mm zone is adjusted to correct intermediate and distance vision. Both eyes thereby are treated the same way, except that the non-dominant eye is targeted at −0.5D from plano.

The results in this study suggest that the used procedure for presbyLASIK improves vision of presbyopia patients. Hence, we propose to include subjects for the presbyopia treatment older than 48 years, with a mesopic pupil of 3.5–6.5 mm diameter, and with a postoperative Kmean between 35.0D and 47.0D. The central near vision add-ons should be chosen >2.0D. We further suggest that cases where eye surgery was previously performed should not be included, especially cases where corneal refractive surgery was performed. Also, those cases with irregular corneal morphology, lens opacification, natural preoperative multifocality in the cornea, or a central corneal thickness CCT < 500 μm microns should not be included.

**Author Contributions:** B.P. and the team from the Orasis clinic in Switzerland conducted the clinical study and collected all the data and contributed substantially to writing the manuscript. Z.C. contributed substantially to the methodology, collecting datas and contributed substantially to writing the manuscript. H.M. performed data analyses and substantially contributed advising regarding the paper contents. B.P.-E. perform substantially data curation and contributed the study design. M.R. performed data anlysis and substantially contributed the study design. H.P.S. did the data analysis, statistical analysis and created all the plots and figures, and contributed substantially to writing the manuscript. All authors have read and agreed to the published version of the manuscript.

**Funding:** The clinical study funded by the Swiss research project CTI 13404.1, by the commission for technology and innovation, Switzerland.

**Conflicts of Interest:** All authors declare to have no conflict of interest.

#### **References**


© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## *Article* **A Feasibility Study of a Novel Piezo MEMS Tweezer for Soft Materials Characterization**

#### **Fabio Botta \*, Andrea Rossi and Nicola Pio Belfiore**

Dipartimento di Ingegneria, Università degli Studi Roma Tre, Via della Vasca Navale, 79, 00146 Roma, Italy; andrea.rossi@uniroma3.it (A.R.); nicolapio.belfiore@uniroma3.it (N.P.B.)

**\*** Correspondence: fabio.botta@uniroma3.it; Tel.: +39-06-57333491

Received: 1 May 2019; Accepted: 28 May 2019; Published: 2 June 2019

**Abstract:** The opportunity to know the status of a soft tissue (ST) in situ can be very useful for microsurgery or early diagnosis. Since normal and diseased tissues have different mechanical characteristics, many systems have been developed to carry out such measurements locally. Among them, MEMS tweezers are very relevant for their efficiency and relative simplicity compared to the other systems. In this paper a novel piezoelectric MEMS tweezer for soft materials analysis and characterization is presented. A theoretical approach has developed in order to carry out the values of the stiffness, the equivalent Young's modulus, and the viscous damping coefficients of the analyzed samples. The method has been validated by using both Finite Element Analysis and data from the literature.

**Keywords:** MEMS; tweezer; piezoelectric; soft tissue; microsurgery

#### **1. Introduction**

Early diagnosis is crucial to prevent disease progressions [1]. The correlation between the mechanical characteristics of a soft tissue and its status has been highlighted by several studies in many cell types like cancer cells, epithelial cells and laminopathies associated with diseases of the nuclear membrane [2]. In cancer cells, for example, the malignant transformation influences the mechanical properties by disruption and/or reorganization of cytoskeleton [3]. The stiffness, the elastic modulus, and the dynamic viscosity are among the most commonly used mechanical quantities to evaluate the state of a soft tissue. However the possibility to identify a diseased soft tissue in situ, at the microscale, can increase significantly the possibility of the cure.

Different techniques are used to perform such measurements as micropipette aspiration [4], magnetic bead twisting [5], atomic force microscopy [6], optical tweezers [7] or mechanical tweezers [8]. In recent years, researchers focused on the developing of micro-electro-mechanical systems (MEMS) tweezers because of their efficiency and relative simplicity with respect to other systems [9]. New gripping tweezers have been built taking cue from the kinematics of articulated mechanisms [10] as the property of parallelograms [11–15]. More complex motion, with an increasing of the number of degrees of freedom, can be obtained adopting the concept of lumped compliance. In fact, concentrated flexibility has been used in flexure hinges in several investigations [16–20]. In order to improve the displacement accuracy and to lower the stress levels in the flexible elements a new conjugate surfaces flexure hinge (CSFH) flexure has been proposed [21–25] and optimized [26,27]. The system has shown promising results in terms of of versatility and applicability to different types of tissue [28]. Thanks to their high level of miniaturization, MEMS-Technology based tweezers can be employed also in minimal invasive [29–31] or gastrointestinal surgery [32], and more generally speaking, in endoluminal surgery, for example, in TEM [33–35].

The actuation of the tweezer can be obtained by different systems, such as linear electrostatic actuators [36,37], rotatory electrostatic actuators [38,39] or electrothermal actuation [40–46]. However the advent of smart materials in the last decades has greatly increased the possibilities of development of new smart structures [47–49] with the ability, not possible for the traditional systems, to adapt to external conditions variations. Because of their speed of response, low power consumption and high operating bandwidth the piezoelectric materials are, among the smart materials, the most promising ones for active vibration control [50–53] and MEMS applications [54]. However the research in the latter field mainly focuses on the energy harvesting [55–58] or MEMS tweezers for manipulating micro-objects and microassembly [59–61].

This paper presents the design of a novel piezoMEMS tweezer for the analysis and characterization of soft materials. Each jaw can be built as a sandwich composite beam and activated by an electric field.

The tweezer is supposed to be force controlled because the piezoelectric materials produce a stress proportional to the applied electrical field. Furthermore, a sensor is supposed to be integrated into the structure for displacement control. This gives rise to improve the analysis of the cell properties. In fact, the displacement-controlled actuator is able to identify the beginning of a rupture during straining or softening, while a force-controlled system maintains a constant force regardless of the required displacement [62]. The action of the piezoelectric material has been modeled by the Pin Force Model [63].

By applying symmetric electric fields to the composite jaws, they will bend in opposite directions allowing the gripping of the soft tissue.

A new mathematical model to measure the stiffness, the equivalent Young's modulus, and the viscous damping coefficient of the soft tissue has been developed. The model has been tested on three different soft test specimens and the results were in good agreement with those obtained by COMSOL finite elements code.

#### **2. The Adopted Piezo-Mems Microgripper**

The purpose of this paper is to develop a theoretical model of a piezo-MEMS microgripper, which can be used to characterize a grasped sample tissue. Therefore, the actual fabrication process of this instrument will not be herein considered. However, for the sake of completeness, a selection of possible materials and technological processes is briefly recalled.

In the last decades, several actuation methods have been proposed to induce motion in MEMS devices such as electrostatic, thermal and piezoelectric. The electrostatic devices are widely adopted but the piezoelectric MEMS's offer some attractive advantages: lower power consumption, broader bandwidth and approximately ten times lower voltages to obtain the same given displacement [64]. Furthermore the piezoelectric materials can be manufactured using the same MEMS conventional technologies and for this reason these materials have been preferred to develop piezo-MEMS devices in the last decades. Typical applications include vibration energy harvesters [65,66], resonators [67], capacitors [68], micro sensors/actuators [69,70], micromachined ultrasonic transducer [71], gyroscopic sensors [72], microlens [73,74], 1D and 2D micro-scanners [75,76].

The piezoelectric materials can be gathered into two groups: ferroelectric (lead zirconate titanate, PZT compounds) and non-ferroelectric (ZnO and AlN). The piezoelectric characteristics (piezoelectric coefficient, Q factor, dielectric constant, etc.) rely on the crystalline structure. In fact ZnO and AlN thin-films show wurtzite structure that entails lower piezoelectricity if compared to PZT materials (perovskite structure). Nevertheless ZnO and AlN exhibit large mechanical stiffness, high *Q* factor and do not require a polarization process so they can be attractive for sensors applications. PZT thin-films provide high piezoelectric properties, lower cost and stability against temperature but require a poling process before using the piezo-MEMS device [77]. The electric field poling direction depends on the functional configuration of the piezo-MEMS.

Usually the piezoelectric MEMS actuators/sensors are based on cantilever structures and the number of active layers identifies their working configuration:


When a PZT bimorph bending beam and the transverse piezoelectric effect (*d*31) are considered, the PZT layers must be poled in opposite directions in order to maximize the bending action. Then the electrodes of the PZT layers in contact with the structural layer share the same electric potential, whereas the outer electrodes share the same opposite sign potential (see Section 3). The design and fabrication process of piezo-MEMS devices have been extensively explored for the above mentioned unimorph and bimorph cantilever configurations using the aforementioned materials:


Various technologies can be applied to deposit piezoelectric thin-films such as


Usually the sol-gel and sputtering methods are the preferred ones both for research and commercial production because they allow the piezoelectric thin-film to be homogeneously deposited on large Si wafers [79]. The beam structural layer can be metal-based or silicon-based and the etching processes could be accomplished relying on conventional techniques (RIE, D-RIE, ECR).

A schematic view of the target piezo-MEMS tweezer is qualitatively depicted in Figure 1. The system can be obtained by using a multilayer wafer that can be built by using the above mentioned techniques. At the end of the process, the whole microsystem is composed of two bimorph beams (**a**)-(**b**)-(**c**) (see Figure 1). The two bimorph beams are supported by the handle layer (**d**). The specific steps of the process (deposition, etching, exposure, etc.) will depend on the peculiar materials and technology selected for the construction. In the case under study, the system is conceived in such a way that the mask geometry could be quite elementary for any etching step.

**Figure 1.** A schematic view of the microsystem: outer layers with a same voltage *V*<sup>0</sup> (**a**); structural material for the beams (**b**); internal layers with voltage *Vi* (**c**) and structural layer for the handle (**d**).

Another possible layout is represented in Figure 2, where two new layers (**e**) have been added with respect to the previous example of fabrication. Layers (**a**), (**b**), (**c**), and (**d**) have the same function as described for the previous layout. The second design is better for the operational aspects because a clamping tooth has been added for each jaw. However, these two teeth are more difficult to obtain during the process because they require at least two more deposition layers (**e**) and also a more complex series of intermediate etching-deposition steps that depend on the selected materials.

**Figure 2.** An alternative layout for the microgripper: outer layers with a same voltage *V*<sup>0</sup> (**a**); structural material for the beams (**b**); internal layers with voltage *Vi* (**c**) and structural layer for the handle (**d**).

#### **3. Modeling Piezoelectric Actions on the Microbeams**

Concerning the piezoelectric actions, many studies [63,80–82] have confirmed that, under certain assumptions (piezoelectric plates are perfectly bonded to the structure, the ratio between their thickness and the thickness of the beam is very low and their inertia and mass negligible with respect to those of the beam) the stresses applied to the beam can be considered as they were concentrated at the piezoelectric plate ends. Moreover, if the electric field to the upper plate is opposite in sign to the one applied to the lower plate, such action is equivalent to a flexural moment (see Figure 3) applied to the end of the beam of magnitude equal to:

$$M\_a(t) = \frac{\psi}{\theta + \psi} E\_a c T\_a T\_b \Lambda(t) \tag{1}$$

with

$$\begin{cases} \begin{cases} \Lambda(t) = \frac{d\_{\mathcal{U}}}{T\_a} V(t) \\\\ \Psi = \frac{E\_b T\_b}{E\_a T\_a} \end{cases} \end{cases} \tag{2}$$

**Figure 3.** Piezoelectric action (PIN force model).

By activating the piezoelectric plates pairs on the two jaws-beams of the tweezer in opposite manner the two moments *Ma* will have opposite sign and the beams will bend in opposite direction allowing the gripper to grasp the soft tissue, as depicted in Figure 4.

**Figure 4.** PiezoMEMS grip of the soft tissue.

#### *3.1. Static Model*

The value of the stiffness *KST* and of the equivalent Young's modulus *EST* can be established by a static test with a constant voltage *V*<sup>0</sup> applied to the piezoelectric plates: *V*(*t*) = *V*0. In this case, the bending of the beams will cause the compression of the soft tissue and consequently a reaction force *FST* will be applied from the soft tissue to the beams, through the clamp teeth (see Figure 5).

**Figure 5.** Scheme for the calculation of the tip displacement.

Considering that the Euler Bernoulli model is appropriate for the present case because of the high length-to-thickness aspect ratio of the beams, the tip deflection:

$$w\_L = \frac{M\_b L^2}{2E\_b I\_b} - \frac{F\_{ST} L^3}{3E\_b I\_b} \, ^\prime \tag{3}$$

is due to a combination of the loads *FST* and *Ma*. Therefore, the first load

$$F\_{ST} = \frac{3E\_b I\_b}{L^3} \left(\frac{M\_d L^2}{2E\_b I\_b} - w\_L\right) \tag{4}$$

can be obtained by measuring *wL*.

Due to the high value of the axial stiffness of the clamp teeth, the deflection *wL* can be considered equal to the axial displacement of the soft tissue (see Figure 5) so that the axial strain

$$
\epsilon\_{ST} = \frac{2w\_L}{L\_{ST}}\tag{5}
$$

is calculated.

Under the assumption of linear elastic behavior for the soft tissue (ST), the relationship between the normal stress *σST* applied to the cross section of the soft tissue and  *ST* can be written as:

$$
\sigma\_{ST} = \frac{F\_{ST}}{S\_{ST}} = E\_{ST} \frac{2w\_L}{L\_{ST}} \tag{6}
$$

from which the equivalent Young's modulus

$$E\_{ST} = \frac{F\_{ST}L\_{ST}}{2S\_{ST}w\_L} \tag{7}$$

is evaluated. Moreover, the stiffness

$$K\_{ST} = \frac{2E\_{ST}S\_{ST}}{L\_{ST}}\tag{8}$$

is calculated given the dimensions of the ST sample.

#### *3.2. Dynamics Model*

To determine the value of the viscous damping *CST*, a dynamic test has been conceived by applying a variable harmonic excitation voltage *V*(*t*) = *V*0*sin*(*ωt*).

By referring to *δLint*, *δLin*, *δLa* and *δLST* as the virtual works of internal, inertial, actuator and ST forces, respectively, and to *δLinm* as the virtual work of the inertial forces of the clamp teeth, the virtual work principle can be written as:

$$
\delta L\_{int} = \delta L\_{in} + \delta L\_d + \delta L\_{in\_m} + \delta L\_{ST} \tag{9}
$$

where (the quantities over signed by a tilde are virtual quantities):

$$\begin{cases} \begin{aligned} \delta L\_{int} &= E\_b I\_b \int\_0^L \frac{\partial^2 w}{\partial x^2} \frac{\partial^2 \widetilde{w}}{\partial x^2} dx \\\\ \delta L\_{in} &= -\rho \mathcal{S} \int\_0^L \frac{\partial^2 w}{\partial t^2} \, \widetilde{w} \, dx \\\\ \delta L\_d &= M\_d \frac{\partial \widetilde{w}}{\partial x} \Big|\_{x=L} \\\\ \delta L\_{in\_m} &= -m \frac{\partial^2 w\_l}{\partial t^2} \, \widetilde{w}\_L \end{aligned} \tag{10} \\\\ \delta L\_{ST} &= F\_{ST} \, \widetilde{w}\_L \end{aligned} \tag{11}$$

with (see Figure 6):

$$F\_{ST} = K\_{ST} w\_L + C\_{ST} \,\dot{w}\_L \tag{11}$$

**Figure 6.** Scheme for the calculation of the stiffness and viscous damping of the soft tissue.

The viscous damping coefficient *CST* can be identified by measuring the amplitude |*wL*| in correspondence of the *i*-th vibration mode of the structure that has been excited by means of the piezoelectric elements, where the flexural modes of the beams are obtained as

$$p(\mathbf{x}) = B\_1 \sin(\lambda \mathbf{x}) + B\_2 \cos(\lambda \mathbf{x}) + B\_3 \sinh(\lambda \mathbf{x}) + B\_4 \cosh(\lambda \mathbf{x}) \tag{12}$$

with

$$\begin{cases} \left. \varrho(0) = 0 \\\\ \left. \frac{\partial \varrho(\boldsymbol{x})}{\partial \boldsymbol{x}} \right|\_{\boldsymbol{x} = 0} = 0 \\\\ \left. \frac{\partial^2 \varrho(\boldsymbol{x})}{\partial \boldsymbol{x}^2} \right|\_{\boldsymbol{x} = \boldsymbol{L}} = 0 \\\\ EI \frac{\partial^3 \varrho(\boldsymbol{x})}{\partial \boldsymbol{x}^3} \Big|\_{\boldsymbol{x} = \boldsymbol{L}} = \mathbb{K}\_{ST} \varrho(\boldsymbol{L}) - \omega^2 m \varrho(\boldsymbol{L}) \end{cases} \tag{13}$$

By substituting Equation (12) in (13), a system of four equations in four unknowns (*B*1, *B*2, *B*3, *B*4) is obtained. The eigenfrequencies are obtained setting to zero the determinant of the matrix coefficient (with *ω*<sup>2</sup> = *λ*<sup>4</sup> *EI <sup>ρ</sup><sup>S</sup>* ) and then the eigenmodes can be calculated.

The *i*-th flexural mode can be excited by applying a potential function

$$V(t) = V\_0 \sin(\omega\_i t) \tag{14}$$

where *ϕi*(*x*) and *ω<sup>i</sup>* are the *i*-th flexural mode and its related frequency, respectively. In these conditions the displacement *w*(*x*, *t*) and the virtual displacement *w*˜(*x*, *t*) can be written as:

$$\begin{cases} \ w(\mathbf{x},t) = A\_i(t)\varrho\_i(\mathbf{x}) \\\\ \tilde{w}\,(\mathbf{x},t) = \varrho\_i(\mathbf{x}) \end{cases} \tag{15}$$

By substituting Equations (15) and (10) in (9), the following equation is obtained:

$$\begin{split} &E\_b I\_b A\_i(t) \int\_0^L \frac{\partial^2 \varrho\_i(\mathbf{x})}{\partial \mathbf{x}^2} \, d\mathbf{x} = -\rho S \, \bar{A}\_i(t) \int\_0^L \varrho\_i(\mathbf{x})^2 d\mathbf{x} - m \, A\_i^\dagger(t) \, \varrho\_i(L)^2 + \\ &+ M\_d \frac{\partial \varrho\_i(\mathbf{x})}{\partial \mathbf{x}} \Big|\_{\mathbf{x}=L} - K\_{ST} A\_i(t) \, \varrho\_i(L)^2 - \mathbb{C}\_{ST} \, A\_i(t) \, \varrho\_i(L)^2 \end{split} \tag{16}$$

assuming (see Equation (1)):

$$\begin{cases} \begin{aligned} \mathcal{M} &= \rho \mathcal{S} \int\_0^L \boldsymbol{\varrho}\_i(\mathbf{x})^2 d\mathbf{x} + m \boldsymbol{\varrho}\_i(\mathcal{L})^2 \\\\ \mathcal{C} &= \mathbb{C}\_{ST} \boldsymbol{\varrho}\_i(\mathcal{L})^2 \\\\ K &= E\_b I\_b \int\_0^L \frac{\partial^2 \boldsymbol{\varrho}\_i(\mathbf{x})}{\partial \mathbf{x}^2} d\mathbf{x} + K\_{ST} \boldsymbol{\varrho}\_i(\mathcal{L})^2 \end{aligned} \tag{17} \\\\ \begin{aligned} \mathcal{Q} &= \frac{\boldsymbol{\psi}}{\boldsymbol{\theta} + \boldsymbol{\psi}^\mu} E\_d \boldsymbol{c} \boldsymbol{T}\_b d\_{31} \left. \frac{\partial \boldsymbol{\rho}\_i(\mathbf{x})}{\partial \mathbf{x}} \right|\_{\mathbf{x} = \boldsymbol{L}} V\_0 \end{aligned} \end{cases} \tag{17}$$

and therefore Equation (16) becomes:

$$M\ddot{A}\_i(t) + \mathcal{C}\dot{A}\_i\ (t) + KA\_i(t) = \mathcal{Q}\sin(\omega\_i t) \tag{18}$$

By neglecting the transient part (see Equation (15.1)), the amplitude of the free end displacement is:

$$\left| w\_L \right| = A\_{i\_f} \varphi\_i(L) \tag{19}$$

where

$$A\_{i\_f} = \frac{\mathbb{Q}}{\mathbb{C}\omega\_i} \,. \tag{20}$$

Finally, the damping coefficient of the soft tissue

$$\mathcal{C}\_{ST} = \frac{\mathcal{Q}}{\left| w\_L \right| \omega\_i \varphi\_i(L)} \tag{21}$$

can be found from Equation (17.2).

#### **4. Results and Discussion**

To validate the proposed model, numerical simulations have been done. The dimensions and the material characteristics are summarized in Table 1:

**Table 1.** Beams, piezoelectric plates and end masses specifications; lengths are expressed in μm.


In this work, the FEM results have been chosen as the reference values. Three typical soft tissues (liver, muscle and uterus) of known characteristics [83], have been considered. The value of the beam tip displacement, obtained by the FEM simulations, has been included in the mathematical model to calculate the equivalent Young's modulus and the viscous damping coefficient. The ST sample stiffness can be calculated by means of Equation (8). The values of the Young's modulus and the viscous coefficients reported in the literature have been compared with the ones calculated by the new method. Because of the symmetry of the structure with respect to its mid-plane (see Figure 7) only the upper part has been considered in the simulations.

In Table 2 the results of the static simulations, obtained by the above described procedure, have been reported. It is possible to observe that the model results are in good agreement with the real values with a percentage error less than 6% in all the cases.

**Figure 7.** Scheme used for the simulations.

**Table 2.** Comparison between the actual Young's modules and those obtained by the model; *Emm* is the Young's modulus obtained by the mathematical model.


To obtain the viscous damping coefficient, dynamics simulations are necessary. As described above, the chosen strategy consists in exciting, by the piezoelectric plates, the *i*-th mode of the structure, in order to obtain the amplitude of the free end displacement |*wL*| and then in including this in the model.

A comparison between the eigenfrequencies obtained by the COMSOL FEM code and the proposed model is reported in Table 3.

**Table 3.** Comparison between the eigenfrequencies obtained by the COMSOL FEM code and the proposed model.


In the FEM simulations the first mode has been chosen to excite the structure with the values of the electrical potential reported in Table 4.

**Table 4.** Electrical potential used for the simulations.


By neglecting the initial transient part, the axial displacements for the various soft tissues have been reported in Figure 8.

**Figure 8.** Axial displacement for the various soft tissues.

Finally, the comparison between the actual viscous damping coefficients and those obtained by the model results have been highlighted in Table 5.

**Table 5.** Comparison between the effective viscous damping and those obtained by the model.


A good agreement between the relative coefficients is also observed with a percentage error always less than 5%.

#### **5. Conclusions**

In this paper a novel piezo MEMS tweezer for soft materials characterization has been proposed. The tweezer mechanical structure is compatible with the known fabrication processes. A new mathematical model to calculate the stiffness, the equivalent Young's modulus and the viscous damping coefficient of the soft tissues is suggested. The method has been tested by comparing its results with Finite Element

Analysis based on experimental data from the literature. The two sets of data are in good agreement with a difference less than 6% in all the considered cases.

**Author Contributions:** F.B. has designed and developed the mathematical model. A.R. and F.B. carried out the numerical simulations. N.P.B. has reviewed the theoretical approach and the compatibility of the structure with some technological fabrication process.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Abbreviations**

The following abbreviations are used in this manuscript:


#### **References**


c 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## *Article* **Toward Operations in a Surgical Scenario: Characterization of a Microgripper via Light Microscopy Approach**

#### **Federica Vurchio 1, Pietro Ursi 2, Francesco Orsini 1, Andrea Scorza 1, Rocco Crescenzi 3, Salvatore A. Sciuto <sup>1</sup> and Nicola P. Belfiore 1,\***


Received: 24 March 2019; Accepted: 2 May 2019; Published: 9 May 2019

**Abstract:** Micro Electro Mechanical Systems (MEMS)-Technology based micro mechanisms usually operate within a protected or encapsulated space and, before that, they are fabricated and analyzed within one Scanning Electron Microscope (SEM) vacuum specimen chamber. However, a surgical scenario is much more aggressive and requires several higher abilities in the microsystem, such as the capability of operating within a liquid or wet environment, accuracy, reliability and sophisticated packaging. Unfortunately, testing and characterizing MEMS experimentally without fundamental support of a SEM is rather challenging. This paper shows that in spite of large difficulties due to well-known physical limits, the optical microscope is still able to play an important role in MEMS characterization at room conditions. This outcome is supported by the statistical analysis of two series of measurements, obtained by a light trinocular microscope and a profilometer, respectively.

**Keywords:** microactuators; microgrippers; MEMS; displacement measurement; comb-drives; microscopy; profilometer; characterization; minimally invasive surgery

#### **1. Introduction**

The recent developments of the microsystems have been so promising that nowadays they offer a great potential to many applications which require a high grade of miniaturization. Nevertheless, using microsurgery to heal diseases with a minimal invasive approach is still an ambitious challenge because of severe requirements (accuracy, precision, reliability, reduced consumption, limited costs, small size, high performance repeatability, short response time, efficiency in wet or liquid environments). One way of coping with this challenge consists in modifying the common Micro Electro Mechanical Systems (MEMS) to increase their degrees of freedom (usually unitary) and dexterity, for example, providing them with several revolute pairs. These microsystems need to be tested in a significant environment, starting from room environment (in air), but this is not so obvious as it could appear at first sight. In fact, these systems need to be analyzed by means of SEM, which implies putting the mechanisms within a vacuum chamber, rather than a particular environment. Therefore, significant operational tests must be performed by other means of observations, such as microscopy or interferometric profilometry. However, the latter instruments have less resolution than a SEM and their use can be critical to inspect the smallest parts of a microsystem.

This paper shows that microscopy observation can still be very effective in MEMS operational tests under environmental conditions. An effort has been made to assess microscopy observation of MEMS by comparing this means with a higher class, but also a more expensive and difficult-to-use instrument, namely, a profilometer. The statistical treatment of the results of two experimental campaigns (optical microscope and profilometer) shows that the characterization and image acquisition capability of the optical microscope is comparable to that of the profilometer, while the optical microscope maintains a larger degree of freedom in setting the operational parameters.

Given the interdisciplinary nature of the present investigation, it is helpful to give a glimpse to the different types of involved competences. It is particularly important to review some previous contributions concerning the operational conditions that would be required to a micro-electromechanical system in surgery.

A first survey of MEMS for surgical applications [1] showed how MEMS technology may improve the functionality of existing surgical devices and also add new capabilities that give rise to new treatments. For example, MEMS can improve surgical outcomes, with lower risk, by providing the surgeon with real-time feedback on the operation. From the mechanical and operational point of view, microgrippers for different applications have been extensively proposed in literature [2,3].

There are many other different applications where MEMS can play a significant role. For a representative example, MEMS-Technology based micro-accelerometers [4] are able to measure the heart wall motion of patients who have undergone coronary artery bypass graft surgery (CABG). Furthermore, there are many other applications where MEMS could be conveniently used to improve success in surgery, such as in laparoscopic sleeve gastrectomy (LSG) with cruroplasty [5], in surgical treatment of gastrointestinal stromal tumors of the duodenum [6] in colovesical fistula surgery with minimally invasive approach [7], in Endoluminal loco-regional resection by Transanal Endoscopic Microsurgery (TEM) [8–10], and in Low Rectal Anterior Resection (LAR) [11].

These kinds of applications require very specific actions during the different stages of design, fabrication and packaging, because their correct working is depending on many physical parameters, such as temperature, humidity of the environment, presence of water or other liquids, chemical reactions and pressure. For example, the influence of temperature and humidity on the adsorbed water layer on micro scale monocrystalline silicon (Si) films has been investigated in air, using an Si-MEMS kHz-frequency resonator [12]. Water proof or water insensitive three-axis MEMS based accelerometers have been presented [13] for encouraging their operation in laboratory scale experiments. The theory of water electrolysis in a closed electrochemical cell has been described [14] to develop a new actuation principle for MEMS. A special apparatus has been employed to study the adhesive friction due to water in the nanometer range, where the water layer thickness greatly affects friction and adhesion [15]. Heat transfer characteristics of isolated bubble of water were investigated by local wall temperature measurement using a novel MEMS based sensor [16]. MEMS-OR-PAM (optical-resolution photoacoustic microscopy) has also been proved [17] to be a powerful tool for studying highly dynamic and time-sensitive biological phenomena.

Although MEMS still have not developed their potential for surgery applications, there are many more examples of their use in biomedical instruments [18–20]. The mechanical characteristics of cells provide information on their functionality and their state of health, while their geometry can be linked to genetic alterations and apoptosis; the importance of these analyses could help in the collection of phenotypic information or for the diagnosis of pathological disorders [21]. For example, a study[22] was conducted about the viscoelasticity of L929 cells, to investigate their cellular structure, notoriously linked to important physiological functions. In addition, applications of microspectroscopic techniques [23] have been conducted to characterize the viscoelastic properties of living cells. The study of the mechanical properties of cells, also concerns the muscle cells: for example the mechanical response, in terms of strength and displacement, of some smooth muscle cells subjected to elongation has been studied [24] with the aim of better understanding the links between their functionalities and their structure. A study [25] on skeletal muscle cells described how the relationship between

the stiffness and the force exerted by some actin filaments can indicate the physiological state of the actin cytoskeleton. Moreover, the mechanical properties of tissue-engineered vascular constructs have been studied by monitoring pressure and diameter variations of vascular constructs submitted to hydrostatic loading [26]. A silicon microgripper has also been proposed [27] to characterize the mechanical stiffness of biological tissues, with the wider prospective of developing a professional inspecting instrument for laboratory measurements or surgical operations.

More recently, new emerging MEMS-Technology based instruments for biomedical and surgical applications have been developed. In fact, based on a new concept hinge [28,29], a class of different microgrippers, equipped with rotary comb-drives, has been developed [30–33], also in significant environments [34], and fabricated [35,36]. Thanks to their size, these instruments are expected to be employed in surgery and diagnostics. This class of microsystem is the focus of the present investigation.

#### **2. Experimental Characterization of MEMS-Technology Based Instruments in Operational Environments**

In spite of MEMS' great potential for biomedical applications, only a few studies [37] focus on their characterization in an operational environment.

In fact, SEM observation is often a necessity to characterize MEMS, but this means it could be detrimental for the assessment of tests under real operational conditions, basically because tests are performed in vacuum conditions.

Considering the extensively spread biomedical applications, it is also worth mentioning the Optical Coherence Tomography (OCT), which is an optical imaging technique used primarily to investigate the internal microstructure of biological tissues, in ophthalmology and in dentistry [38]. The main advantage of OCT compared to other traditional systems is that this method offers the possibility of a non-invasive in vivo visualization of the tissue with high-resolution three-dimensional images [39]. Despite the axial resolution of some OCT systems (such as Ultrahigh-resolution OCT) [40] that can reach a few micrometers [41], the lateral resolution is affected by the diffraction limits due to the spot size in the focal plane of the probe beam. In fact, the lateral resolution often presents values between 10 and 20 μm [42,43]. Indeed, the above mentioned values of lateral resolution, together with higher costs, make OCTs less attractive than the light microscopy for the characterization of microgrippers in operational conditions.

Considering the above mentioned characteristics for SEM and OCT, traditional light microscopy is quite competitive since it allows test stands to be less expensive in a widespread range of test conditions.

In this investigation a performance characterization of some comb-driven microgrippers in operative condition has been carried out.

The characterization of MEMS-Technology based microgrippers has been recently approached by using a profilometer [44], while the present work will show that a more simple commercial light microscope is still capable to satisfy the same activity with no detriment of measurement significance. Since optical microscopy is widely used in laboratories, it is believed that this paper might have some impact on the future characterizations of microsystems in air, wet or liquid environments. The importance of micromanipulation of mobile micro-particle suspended in liquid well has been recently underlined and a visual-servo automatic micromanipulating system has been presented [45].

Since the intrinsic resolution of optical microscopy is generally rather worse than SEM or profilometer imaging, its real aptitude and efficacy in examining micro-objects remains something that must be validated. Therefore, the present paper will endorse microscopy observation to characterize a microsystem in environmental conditions, by comparing the results obtained by means of both optical microscope and profilometer image analysis techniques. This is justified since the optical devices are the most suitable for carrying out measurements on microsystems without contact and in operative conditions.

In this work, the above mentioned characterization involved the measurements of the angular displacements of a rotary comb-drive embedded into an independently developed microgripper, when a voltage is applied to the device. This is obtained by an in-house Image Analysis Software (IAS) implemented by the authors. The analysis of the measurement results has been achieved by means of uncertainty models for the evaluation of the corresponding error sources. For this purpose, the two image acquisition systems and the corresponding measurement chains will be described, together with the analysis of the relative sources of uncertainty. Finally, the measurements carried out with the Optical Profilometer System (OPS) and Light Trinocular Microscope (LTM) systems will be analyzed to check whether the two groups of results could be considered comparable and consistent within the interval of experimental uncertainties.

#### **3. Materials and Methods**

The evolution of MEMS gave rise to different kinds of microsystems that have been based on MEMS Technology. However, despite the relevant elements mentioned above, one cannot help but notice that, in the international technical-scientific panorama, guidelines, protocols and regulations regarding the characterization of these devices are still lacking, both under the metrological and the mechanical point of view. The present investigation is part of a larger project dedicated to the development of new concept microgrippers for surgical applications and it attempts to partially fill this gap and to validate the optical image analysis as a proper means of characterization of the developed microsystems under operative conditions.

The peculiar object of this investigation is a rotary comb-drive depicted in Figure 1. This component consists in an electrostatic actuator that provides motion to the microgripper illustrated in Figure 1a. The rotary comb-drive is composed of a pair of sets of fingers, as shown in the more detailed Figure 1b. The mobile series of fingers rotates as a function of the applied voltage and the determination of the voltage-rotation curve is greatly important for the operational aspects. Two measurement chains have been set up to measure such voltage-rotation function. The first is composed by a Fogale Zoomsurf 3D Optical Profiling System (OPS, Table 1), while the second is composed of a NB50TS Eurotek Light Trinocular Microscope (LTM, Table 2).

For the sake of the present investigation it is convenient to underline that the two sets of images from the two devices have been both processed using the same in-house built software in order to properly discriminate which one, between OPS and LTM, is the most suitable system to characterize the microgripper devices.

**Figure 1.** Image of a microgripper prototype obtained from optical microscope (**a**) and a detail of the rotary comb-drive (**b**).



**Table 2.** Light Trinocular Microscope (LTM) experimental setup (DUT, micropositioner, probes and PC as in Table 1).


#### *3.1. OPS and LTM Experimental Setups*

The Device Under Test (DUT) consists of a microgripper prototype made up of pseudo-rigid beams and flexure hinges. Any jaw of the microgripper is actuated by a capacitive rotary comb-drive that provides a torque when a voltage is applied to the electrodes.

During the first experimental campaign, performed with the Optical Profiling System, a variable voltage source has been used to supply the DUT and to evaluate the angular displacements of its comb drive. In this investigation, a power supply Keithley 236 SMU with 0.06 V output voltage accuracy (Range ±110.00 V) has been used (Figure 2).

**Figure 2.** The two micropositioners with probe arms and tungsten needles (*a*) and (*b*), used in both the experimental setups; a voltage is applied to the comb-drive (*c*) of the DUT, in order to supply the device.

Two micropositioners with 5 μm resolution have been used, each one being equipped with tungsten needles, in order to apply the voltage to the DUT electrodes, Figure 3, and a set of digital images have been acquired using a Fogale Zoomsurf 3D OPS. The digital image resolution of 0.6 pixel/μm is provided by the Profilometer embedded software.

**Figure 3.** The two micropositioners with probe arms and tungsten needles.

During the image acquisition campaign performed by means of the LTM system the same microgripper sample has been analyzed. The power supply device is a HP E3631A, with 0.04 V output voltage accuracy (Range 0 to +25 V). An electric protection circuit, equipped with a fuse, has also been connected in series, between the power supply and the DUT, to cautiously prevent the passage of a current exceeding 200 mA, which could compromise the device. Two micropositioners have been used (Figure 3) and the microgripper angular displacements have been measured by means of acquired images and collected by a NB50TS Eurotek trinocular microscope system. The optical resolution is limited by the diffraction of the visible light and it is about 0.45–0.6 μm, as in conventional light microscopes [46]; in this study, the worst case of 0.6 μm has been considered. The pixel resolution has been provided by means of calibration procedure; by means of Matlab software, a length of 1000 μm on an image of a micrometer slide was considered and 15 tests were performed. By means of this procedure, the pixel density of 1.359 ± 0.007 pixel/μm was calculated. Furthermore, the sampling constraints (Nyquist limit) and the density of the photo sites on the digital sensor also limit the whole systems resolution. To achieve a *higher level* particle characterization (i.e., differentiation based upon higher order measurements such as circularity), the size of the particle or the object under examination must be greater than 4 μm [46]. In our case, in fact, it is possible to verify that it is impossible to resolve the comb-drive finger gap, that is 3 μm. However, the distance between two fingers, that is 10 μm, is clearly discriminated (see also Ref. [27]); for all these reasons, a overall resolution of about 4 μm for the LTM system is assumed. In Figure 4, the entire LTM setup is shown and some specifications of its main components are reported in Table 2. Once the device has been positioned on the DUT stage, it has been powered by means of two probes with tungsten needles. Through the micropositioners, the tungsten needles are approached to the microgripper electrical connections.

**Figure 4.** Optical Microscope measurement setup. Microgripper prototype (*a*), Supply voltage with protection circuit (*b*), micropositioners with two embedded probe arms and tungsten needles (*c*), Optical Microscope (*d*), embedded camera for images acquisition (*e*), a monitor for displaying and monitoring the device movement in operating conditions (*f*), instrumented support with micrometric screws (*g*), pneumatic suspension table (*h*).

Considering the OPS measurement chain, a set of images has been acquired, each one corresponding to a specific voltage setting: to calculate the angular displacement of the comb-drive, the first acquired image referred to 0 V, has been compared with the others (i.e., 2 V, 4 V, ... , 28 V); Figure 5a illustrates an example of an image that has been processed by the in-house built software. Considering the LTM measurement chain, the same steps have been carried out. However, in order to calculate the angular displacements, the first acquired image (0 V) has been compared with the other images referred to voltages up to 24 volts (i.e., 2 V, 4 V, ... , 24 V) instead of 28 V (as in the previous case); Figure 5b shows an example of image that has been processed by the in-house software. Considering the OPS, a set of 12 images has been acquired at each voltage, for a total of 180 images; considering the LTM image acquisition system, a set of 16 images has been acquired at each voltage, for a total of 208 images.

**Figure 5.** Two examples of images of the Microgripper comb-drive, acquired by optical profilometer (**a**), and optical microscope (**b**); both images (**a**,**b**) are referred to 0 V.

The OPS experimental investigation was made before the LTM campaign. Therefore, the testing voltages used in the second campaign have been influenced by the need of not imposing values that could damage the comb-drives, avoiding the pull-in effect. Such phenomenon occurred during the OPS campaign when the applied voltage was greater than 25 V. Above this value the fingers were unstable; in fact, they were used to get in contact quite often, inducing a short circuit.

Despite that the LTM system has a higher digital resolution of the acquired images, its Signal-to-Noise Ratio (SNR) is lower than the OPS SNR. This characteristic can be related to multiple factors, such as environmental noise, light source (i.e., non-homogeneous light source), optical aberrations, image A/D conversion and processing.

#### *3.2. Image Analysis Software*

A semi-automatic software has been implemented in Matlab according to the following steps.


**Figure 6.** Two images of the microgripper comb-drive acquired by optical profilometer (**a**) and microscope (**b**), respectively.

**Figure 7.** Manual selection of a particular region of the image (ROI), to find its center of gravity (COG) on OPS image (**a**) and on LTM image (**b**).

The first and second above described steps of the implemented software are the only ones in which the manual selection of an operator is necessary to properly select points on the images and the positions and dimensions of the ROI. The following ones have been automated.

	- The most distant point from the ICR on the fixed part of the comb-drive (a);
	- The ICR of the comb-drive (b);
	- The center of the ROI (c);

The first two points remain fixed for all the following images, under the hypothesis of no deformation due to the movement of the comb-drive, while the only point, whose coordinates change for each considered image, is the center of the ROI.

4. These three points determine a triangle, where the vertex ICR corresponds to the angular opening *α* of the comb-drive. With reference to Figure 9, points *a*, *b* and *c* are considered to be the vertices of an isosceles triangle, where

$$\alpha = 2 \arcsin\left(\frac{A}{B}\right) \tag{1}$$

with *A* = *ca* <sup>2</sup> and *B* = *cb*. Using a template matching algorithm, a match is found between the coordinates of the center of the selected ROI on the first image (i.e., that corresponds to 0 V supply) and on all the subsequent images. Through this operation the in-house software detects the new coordinates of the ROI center of gravity (ROIGC) for each subsequent image and therefore for each applied voltage. The ROIGC changes its coordinates and, consequently, it changes also the shape of the corresponding triangle and the angular aperture of the DUT comb-drive, depending on the different voltage supply.

5. The angular displacement is obtained from the comb-drive angular aperture at each voltage value.

**Figure 8.** The determination of three points on the profilometer (**a**) and the microscope (**b**) images: the most distant point from the ICR on the fixed part of the comb-drive, the ICR of the comb-drive and the center of the ROI.

**Figure 9.** The triangle used by the software to evaluate the comb-drive angular displacement.

The above described software can be used with any type of image. For example, in this study two sets of images have been considered, acquired by the optical profilometer and the light microscope, respectively. The limit associated with this type of analysis is that the procedure provides a first semi-automatic part, which must be carried out by the operator. This approach introduces some sources of uncertainty, due to the variability in selecting the initial points for the determination of the comb-drive ICR, as well as the variability in the selection of the size and position of the Region of Interest, together with the uncertainty of the code itself. These sources of uncertainty will be considered in the next section, where a model will be proposed for the analysis of the uncertainty of both the entire measurement chains.

#### *3.3. A Model for the Uncertainty Analysis of the Measurements*

The purpose of this section is to estimate the overall uncertainty associated with the two measurement systems and for this reason a model for measurement uncertainty analysis is proposed; an analysis of the main uncertainty sources of the two measurement setups is carried out and the calculation of the measurement uncertainty relative to the angular displacements of the comb-drive device is performed, both for the profilometer and the light microscope.

For each value of the angular displacements, the mean *x*¯ and standard deviation of the mean *Sx*¯ have been obtained, based on a statistical analysis conducted on a number of observations *N* = 12 for the profilometer and *N* = 16 for the light microscope, for each considered voltage. On the hypothesis that the sample comes from a normal population, a Student's t-distribution has been used. For the calculation of the overall uncertainty of the measurement systems considered, it is necessary to combine the type A and type B uncertainties [47], using the following expression:

$$
\delta\_T = \sqrt{\delta\_A^2 + \delta\_B^2} \,. \tag{2}
$$

First, the main uncertainty sources for both measurement systems have been identified and evaluated, as shown in Table 3, where for each source a probability density function *PDF* together with the uncertainty type and mean *m* is determined.


**Table 3.** OPS and LTM measurement setup uncertainty sources.

Notes: (1) *N* (*μ*, *σ*) is a Gaussian *PDF* with mean *m* and standard deviation *σ*; *U* (*μ*, *σ*) is a uniform *PDF* with mean *m* and standard deviation *σ*; (2) Type A and type B uncertainty as in standard [47]; (3) the uncertainty value *δ* for OPS and LTM is referred to 95% of confidence level.

#### 3.3.1. Uncertainty Analysis for OPS Measurement Setup

Type A, namely *δA*, uncertainty are evaluated by statistical methods (statistical analysis of a series of observations) and have been calculated from standard deviation of the experimental measurements; Type B, *δB*, uncertainty are evaluated by means other than the statistical analysis of series of observations. The main sources of type B uncertainty considered are:


#### 3.3.2. Uncertainty Analysis for LTM Measurement Setup

In this case, *δ<sup>A</sup>* still represents Type A uncertainty, whereas *δ<sup>B</sup>* are the Type B uncertainty. The main sources of type B uncertainty considered are:


To evaluate the total uncertainty of the two measurement systems, according to Equation (2), two contributions have been determined: the first is related to the uncertainty contribution evaluable with a statistic analysis of the measurements dispersion obtained with the measurement system (*δA*), while the other is due to the overall uncertainty from the main error sources related to the experimental setup (*δB*). In order to evaluate the *δ<sup>B</sup>* uncertainty, two main contributions have been determined: the first is associated to the derivative of the function that expresses the angular displacement *θ* of the comb-drive with respect to the applied voltage *∂θ <sup>∂</sup><sup>V</sup>* , multiplied by the uncertainty due to the power supply *δV*, while the other is related to the measurement of the comb-drive angle *δα<sup>t</sup>* [47]

$$
\delta\_B = \delta\_\theta = \sqrt{\left(\frac{\partial \theta}{\partial V} \delta\_V\right)^2 + \left(\delta \alpha\_t\right)^2} \tag{3}
$$

In particular, a second order polynomial function

$$
\theta = a \cdot V^2 + b \cdot V + c \,, \tag{4}
$$

where *a*, *b*, and *c* are obtained experimentally, approximates the trend of the angular displacements.

The term *δα<sup>t</sup>* is composed by two terms, the first *δα<sup>p</sup>* is the angle measurement uncertainty due to the OPS and LTM system, associated to the variability of the parameters related to the manual measurement of the lengths Δ*xa*, Δ*xb*,Δ*ya*, and Δ*yb*, carried out by the operator; while the other *δαs*, is the angle measurement uncertainty due to the template-matching algorithm of image processing software. This last contribution is evaluated [44] by means of a Monte Carlo Simulation (with 10,000 iterations) implemented in MATLABc ; *δα<sup>s</sup>* corresponds to ±0.02◦, at 95% confidence level.

$$
\delta a\_l = \sqrt{\left(\frac{\delta a\_p}{a} \cdot a\right)^2 + \left(\delta a\_s\right)^2} \tag{5}
$$

The angle measurement uncertainty *δα<sup>p</sup>* has been measured by means of the triangular properties as shown in Figure 10. For the measurement of values Δ*xa*, Δ*xb*, Δ*ya* and Δ*yb*, 10 tests were carried out for each of the segments and their mean value has been considered.

**Figure 10.** Angle measurement for the uncertainty evaluation related to the profilometer image, on the **left** and microscope image, on the **right**.

The uncertainty related to the light microscope and profilometer error can be obtained as approximated in [44]:

$$
\frac{\delta a\_p}{a} = \sqrt{\left(\frac{\delta a}{a}\right)^2 + \left(\frac{\delta b}{b}\right)^2},\tag{6}
$$

where

$$\begin{aligned} a &= \sqrt{\Delta \mathbf{x}\_a^2 + \Delta \mathbf{y}\_a^2} \\ b &= \sqrt{\Delta \mathbf{x}\_b^2 + \Delta \mathbf{y}\_b^2} \end{aligned} \tag{7}$$

and

$$\begin{aligned} \delta a &= \sqrt{\left(\frac{\partial a}{\partial x} \delta \mathbf{x}\right)^2 + \left(\frac{\partial a}{\partial y} \delta y\right)^2} = \sqrt{\left(\frac{\Delta x\_a}{\sqrt{\Delta x\_a^2 + \Delta y\_a^2}} \delta \mathbf{x}\right)^2 + \left(\frac{\Delta y\_a}{\sqrt{\Delta x\_a^2 + \Delta y\_a^2}} \delta y\right)^2} \\ \delta b &= \sqrt{\left(\frac{\partial b}{\partial x} \delta \mathbf{x}\right)^2 + \left(\frac{\partial b}{\partial y} \delta y\right)^2} = \sqrt{\left(\frac{\Delta x\_b}{\sqrt{\Delta x\_b^2 + \Delta y\_b^2}} \delta \mathbf{x}\right)^2 + \left(\frac{\Delta y\_b}{\sqrt{\Delta x\_b^2 + \Delta y\_b^2}} \delta y\right)^2} \end{aligned} \tag{8}$$

The quantities *a* and *b* in (7) depend on the image resolution and size. For this study, the lengths of the comb-drive triangle in the profilometer image are considered for the maximum rotation (1.3◦), i.e., Δ*xa* = 25 pixel, Δ*ya* = 150 pixel, Δ*xb* = 680 pixel, and Δ*yb* = 150 pixel, therefore *a* = 152 pixel, and *b* = 696 pixel. Instead, the lengths of the comb-drive triangle in the microscope image are considered for the maximum rotation (0.93◦), i.e., Δ*xa* = 130 pixel, Δ*ya* = 330 pixel, Δ*xb* = 1550 pixel, and Δ*yb* = 450 pixel, therefore *a* = 355 pixel, and *b* = 1614 pixel.

#### **4. A Comparison between the Two Measurement Systems**

At first, a comparison between the results obtained from the uncertainty analysis for both image acquisition systems has been carried out; from the results obtained through the analysis software it has been possible to collect a series of measurements attributable to the comb-drive angular displacement depending on the voltage supply. In particular, 12 measurements were obtained for each applied voltage value, for the OPS, and 16 measurements for each applied voltage value, for the LTM system. In a second stage, it has been necessary to verify whether the two sets of results are comparable, within the interval of the experimental uncertainties.

To verify the initial hypothesis that, using two different measurement systems, the angular displacement measurement of the comb-drive is the same, the approach described in Ref. [50] has been followed. Considering the average values, the total uncertainties *δ<sup>T</sup>* of OPS and LTM have been obtained by using Equation (2) and then reported in the form of standard deviations in Table 4. The available data are expressed in the form:

$$
\dot{X} = \ddot{X} \pm \delta\_X \tag{9}
$$

$$
\hat{Y} = \bar{Y} \pm \delta\_Y \tag{10}
$$

where *X*¯ and *Y*¯ are the mean values of *X* and *Y* (OPS and LTM measurements, respectively), while *X*ˆ and *Y*ˆ represent the measured values according to the standard [47]. To evaluate whether the two different measurements can be considered consistent or not, it is necessary to find the best estimate for the difference <sup>Δ</sup>*XY* <sup>=</sup> *<sup>X</sup>*<sup>ˆ</sup> <sup>−</sup> *<sup>Y</sup>*<sup>ˆ</sup> and establish the highest and the lowest probable values of <sup>Δ</sup>*XY*. The highest probable value for Δ*XY* is obtained if *X*¯ assumes its higher probable value, *X*¯ + *δX*, and at the same time *<sup>Y</sup>*<sup>ˆ</sup> assumes its lowest probable value, *<sup>Y</sup>*¯ <sup>−</sup> *<sup>δ</sup>Y*. In this way the highest probable value for Δ*XY* is

$$p\_{\text{max}} = (\mathcal{X} + \delta\_X) - (\mathcal{Y} - \delta\_Y) = (\mathcal{X} - \mathcal{Y}) + (\delta\_X + \delta\_Y) \ . \tag{11}$$

Similarly, the lowest probable value for Δ*XY* is obtained if *X*ˆ assumes its lowest probable value, *<sup>X</sup>*¯ <sup>−</sup> *<sup>δ</sup>X*, and at the same time *<sup>Y</sup>*<sup>ˆ</sup> assumes its highest probable value, *<sup>Y</sup>*¯ <sup>+</sup> *<sup>δ</sup>Y*,

$$p\_{\text{max}} = (\vec{X} - \delta\_X) - (\vec{Y} + \delta\_Y) = (\vec{X} - \vec{Y}) - (\delta\_X + \delta\_Y) \tag{12}$$

Combining (11) and (12), the difference between the measured values is

$$
\Delta\_{XY} = (\ddot{X} - \ddot{Y}) \pm (\delta\_X + \delta\_Y) \,. \tag{13}
$$

The evaluation of the difference *X*¯ <sup>−</sup> *<sup>Y</sup>*¯ and the sum *<sup>δ</sup><sup>X</sup>* <sup>+</sup> *<sup>δ</sup><sup>Y</sup>* is fundamental for the sake of our investigation. In fact, if the difference *X*¯ <sup>−</sup> *<sup>Y</sup>*¯ has the same order of magnitude as, or even less than, the sum *X*¯ <sup>−</sup> *<sup>Y</sup>*¯ , then the two different systems, namely OPS and LTM, measure the angular displacement of the comb-drive without significant difference.

#### **5. Results**

All the measurement data have been processed and interpolated to provide a curve fitting of the motion of the comb-drive depending on the voltage supply; in Figure 11 the two curves related to the two measurement setups are shown, while the detailed results are reported in Tables 4.

**Table 4.** Angular rotation, Total Uncertainty, expressed as standard deviation, and Total Relative Uncertainty of comb-drive depending on the applied voltage.


For low values of the voltage, the observations reveal that the microgripper mobile parts face a certain resistance while attempting to move, showing a certain instability. In fact, the torque-voltage function presents an increasing rate of change. This phenomenon is one of the main source of a high dispersion of the results at low values of voltage, while this problem does not occur for higher values (>4 V).

In Table 5 the results of the comparison between the OPS and LTM systems are shown.

As already observed in Ref. [44], for the optical profilometer, even if we consider the image acquisition system of the light microscope, it is possible to observe a concordant behavior with the results reported in Refs. [35,37].

Second order polynomial regression curves have been determined by a least squares fitting method to describe the outcome from the OPS and the LTM systems: the fitting capacity is confirmed by the high value *R*<sup>2</sup> coefficients [51], equal to 0.999 for both the OPS and LTM systems.

The Equations (3) and (4) have been used to calculate the type B uncertainty *δB*.


**Table 5.** Applied voltage vs parameters differences.

Table 4 shows that above 16 V the total relative uncertainty of the optical profilometer is less than 4.0%, while for the microscope it is less than 7.2%. Since the same software for digital image processing has been used, these results may be mainly related to the two different setups. The greatest contribution in the calculation of uncertainty is given by the *δα<sup>t</sup>* uncertainty, composed by the angle measurement uncertainty due to the OPS and LTM, *δα<sup>p</sup> <sup>α</sup>* · *α* , and the angle measurement uncertainty due to the template-matching algorithm of the image processing software *δαs*, that correspond to 0.02◦ both for OPS and LTM systems. As mentioned above, the OPS and the LTM generally have different typical values of SNR and this fact is also affecting uncertainty in the two measurement systems.

**Figure 11.** Relationship between angular displacement vs the applied voltage for the OPS (**a**) and the LTM (**b**) systems.

A second evaluation of the two experimental setups has been conducted; indeed, it has been necessary to evaluate whether the different results relative to the mean values of the angular displacement of the comb drive for the two experimental setups are comparable or not, to properly establish if the two measurement systems produce the same results, based on the verification that the differences between the measured mean values are smaller or comparable with the sum of the original uncertainties. Table 5 shows that, for each applied voltage value, there is no significant difference between the results obtained by the two methods. It is therefore possible to conclude that the measurements carried out with the OPS and LTM systems can be considered consistent, within the interval of the experimental uncertainties. From the point of view of total relative uncertainty, the results obtained with the profilometer appear to be better than those obtained with the microscope. However, considering the high costs of a profilometer system (about two times higher than the light microscope here used) and also the ease of use of a system such as the light microscope, the latter appears to be the best trade-off system able to carry out performance characterization of a device like

microgripper for biomedical application. Furthermore, despite both image acquisition systems being able to characterize the microgripper in operating conditions, only the microscope permits a real-time study; this last feature is certainly the most important because it allows LTM to characterize the device in static and dynamic conditions.

#### **6. Discussion**

The first step of this investigation has been the mechanical characterization of a microgripper prototype. The comb-drive angular displacement has been expressed as a function of the applied voltage. Two different measurement systems, OPS and LTM, have been used. Both systems showed that the two rotation-voltage curves follow the same quadratic trend. In order to perform the measurements, a systematic approach has been developed based on in-house built software. This gave rise to a system which has quite high repeatability and low-operator-dependence. Moreover, an analysis of the uncertainties has been carried out, with the construction of a model that considers the main sources of uncertainty present in the measuring setups. The evaluation of the accuracy of the considered setups has shown that for voltages greater than 14 V, the total relative uncertainty of OPS is less than 4.0%, while for the LTM is less than 7.2%. A verification to check whether the two sets of results are consistent, within the interval of the experimental uncertainties has been carried out.

The same in-house software has been used for image processing and therefore the differences in the obtained results are due to the uncertainty of the two image acquisition systems. The main considered contributions were:


Despite the obtained results showing that the OPS system has a total relative uncertainty lower than those of the LTM system, the light microscope is still the image acquisition system that will best suit the characterization of MEMS-Technology based microgrippers. In fact, profilometer or electronic microscopy are not practical or even unfeasible for the characterization of these devices in working or in real-time conditions. Therefore, the light microscope is the most promising image acquisition system because it may perform a mechanical characterization, and because of its use in biomedical or surgical real-time scenarios.

#### **7. Conclusions**

Nowadays there is a growing need of more accurate and precise devices, especially in microsurgery or diagnostics. The developments of the manufacturing technology offer new tools, such as microgrippers, suitable for a variety of biomedical applications, including minimally invasive surgery. However, SEM observation is impossible in air, wet or liquid environments, while profilometer or OCT measurements are often unpractical or more expensive in operational or real-time scenarios. The aim of this paper is therefore encouraging the use of light microscopes in future investigations, by validating, for the test case, light microscopy as the best trade-off among the characterization accuracy and the need of a large operational range and real time response. The validation method has been applied to a MEMS-technology based microgripper developed earlier by the research group.

**Author Contributions:** Conceptualization and investigation, all the Authors; methodology, A.S.; software, data curation and validation, F.V. and F.O.; formal analysis, F.V., F.O. and A.S.; writing, N.P.B.; supervision, S.A.S. and P.U.; resources, S.A.S. and R.C.

**Funding:** This research received no external funding.

**Acknowledgments:** The microgrippers under study have been fabricated by MTLAB-FBK, Micro Technology Laboratory-Fondazione Bruno Kessler.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Abbreviations**

The following abbreviations are used in this manuscript:


#### **References**


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