**1. Introduction**

The knee joint is the largest joint in the human body. Osteoarthritis-induced wear and tear of the articulating surfaces of the knee causes discomfort to the patient [1]. Arthroplasty is considered to be the permanent solution to treat the most severe knee arthritis [2]. Surgeons perform total knee arthroplasty (TKA) relying either on an imaging technique like ultrasound [3] or an imageless computer-based technique [4]. The computer-assisted TKA is becoming popular, because most of the alignment work is done by computers; hence, the transplanted joint is expected to be accurately aligned, with quicker recovery time, due to minimal incision [5]. The computer-assisted TKA device consists of software that takes some anatomical points as input. The marking system of these anatomical points usually relies on an infrared, laser, or electromagnetic pulses emitter, and reflectors paired with an optical camera to obtain the real-time position of the marked point [6–8].

The software constructs a virtual coordinate system for the knee to undergo arthroplasty, and based on the coordinate system, it guides the surgeon to prepare the bone surface for implant. The coordinate system can be assigned by different methodologies, for example, the transverse axis at the distal femur for assigning a femoral coordinate system (FCS) can be obtained by fitting a circle, a sphere, or a cylinder in the articulating surfaces of the distal femur, and using the center of the fitted geometry, the transverse axis is assigned [9,10]. Another approach is to join the most prominent points on the lateral and medial epicondyles to construct an anatomical transepicondylar axis (aTEA) [11]. Similarly,

**Citation:** Sohail, M.; Park, J.; Kim, J.Y.; Kim, H.S.; Lee, J. Modified Whiteside's Line-Based Transepicondylar Axis for Imageless Total Knee Arthroplasty. *Mathematics* **2022**, *10*, 3670. https://doi.org/ 10.3390/math10193670

Academic Editor: Mauro Malvè

Received: 7 September 2022 Accepted: 1 October 2022 Published: 7 October 2022

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a surgical transepicondylar axis (sTEA) can be defined by joining the lateral epicondyle and medial sulcus [12]. In some cases, the posterior condylar axis (PCA) being in front of the surgeon can be easily used to define the transverse axis [13]. PCA and sTEA are parallel to each other, and perpendicular to the anterior posterior axis (AP axis) or Whiteside's line [14,15]. Whiteside's line is defined by using the deepest part of the patella groove (PG) anteriorly and the center of intercondylar notch (N) posteriorly [16]. sTEA is considered to be a standard to set the rotational alignment for TKA [17,18]. However, some studies have compared the sTEA and aTEA for their ability to be chosen as a transverse axis for FCS. For example, Tanavalee et al. studied the CT scans of 55 osteoarthritic knees considering both sTEA and aTEA, and they concluded that aTEA is near perpendicular to the AP axis and more reliable for rotation alignment compared to sTEA [19]. In the same year, Yoshino et al. examined 48 patients eligible for TKA and found that the medial sulcus was detectable in only one-fifth of the severe osteoarthritis cases; for less severe cases, it was detectable in half of the cases [20]. Hence, it was concluded that the chances of detecting the medial sulcus decrease with an increase in the severity of osteoarthritis.

Deterioration of PCA in severe osteoarthritis makes it less favorable for the selection of the transverse axis [20]. Whiteside's line being a smaller landmark leads to rotational error of up to 10◦, even for small uncertainties [21]. It is a well-known fact that alignment error >3◦ from the natural alignment of the knee leads to quick wear and discomfort of the patient, and finite element analysis can accurately predict initial stability of an implant; however, the computational cost increases [15,22,23]. The sTEA, being an inconsistent landmark [24], leaves only aTEA to be a reliable choice for assigning the FCS and setting the rotational alignment of the implant [19,25]. Malrotation alignment leads to instability of implant, the discomfort of the patient, patella maltracking, and quick wear of inserted polyethylene [26]. So, the TKA is sometimes required to be revised. Fehring et al. summarized the 15-year data of revised TKA cases and found that 41% of the cases showed conditions related to rotational malalignment [27]. Another similar case study of 1632 revised TKA cases showed that 42% of the cases were linked with wear of the insertion and instability of the implant [28]. Dalury et al. also investigated the reasons why TKAs are revised, based on the analysis, 48% of the cases were linked with the symptoms attached to rotational malalignment [29]. Choosing a perfect aTEA is not always possible, which leads to rotational malalignment. Stoeckl et al. invited a team of four experienced surgeons to mark six cadaveric human legs. Skin and soft tissues were removed, and surgeons had to pick the most prominent point on lateral and medial epicondyles using an optical navigation system under perfect laboratory conditions. Each surgeon marked aTEA for three consecutive days; 144 points were marked by all the surgeons. Excluding extreme values, the selected points were distributed in an area of 298 mm<sup>2</sup> on the medial and 278 mm<sup>2</sup> on the lateral side of the bone. Using the extreme values of the marked area, a maximum of 8◦ of internal rotation was calculated (3◦ allowed) [30]. Another study investigating the reproducibility of aTEA, where eight surgeons marked lateral and medial epicondyles on Thiel-embalmed cadaver specimens, shows the distribution of lateral and medial epicondyles on an area of 116 and 102 mm2, respectively [31]. A team of another five surgeons studied the effect of errors in registering anatomical points on five cadavers for five days. Key anatomical points, including lateral and medial epicondyles, were intentionally marked wrong. The wrong registration of lateral and medial epicondyles led to an error in rotational alignment ranging from 11.1◦ external to 6.3◦ internal rotation [32]. Similarly, there are various studies in which the errors are either intentionally added, or induced due to human error, by the repetitive marking of points during a course of time. The objective of such studies is to show the effect of errors on the rotational alignment of TKA [32–36].

To reduce the errors caused by choosing a single point, bone morphing or selection of multiple points on the landmark have been reported in the literature. For example, Liu et al. marked a group of points and fitted an algorithm to choose the optimal point for defining TEA [37]. Perrin et al. studied the reproducibility of implant positioning in TKA using both morphing and conventional single-point selection techniques, and found

the bone morphing technique to be more repeatable [38]. A system using bone morphing relies on a database gathered by CT scans from a large number of patients supplied by the device manufacturers. Once multiple anatomical points are registered by the surgeon, the algorithm finds the bone model that best fits the marked points [39]. Instead of model fitting, statistical shape models of the bone can be fitted in a marked cloud of points. The bone morphing requires the surgeon to carefully mark the entire distal femur. This is a time-consuming job, and error at this stage can lead to the failure of TKA [40]. This is because bone morphing requires model fitting, which increases the computational cost, and hence, the cost of TKA.

From the above literature review, it can be concluded that, since the beginning of computer-based TKA, researchers have relied on an individual anatomical axis to set the transverse axis of FCS. However, the reported outcomes are not repeatable and certain. Thus, it is necessary to investigate the repeatability and accuracy of a transverse axis defined by the combination of more than one anatomical axis. Currently, the aTEA is the most reliable transverse axis for FCS; however, it is not a repeatable axis. This work proposes a modified Whiteside's line, which combines the Whiteside's line and aTEA to define a repeatable transverse axis. Moreover, this method can also be added to the existing TKA devices just by their software upgradation. The rest of the paper is organized as follows: Section 2 reviews the generalized method to define FCS, the tibial coordinate system (TCS), and presents the proposed modified Whiteside's line. Section 3 describes the CAD and experimental setup. Section 4 presents and interprets the results, while Section 5 concludes the work.
