Surface Acoustic Wave Sensor for Selective Multi-Parameter Measurements in Cardiac Magnetic Field Detection

Abstract

Measuring parameters like heart temperature, heart rate, and cardiac magnetic field aids in analyzing cardiac health and disease. A multi-parameter sensor tailored to the heart can significantly enhance convenience in medical diagnosis and treatment. This work introduces a multi-parameter sensor based on Surface Acoustic Wave Sensors (SAWSs) and magnetostrictive materials, designed to selectively measure various cardiac parameters. SAWSs are characterized by their compact dimensions, which facilitate integration into various medical devices. The wireless and passive characteristics of the sensors enable flexibility in the detection process. This sensor can detect various common physical quantities like weak magnetic fields by the control variable method, ensuring a high degree of accuracy. The working mode of SAWSs is investigated in this study, and the relationship curve concerning various influencing factors is established.

1. Introduction

Surface Acoustic Wave Sensors (SAWSs) have attained widespread utilization in the sensor technology arena owing to their advantages such as cost-effectiveness, compact dimensions, durability, high sensitivity, easy integration, high compatibility, and wireless and passive operation [1]. Depending on the detection method, SAWS can measure various physical quantities, including temperature, humidity, chemical concentration, and biological signals. With the wireless and passive characteristics of SAWSs, these devices can adapt to complex and even hazardous or toxic detection scenarios [2].

As the core of the human body, the heart requires precise detection and sensing of its parameters to evaluate overall health. The detection of heart conditions requires sensing multiple parameters, which necessitates the assistance of sensors or AI. Advanced medical devices integrate various sensing platforms and AI algorithms for health monitoring or disease prediction [3,4,5]. Conventional cardiac parameters, such as temperature and heart rate, are relatively easy to obtain. The magnetic field generated by the heart, known as the cardiac magnetic field, is difficult to measure yet contains unique information about the heart’s condition. Measuring the cardiac magnetic field requires magnetic field sensors.

There are many types of temperature sensors, but research on temperature sensors specifically for the heart is still limited. One commonly used clinical method for temperature measurement is Infrared Thermography (IRT) [6,7]. This method is non-contact and provides real-time imaging. However, infrared cameras are expensive and entail high costs. Another proposed method for cardiac temperature measurement is Velocimetric Ultrasound (VUS), which features a simple sensor structure and exhibits low measurement error [8]. However, the size of the device makes it more suitable for measuring the overall temperature of a single object rather than two-dimensional temperature distribution. MP-SAWS is compact, easily integrable, and cost-effective. It can be arranged in arrays to measure the temperature distribution of the heart. Due to the rapid response to temperature changes, SAWS can provide real-time measurement of heart temperature [9].

Heart rate detection is a common component in medical diagnostics. There are numerous methods for detecting the heart rate, most of which are fast, accurate, and cost-effective. Recent trends in heart rate detection research focus on integrating these sensors into wearable devices, not just for medical purposes but also for dynamic monitoring during physical activity. For example, hand-worn sensors are based on piezoresistive sensing, and in-ear sensors are based on Photoplethysmography (PPG) [10,11]. There are also non-wearable sensors that detect heart rate during movement, such as those integrated into vehicle seats using ultrasonic or electrocardiogram (ECG) technologies to monitor the driver’s condition [12,13]. A heart rate sensor based on SAW technology represents a novel concept; its miniaturization makes it suitable for integration into wearable devices to detect both static and dynamic heart rate signals.

Magnetic field sensors are currently extensively used in electronic information [14], biomedical [15,16], industrial production [17], monitoring and detection[18,19,20], and other fields. These types of magnetic field sensors now include surface plasmon resonance (SPR) sensors [21,22,23], fiber optic sensors [24,25,26], magnetoresistance sensors [27], magnetoelectric sensors [28], photonic crystal sensors [29], and more.

Human body magnetic field detection is a branch of medical diagnostics that enables health assessment and monitoring of certain diseases. One characteristic of the human magnetic field is its weak signal, which makes it susceptible to interference. Currently, research on biological magnetic fields is primarily limited to laboratory settings. Early detection methods for biological magnetic fields involve the development of highly sensitive tools, such as superconducting quantum interference devices (SQUIDs) [30], atomic magnetometers [31], and fluxgates [32], which can detect similar weak magnetic signals. However, the clinical application of human magnetic field detection is not yet widespread due to cost and technical limitations [33].

There have been studies on weak magnetic sensors based on the magnetostrictive effect, specifically targeting the human body’s magnetic field, including brain magnetic fields [34,35], muscle magnetic fields [36], and cardiac magnetic fields [37]. Many magnetic field sensors that combine SAWS with magnetostrictive materials rely on the delta-E effect [38,39]. The delta-E effect, generated by inverse magnetostriction, introduces additional strain beyond the pure elastic Hooke strain, typically occurring in multiple components of the elastic modulus and elastic stiffness tensor [40]. This paper proposes a novel approach that couples SAWS and magnetostrictive materials in a two-dimensional planar configuration, harnessing the sensing capability of the piezoelectric substrate to detect stress in the lateral direction for magnetic field measurement.

Sensing the cardiac magnetic field is challenging, as is the selective detection of different cardiac parameters with a single sensor. Selective sensors enable higher integration in medical devices, reducing the need for multiple sensing modules and facilitating miniaturization and cost reduction. As some cardiac parameters interrelate, advanced designs are crucial for selective detection.

In the field of acoustics, longitudinal critically refracted (LCR) waves also have potential applications in detection and sensing. For instance, LCR waves can be utilized for stress analysis or non-destructive testing [41,42]. For the study of acoustic issues, establishing numerical models and using simulation software is an effective solution [43]. In the research of the LCR wave, inputting the proposed numerical model into simulation software provides significant preliminary support for analyzing problems [44]. Similar solutions can be applied to the simulation studies of SAWSs.

To analyze the SAWS, the finite element analysis method is employed, establishing a model to examine its resonant frequency, resonant mode, admittance curve, S parameter curve, and mechanical quality factor. Furthermore, this paper performs tests on noise resistance, stress, and thermal factors to explore how the resonant frequency of the multi-parameter sensor based on Surface Acoustic Wave Sensors (MP-SAWSs) correlates with different physical variables. Finally, the magnetic field sensing characteristics of MP-SAWS are explored, and the sensor is validated by comparing it with existing data in the database.

In this paper, an MP-SAWS is simulated and designed, taking advantage of SAWS’s high sensitivity and adaptability. The proposed approach involves integrating lithium niobite (LiNbO₃) piezoelectric film and magnetostrictive material Terfenol-D into a sensing array [45]. Compared to traditional magnetic field sensors, the designed SAWS offers a wider range of applications due to its wireless and passive characteristics. Novel sensors can achieve selective measurements through the control variable method. It has the ability to adjust to diverse work settings and fulfill a range of demands, even in challenging conditions. Compared to existing sensors, this sensor offers a solution for multi-parameter sensing with selectivity. Achieving selective sensing using a single device is more conducive to integrated design. The approach to enabling multiple sensing capabilities provides more possibilities for the design of new sensors.

2. Materials and Methods

2.1. MP-SAWS Principle

The substrate of the MP-SAWS is made of the piezoelectric material LiNbO₃, integrating interdigitated electrode transducers (IDTs) in the middle layer and metal reflector networks on both sides. The parameters of various piezoelectric materials are listed in

Table 1. Common piezoelectric material parameters [46].

Materials	ZnO	AlN	ST-Cut Quartz	128° Y-X LiNbO3	36° Y-X LiTaO3
Moulus (GPa)	110–140	300–350	71.7	130–170	205
Poisson’s ratio	0.36	0.22–0.29	0.17–0.2	0.24–0.28	0.17–0.2
Piezo-constant d33 (pC/N)	12	4.5, 6.4	2.3 (d11)	12	12
Effective coupling coefficient, k2 (%)	1.5–1.7	3.1–8	0.1–0.2	5–11.3	5–6.6
Acoustic velocity of longitudinal (transverse) waves (m/s)	6336 (2720)	10,150–11,050 (5800)	5000–5960 (3159)	3680–3980	4160–4220

. LiNbO₃ has a higher electromechanical coupling coefficient compared to other common piezoelectric materials [46]. The portion between the interdigital electrodes and the reflector network is used to detect the resonance frequency of the surface acoustic wave (SAW). The schematic diagram is shown in Figure 1.

The IDT serves dual roles as both the transmitter and the signal-conversion element of the MP-SAWS. It is deposited onto the piezoelectric substrate. When an AC electric signal is applied to the IDT, vibrations occur in the piezoelectric material caused by the reverse piezoelectric effect, thus exciting the MP-SAWS, which oscillates at an identical frequency to the AC signal. The wave travels across the surface of the substrate. After the mechanical wave reaches the reflector network, it returns to the IDT via the reflector grids. Following the completion of wave transmission, the IDT converts the mechanical wave into an electrical signal using the positive piezoelectric effect and transmits it to the receiver.

The structure of MP-SAWS allows for the addition of a test area to change the physical field of the measured object. Consequently, the measured information is reflected through the variation in the SAW’s velocity or frequency [2]. In the simulation software, the constitutive equation describing the piezoelectric phenomenon is represented as follows [47]:

Stress–Charge Form:

$$\mathrm{T}=c_{E}S-e^{T}E$$

(1)

$$\mathrm{D}=\mathrm{e}\mathrm{S}+{\epsilon }_{S}E$$

(2)

Strain–Charge Form:

$$\mathrm{S}=s_{E}T+d^{T}E$$

(3)

$$\mathrm{D}=\mathrm{d}\mathrm{T}+{\epsilon }_{T}E$$

(4)

The following equations are also provided:

$$c_E=s_E^{-1}$$

(5)

$$e=d{s}_E^{-1}$$

(6)

$${\epsilon }_S={\epsilon }_T-d{s}_E^{-1}{d}^T$$

(7)

In the equations, S represents the strain tensor, $s_E$ represents the compliance matrix, T represents the stress tensor, d represents the piezoelectric constant, E represents the external electric field, D represents the electric displacement, and ${\epsilon }_T$ represents the dielectric constant.

To enable magnetic field measurements and their application to the human body, magnetostrictive Terfenol-D, and biocompatible, flexible polydimethylsiloxane (PDMS) materials were introduced [48,49,50,51]. When subjected to an external magnetic field, magnetostrictive materials undergo changes in their magnetization state, resulting in alterations in length and volume. Based on magnetostrictive properties, these materials can be effectively coupled with MP-SAWS. The device is encapsulated with a PDMS shell material on its outer side. PDMS is biocompatible, flexible, thermally stable, and non-magnetic. These characteristics allow PDMS to enhance the biocompatibility of MP-SAWS as a casing material without compromising the sensor’s ability to accurately detect cardiac parameters [52]. The fabrication process involves surface photolithography and magnetron sputtering to draw patterns on the piezoelectric substrate and deposit interdigital electrodes. Using surface photolithography technology, IDT patterns are created on the surface of LiNbO₃. Aluminum electrodes are deposited onto the piezoelectric substrate through magnetron sputtering. The pre-patterned design ensures that the deposited aluminum forms an alternating interdigitated structure. Aluminum serves as both the transmitter and receiver of electrical signals, and its thickness should not exceed 1% of the wavelength λ to avoid excessive mass loads. Subsequently, the connection between the magnetostrictive material and the piezoelectric substrate is completed using suitable wafer bonding techniques such as anodic bonding. Finally, the PDMS shell is coated using surface-charge lithography techniques [53,54,55,56,57]. Additionally, during the packaging stage, to protect the interdigital electrodes on the upper surface, Al₂O₃ can be deposited using the atomic layer deposition (ALD) technique. This can potentially protect the piezoelectric layer and the interdigital electrodes in medical application environments [58,59]. The application of an external magnetic field causes the magnetostrictive material to expand, thereby exerting pressure on the MP-SAWS through changes in its volume. Since MP-SAWS exhibits excellent sensing characteristics for pressure, it can be used to sense magnetic field data. By considering parameters such as Young’s modulus and Poisson’s ratio of the material involved in the compression process, specific magnetic field sensing characteristics can be calculated.

2.2. MP-SAWS Modeling

The study of MP-SAWS involves multiple complex physical fields and unique structures, making the calculation of the associated physical properties complex. For accurate and detailed modeling and simulation work, finite element simulation is a commonly used method. During the finite element simulation process, the program divides the physical model into numerous refined grids and converts continuous solids into discrete matrix forms for efficient computer processing while maintaining a high degree of accuracy. This study utilized COMSOL Multiphysics 5.6 finite element analysis software for simulation work. Through modular modeling, the operational modes of SAWS can be analyzed step by step.

Figure 2a illustrates the complete sensor device with a single period extracted from the SAWS. The sensor utilizes a two-channel structure with two sets of SAW resonators to obtain sensing data. Performing post-calibration can enhance accuracy and eliminate spatial residuals. By selecting parallel directions of the IDT, the propagation of SAW can be simplified and considered a 2D model. Figure 2b displays the parameters of the 2D finite element model. The upper layer consists of aluminum electrodes, while the lower layer is a piezoelectric material composed of a 128° Y-X LiNbO₃ substrate. λ represents the wavelength of resonance, a represents the electrode width, b represents the distance between adjacent electrodes, D represents the unit of one period, P represents the half-wavelength, ${\mathrm{h}}_{AL}$ represents IDT’s thickness, and ${\mathrm{h}}_{LN}$ represents the LiNbO₃ substrate’s thickness. All parameters are indicated in Figure 2b.

Figure 3a represents the simulation model of the MP-SAWS in COMSOL, designed with 64 periods. The vibration mode during resonance is presented in Figure 3b. Figure 3c displays the potential distribution of the SAWS under resonance, which exhibits periodicity due to the structure of the IDT.

Table 2. Periodic unit dimensions.

Parameter	Size (μm)
λ	2
a	0.5
b	0.5
P	1
D	2
${\mathrm{h}}_{\mathrm{A}\mathrm{L}}$	0.2
${\mathrm{h}}_{\mathrm{L}\mathrm{N}}$	7

,

Table 3. Material parameters of piezoelectric LiNbO₃.

Material	128° Y-X LiNbO3
$\mathrm{Density},\mathsf{\rho } [\mathrm{kg}/{\mathrm{m}}^3]$	4700
$\mathrm{Relative} \mathrm{dielectric} \mathrm{constant}, {\mathsf{\epsilon }}_{\mathrm{rs}}$	$\left[\begin{array}{ccc}43.6& 0& 0\\ 0& 43.6& 0\\ 0& 0& 29.16\end{array}\right]$
$\mathrm{Coupling} \mathrm{matrix}, {\mathrm{e}}_{\mathrm{ES}}$$[\mathrm{C}/{\mathrm{m}}^2]$	$\left[\begin{array}{cc}\begin{array}{ccc}0& 0& 0\\ -2.53764& 2.53764& 0\\ 0.193644& 0.193644& 1.30863\end{array}& \begin{array}{ccc}0& 3.69594& -2.53384\\ 3.69548& 0& 0\\ 0& 0& 0\end{array}\end{array}\right]$
$\mathrm{Elastic} \mathrm{matrix}, {\mathrm{C}}_{\mathrm{E}}$$\left[{10}^{11}\mathrm{Pa}\right]$	$\left[\begin{array}{cccccc}2.02897& 0.529177& 0.749098& 0.0899874& 0& 0\\ 0.529177& 2.02897& 0.749098& -0.0899874& 0& 0\\ 0.749098& 0.749098& 2.43075& 0& 0& 0\\ 0.0899874& -0.0899874& 0& 0.599034& 0& 0\\ 0& 0& 0& 0& 0.599018& 0.0898526\\ 0& 0& 0& 0& 0.0898526& 0.748772\end{array}\right]$

,

Table 4. Parameters of aluminum IDT.

Material	Al
$\mathrm{Density}, \mathsf{\rho } [\mathrm{kg}/{\mathrm{m}}^3]$	2700
Young’s modulus, E [Pa]	$70 \times {10}^9$
Poisson’s ratio, μ	0.33

,

Table 5. Boundary settings.

Boundary	Mechanical Condition	Electrical Condition
${\mathrm{Г}}_1$	Free	Zero-charged
${\mathrm{Г}}_2$	Fixed	Grounded

and

Table 6. Electrode group settings.

Electrode Group	Al (IDT)
Odd	+1 V
Even	Ground

list the simulation setting of the device components.

2.3. Magnetostrictive Coupling Modeling

MP-SAWS is capable of measuring magnetic fields by coupling with magnetostrictive materials. During testing, MP-SAWS can detect changes in pressure to conduct the sensing test. The magnetostrictive material is affixed to the side of the SAWS base. When an external magnetic field is present, the magnetostrictive material undergoes deformation and extrudes the LiNbO₃ substrate. After SAWS detects different degrees of extrusion, the output results expressed in their characteristic frequency are utilized to obtain the corresponding sensing relationship between the magnetic field and characteristic frequency. Within the magnetostrictive module, the relationship between stress and strain with the magnetic field is represented by the following [60]:

$$\mathrm{S}=C_H:\left(\epsilon -{\epsilon }_{me}\left(M\right)\right)$$

(8)

$${\epsilon }_{me}={\displaystyle \frac{3{\lambda }_s}{2M_s^2}}dev\left(M\otimes M\right)$$

(9)

The non-linear magnetization behavior observed in the magnetostrictive material arises from its inherent non-linear constitutive relationship, expressed as follows:

$$\mathrm{M}=M_{s}L({|H}_{eff}|) {\displaystyle \frac{H_{eff}}{{|H}_{eff}|}}$$

(10)

$$\mathrm{L}=\coth \left({\displaystyle \frac{3{\chi }_0{|H}_{eff}|}{M_s}}\right)-{\displaystyle \frac{M_s}{3{\chi }_0{|H}_{eff}|}}$$

(11)

$$H_{eff}=\mathrm{H}+{\displaystyle \frac{3{\lambda }_s}{{\mu }_0{M}_s^2}}dev\left(S\right)M$$

(12)

S represents the stress, the elastic tensor $C_H$ is determined by Young’s modulus and Poisson’s ratio, M represents the magnetization field, ${\lambda }_s$ is the saturation magnetostriction coefficient, $M_s$ is the saturation magnetization, L is the Langevin function, ${\chi }_0$ is magnetic susceptibility in the initial linear region, and $H_{eff}$ is the effective magnetic field in the material. In the simulation, only the response of the magnetostrictive material to a unidirectional magnetic field is considered; although Terfenol-D is not an isotropic material, the model can be simplified and treated as isotropic. In practical use, the easy-axis direction should be the one actually applied for the measurement. For potential errors, the actual value of the material’s ${\lambda }_s$ may be lower, which could affect the final sensitivity. The magnetostrictive module uses these equations to obtain the device’s response to physical quantities such as magnetic field and stress through finite element analysis methods. The extra symbols are explained in the following equations:

$$\mathrm{A}:\mathrm{B}=\sum _{i=1}\sum _{j=1}{A}_{ij}{B}_{ij}$$

(13)

$$(\mathrm{M}\otimes \mathrm{M}{)}_{ij}=M_i{M}_j$$

(14)

The parameters of the magnetostrictive material are listed in

Table 7. Parameters of magnetostrictive materials.

Material	Terfenol-D
$\mathrm{Density}, \mathsf{\rho } [\mathrm{kg}/{\mathrm{m}}^3]$	9250
$\mathrm{Saturation} \mathrm{magnetostriction}, {\lambda }_s$ [ppm]	2000
Poisson’s ratio, μ	0.45
Electric conductivity, σ [S/m]	$1.7 \times {10}^6$
Young’s modulus, E [Pa]	$60 \times {10}^9$

.

3. Parameter Characteristics of the Sensor

Through the finite element simulation, MP-SAWS’s admittance curve is illustrated and shown in Figure 4a. In circuit theory, admittance refers to the reciprocal of impedance. It describes the resistance to the flow of an electric current through the electric system. During AC scanning, admittance serves as an indicator of the system’s operational mode. In the case of SAWSs, there are two characteristic frequencies at short circuits: the resonant frequency with minimum impedance and the anti-resonant frequency with maximum impedance. The admittance curve in Figure 4a includes information on the vibration mode and deformation degree of the SAWS at the resonant and anti-resonant frequencies. According to Figure 4a, the maximum value of admittance occurs at 1.8852 GHz, which corresponds to the resonant frequency. Conversely, the anti-resonant frequency is found to be 1.9510 GHz. The correspondence among the phase velocity, wavelength, and resonant frequency conforms to Equation (15) as follows:

$$v=f·\lambda$$

(15)

Thus, the initial phase velocity of the SAWS was determined to be 3770.4 m/s, as shown in Figure 4b.

The scattering parameters are used to describe the frequency-domain characteristics of transmission channels, also known as S-parameters. They can be used to calculate various indicators, such as input impedance and frequency response, by measuring the ratio of incident and reflected waves. Thus, S-parameters play a crucial role in studying the performance of SAW resonators. In a two-port network, the S-parameters are categorized into S11, S21, S12, and S22. For multi-port networks, the S-parameters include additional combinations and can form an S-parameter matrix.

The S11 parameter curve of MP-SAWS is shown in Figure 4c. S11 is the input reflection coefficient, which is an important parameter for describing the performance of a single-port resonator. The smoothness of the S11 parameter curve provides a qualitative analysis of the reflectivity of the resonator. As the curve represents the reflection loss (return loss), smaller values indicate lower levels of reflection and higher transmission coefficients. The relationship between the S11 coefficient and the reflectivity of MP-SAWS is as follows [61]:

$$S11={\displaystyle \frac{V_1^{-}}{V_1^{+}}}, P={\displaystyle \frac{V^2}{R}}$$

(16)

$${\displaystyle \frac{P_R}{P_I}}\left(dB\right)=10lg{\displaystyle \frac{P_R}{P_I}}$$

(17)

$$S11\left(dB\right)=10lg{S11}^2=20lgS11$$

(18)

In this set of equations, R represents the resistance value;$V_1^{+}$ and $V_1^{-}$ denote the input voltage signal and output voltage signal (reflection signal) at the resonator port; and $P_R$ and $P_I$ represent the reflection power and the incident power of SAW. Conversion from numerical values to decibels is achieved by taking the logarithm. The S11 parameter curve indicates that the MP-SAWS exhibits a strong response near 1.8852 GHz, displaying a low valley peak. In this frequency range with high-transmission capability, the curve exhibits minimal side lobes and noise, and the amplitude can reach −100 dB. There is also a strong correspondence between the admittance curve and the S11 curve. The low points in the S11 parameter curve correspond to the high peaks in the admittance curve, while the high points in the S11 parameter curve correspond to the low points in the admittance curve. These represent the resonant and anti-resonant frequencies of the MP-SAWS, respectively.

The quality factor $Q_m$ quantifies the energy efficiency during circuit resonance. The SAWS serves as a sensing detection device rather than an energy storage and utilization device. However, the SAWS needs to transmit sensing parameters from the sensor to the reader via wireless communication, which unavoidably leads to energy loss. In the SAWS, a high-quality factor indicates minimal energy loss during the transmission process. Excessive energy loss has adverse effects on signal quality and effective transmission distance in wireless communication. For a single-port resonator, the formula relating the dimension of the MP-SAWS to the quality factor is described as follows [62]:

$$Q_m={\displaystyle \frac{\pi L_c}{{\mathsf{\lambda }}_0\left(1-\mathrm{t}\mathrm{a}\mathrm{n} {\mathrm{h}}_{\mathrm{L}\mathrm{N}}\left(\left|r_s\right|N_g\right)\right)}}$$

(19)

where $L_c$ represents the effective length of the resonance cavity, $r_s$ denotes the reflectivity of an individual electrode, and $N_g$ refers to the number of electrodes within the reflective cavity. The parametric curve of the MP-SAWS mechanical quality factor $Q_m$ is represented in Figure 4d. As depicted in the graph, the MP-SAWS exhibits a strong response near 1.8852 GHz, which is characterized by minimal noise, prominent peak values, and an achievable amplitude of ${10}^{21}$. Evidently, the peak value of the mechanical quality factor also coincides with the resonant frequency.

The sensor’s sensing capability is influenced by noise present in the application environment. Since the working principle of the SAWS involves both positive and converse piezoelectric effects, the interference of external electric fields on the electric field of the SAWS cannot be ignored. To verify the effectiveness of the simulated devices, it is essential to validate the anti-interference ability of MP-SAWS through noise testing. In the anti-noise test, the electrodes are divided into odd and even groups, naturally staggered at intervals. Initially, the even-numbered electrodes are grounded, while the odd-numbered electrodes receive a 1V voltage input, and the resonant frequency is recorded. This is performed by increasing the voltage input to the odd-numbered electrodes and continuing to record the resonant frequency. Figure 5a represents the response result between the excitation terminal voltage and the characteristic frequency. Altering the electrode group voltage setting between electrode group 1 and electrode group 2, the odd-numbered electrodes are grounded, while the even-numbered electrodes receive a voltage input. Figure 5b represents another response result between the excitation terminal voltage and the characteristic frequency. Supplementary experiments can be conducted to eliminate the noise impact caused by the electrode position on external electric fields. In the same model, by outputting the wave velocity, the interference of the voltage on wave speed can be obtained. The results are shown in Figure 5c,d. Similarly, a set of magnetic field anti-interference tests was conducted under two grounding configurations. The magnetic field direction was set to the horizontal direction, and the excitation voltage was 1V for all cases, which is consistent with subsequent magnetic field tests. The interfering magnetic field was scanned from negative to positive. The results are shown in Figure 5e,f.

From the anti-interference test, it is evident that the SAWS exhibits excellent resistance to external electric field noise and magnetic field noise. The sensing error caused by the electric field excited by different voltages can be ignored, as can the response of SAW devices without magnetostrictive units to magnetic fields. This does not affect the normal feedback of the MP-SAWS.

4. Application

The MP-SAWS can detect subtle variations in various physical quantities, including temperature and pressure. After integrating magnetostrictive materials, the MP-SAWS can also detect precise changes in magnetic fields. By utilizing finite element simulation software, incorporating diverse physical fields, and employing parameter scanning, the sensing characteristics of the MP-SAWS for temperature, pressure, and magnetic fields can be obtained. These characteristics can be applied to specific magnetocardiography (MCG) scenarios, and the measurement results can be displayed through characteristic frequency curves.

4.1. Pressure

The MP-SAWS demonstrates a high sensitivity to variations in stress. In medical applications, pressure detection enables heart rate monitoring. The MP-SAWS can contribute to the study of cardiovascular diseases and the evaluation of heart failure through heart rate detection [63]. Leveraging the quantitative research capability of the MP-SAWS in pressure analysis, it can combine hemodynamics to evaluate coronary heart disease under minimally invasive conditions, providing more detailed cardiac information [64].

When measuring pressure through finite element simulations, it is necessary to consider the surface deformation caused by external forces, as it may affect the resonant frequency of the sensor. During stress analysis, the environmental temperature is set at 293.15 K, which corresponds to typical room temperature. The measurement environment is free of external magnetic fields. The stress analysis of the MP-SAWS finite element model is depicted in Figure 6a, illustrating the curve showing the relationship between external stress and the resulting variation in the MP-SAWS characteristic frequency. Figure 6b represents the admittance curve before and after applying stress, demonstrating the deviation of the characteristic frequency under stress. Based on the simulation results, the pressure sensitivity of the MP-SAWS is 10.426 kHz/MPa. This level of response is sufficiently accurate to meet the measurement requirements.

4.2. Temperature

Temperature is a measurable physical quantity that can be detected by MP-SAWS. The MP-SAWS can function as a generic temperature sensor to measure various parameters such as ambient temperature and body temperature. When used as a temperature sensor, it can support certain therapeutic procedures. For instance, it can aid in controlling low temperatures after cardiac arrest to mitigate hypoxic damage, maintaining low temperatures to control toxic damage, and regulating temperature during cardiopulmonary resuscitation [6,65]. Temperature parameters play a vital role as auxiliary parameters in facilitating medical treatments.

In finite element simulations, the consideration of the varying degrees of thermal expansion and stress in different materials resulting from temperature changes is necessary. Temperature also influences the performance of materials. Regarding the MP-SAWS substrate material, temperature exceeding the Curie temperature results in changes in the material’s magnetic properties. The temperature has minimal influence on the material properties of the LiNbO₃ substrate because the Curie temperature of the LiNbO₃ substrate is 1210 °C [15]. Therefore, the thermal analysis of the MP-SAWS primarily focuses on thermal expansion.

The stress analysis of the MP-SAWS is represented in Figure 7a and describes the correspondence between ambient temperature and the resulting variation in characteristic frequency. Figure 7b illustrates the admittance curve within the physiological temperature range, demonstrating the deviation in the characteristic frequency under temperature changes. The measurement environment is free of external magnetic fields. Based on the simulation results, the temperature sensitivity of the MP-SAWS is 68.211 kHz/K. This level of response is sufficiently accurate to meet the measurement requirements.

Based on the relationship curve between stress, temperature, and resonant frequency, resonant frequency decreases linearly with increasing stress and temperature. This linear relationship indicates that processing MP-SAWS sensing data for stress and temperature is relatively straightforward. Employing the control variable method, the transient instants of heartbeats, which correspond to the interval without external stress, are isolated to determine the operating temperature of the sensor. This operating temperature represents the sensor’s temperature measurement output and is also an essential pre-determined environmental parameter when assessing stress and cardiac magnetic fields. It also enables the exclusion of factors such as ambient temperature changes, gravity, and the influence of shell materials on MP-SAWS sensing results when measuring magnetic fields.

4.3. Cardiac Magnetic Field and MCG

The MCG is traditionally measured using SQUIDs, which offer high sensitivity and mature clinical applications. However, the use of these devices requires liquid helium cooling, significantly increasing maintenance costs. Using atomic magnetometers is a method that substantially reduces costs, and the sensitivity of newly developed magnetometers is now approaching SQUIDs [66,67]. Magnetoresistive sensors represent another relatively inexpensive method for MCG measurements, although they currently exhibit lower sensitivity and signal-to-noise ratios [68]. SAWSs based on the delta-E effect also demonstrate high sensitivity in magnetic field sensing [38,39,40]. In this study, the MP-SAWS was compact and capable of 2D dynamic measurements. Although its sensitivity needs further improvement, it shows potential for application in the human magnetic field measurements.

By detecting the cardiac magnetic field, an MCG can be generated. The transducer model is illustrated in Figure 8a. The length ratio of the two materials in the direction of the magnetic field is maintained at 1:1, ensuring the preservation of the stress-sensing relationship. The arrangement of the materials is LiNbO₃-Terfenol-D-LiNbO₃. The length ratio is set at 1:2:1, which satisfies the overall length ratio of 1:1. The established model has the capability to detect the magnetic field in a specific direction. Magnetic field scanning is conducted within simulation software, and the correspondence between the external magnetic field and the lateral stress is presented in Figure 8b. In the simulation model we established, the three materials were closely bonded. The boundary conditions for the left surface of the left LiNbO₃ and the right surface of the right LiNbO₃ were fixed. The boundary conditions between LiNbO₃ and Terfenol-D were set as free. After applying the magnetic field, the stress caused by the magnetostriction of Terfenol-D could be applied to the LiNbO₃ on both sides. During the stress simulation process, a relationship curve (Figure 6a) between the stress and MP-SAWS characteristic frequency was obtained. According to the results of the anti-interference testing process, the magnetic field itself has minimal impact on the operation of the SAW device. The magnetostrictive stress induced by the magnetic field serves as the link connecting the magnetic field and the SAW device. By combining the two corresponding relationship sets, the correspondence between the magnetic field and the MP-SAWS resonant frequency can be computed using computer calculations, as shown in Figure 8c. Based on the relationship curve derived from magnetic field sensing, a non-linear inverse correlation between the magnetic field and the characteristic frequency is shown. MP-SAWS demonstrates higher sensitivity when measuring strong magnetic fields.

The cardiac magnetic field is generated by bioelectric currents originating from the heart. Both MCG and electrocardiograms (ECGs) are used to diagnose heart diseases. MCG provides superior advantages over ECG for diagnosing myocardial ischemia and coronary heart disease [69]. The intensity of the cardiac magnetic field ranges from 50 pT to 100 pT, indicating its weakness and susceptibility to interference from external magnetic fields. Currently, there is limited research on cardiac magnetic field measurements, and the application of MCG has not been widely adopted. MCG can detect the position, size, and shape of the heart. An individual SAWS is compact in size, facilitating integration. Figure 9a illustrates an integrated MP-SAWS arranged in a square-array format. This array format strengthens the signal, reduces errors, and expands the detection range. In the sensing array, sensing units devoid of magnetostrictive materials are incorporated, serving to determine and sense the temperature. Differential processing is applied to the magnetic field signals from distinct sensing units, effectively eliminating the influence of factors such as heartbeats and other forms of stress. The employment of the control variable method enables the sensor to detect diverse physical quantities. By employing appropriate algorithms, a two-dimensional MCG can be constructed. In practical use, the MP-SAWS is attached to the heart, and the test data are wirelessly transmitted to a computer, with the results displayed as a time–magnetic field relationship curve.

In clinical applications, the MP-SAWS combined with a fixed-value constant magnetic field generator can achieve better sensing results. According to the magnetic field sensing curve of MP-SAWS, the sensor exhibits higher sensitivity in areas with strong magnetic fields. The International Commission on Non-Ionizing Radiation Protection (ICNIRP) recommends that human body parts should not be exposed to static magnetic fields above 400 mT in non-work situations [70].

Based on the existing magnetic field-sensing relationship curve, a constant magnetic field strength of 200 mT is selected as it meets the safety standards and significantly enhances the sensor’s sensitivity. This is due to the mechanical relationship shown in Figure 8b, where the slope of the magnetic field is steeper at higher magnetic fields. The direction of the static magnetic field is chosen parallel to the direction of the measured cardiac magnetic field. Since the amplitude of the cardiac magnetic field is very small, only a small portion of the magnetic field sensing curve is required after adding the constant magnetic field, as depicted in Figure 9b. In simulation software, this can be achieved by setting an additional static magnetic field of 200 mT. The weak cardiac magnetic field and the static magnetic field superimpose and act on the sensor. The cardiac magnetic field is obtained by reading the resonant frequency change in the SAW device. In a clinical setting, an additional magnetic field-generating device is required to provide a 200 mT static magnetic field at the heart’s location. Any additional interfering magnetic fields need to be shielded. In this range, the sensing curve is almost linear, reducing the complexity of the sensing relationship. For magnetic field measurements, the environmental temperature is set at 293.15 K, corresponding to the standard room temperature. The enhanced magnetic field sensitivity is 0.171 Hz/μT.

To evaluate the effectiveness of the MP-SAWS for detecting the cardiac magnetic field, simulated cardiac magnetic field testing has been employed. According to reference [69], the trend of changes in a cardiac magnetic field time–magnetic field graph is similar to that of the time–electric field graph of an ECG. Using the MIT-BIH arrhythmia database, a 10 s ECG was selected, and a set of simulated cardiac magnetic field time–magnetic field data was generated by scaling the MCG data of the arrhythmia patient [71]. Additionally, using a program to simulate MCG, a set of 10 s MCG data was generated as a healthy person’s cardiac magnetic field data [72].

In the simulation program, the two sets of simulated magnetic field data were input, and corresponding time–resonance frequency curves were output. The results for patients with arrhythmia are shown in Figure 10b, while those for healthy individuals are shown in Figure 10d. A characteristic of arrhythmia is a significant variation in the intervals between consecutive heartbeats. In contrast, the heart rate intervals of healthy individuals are relatively stable. For instance, in Figure 10a, it is roughly considered that the first cycle spans from 0.2 s to 1.1 s. Then, the seventh cycle is just slightly longer than 0.5 s, which is a short cycle, whereas the eighth cycle exceeds 1 s, indicating a long cycle. The significant disparity between these two adjacent cycles suggests a clear presence of arrhythmia. In contrast, the data in Figure 10c show that the time difference between each cycle is minimal, indicating that the cycles are stable. This heart rate is considered healthy. Based on existing simplified magnetic field-sensing characteristics, the input time–resonance frequency curve data were used to restore the time–magnetic field relationship curve of the cardiac magnetic field, which was then compared with the original data. The results for patients with arrhythmia are shown in Figure 10a, while those for healthy individuals are shown in Figure 10c. Comparing the original signal with the reconstructed data, the results almost overlap. This indicates that the reconstruction was effective.

Based on the comparison between the two sets of original data and restored data, the obtained relationship curve can accurately measure the cardiac magnetic field, and the simulation shows that the relationship curve can truly restore the cardiac magnetic field data with minimal errors.

4.4. Multi-Parameter Selective Sensing

Multi-parameter selective sensing with a single sensor is challenging. The sensor array discussed in Section 4.3 facilitates this. As shown in Figure 11, the array integrates diverse sensing units, split between those with Terfenol-D and those without. This distribution enhances spatial resolution and signal strength. Units with distinct structures serve different functions. Units without a magnetostrictive material output time–frequency diagrams. Based on heartbeat characteristics, an average stable interval in the curve is chosen as the “stable frequency”. The “stable frequency” is unaffected by heartbeat stress; it enables the heart temperature to be determined at this point. According to the curve in Figure 7a, an accurate single-point temperature can be obtained. For instance, the stable frequency 1.88470 GHz in Figure 11 corresponds to 311.15K (38 °C). Heart rates are also derived from these units by averaging several heartbeat cycles in the time–frequency data. The measurement of the cardiac magnetic field requires both types of units due to overlapping between the cardiac magnetic field and heartbeat peaks; a single sensing unit cannot exclude the influence of heartbeat stress. Differentiating the two sets of time–frequency graphs yield the Terfenol-D contribution to the sensor output, which represents the cardiac magnetic field isolated from heartbeat stress. Converting frequencies to magnetic fields via the relationship in Figure 9b yields a point-specific cardiac magnetic field. By processing varied outputs, the array selectively measures heart temperature, heart rate, and cardiac magnetic field.

According to specific application scenarios, the detailed design of the MP-SAWS array is shown in Figure 12a. The array layout adopts a regular periodic design. The sensing unit without Terfenol-D consists of four independent SAWS units, each in the shape of a square. Based on the design of 64 interdigital electrode pairs shown in Figure 3a, the SAWS units are squares with a side length of 0.2 mm. The sensing unit with Terfenol-D consists of two sets of the SAWS–Terfenol-D–SAWS structures depicted in Figure 8a. The Terfenol-D is designed as a rectangle with a length of 0.4 mm and a width of 0.2 mm to maintain consistency in the arrangement of the SAWS units. Two different types of sensing units are arranged in a cross pattern to form a larger periodic unit, as shown in Figure 12a. The SAWS units form a square lattice with equal spacing, ensuring uniform measurement. The average planar dimensions of the human heart plane are approximately 12 cm in length and 8 cm in width [73]. According to the size of the periodic unit in Figure 12a, an array of 64 by 48 periodic units was designed. Along the longer side, there are 256 SAWS units, and along the shorter side, there are 192 SAWS units. The total size of the MP-SAWS is approximately 15 cm by 11 cm, producing 256 by 192 SAWS units that can deliver two-dimensional cardiac data.

Different parameters to be measured are extracted from the resonant frequency results of a single-channel output. When applying the MP-SAWS, the environment is kept free of external magnetic fields. During temperature measurement, each SAW unit provides a continuous output for a single point. By selecting a point and using appropriate algorithms, such as excluding outliers and taking the average, the average resonant frequency of the point in the stable state (stable frequency) of the heart is estimated to determine the heart temperature. To measure heart rate, the periodic information of the resonant frequency is extracted from the SAWS units. This can be achieved by averaging the total duration of multiple heartbeats or by performing a Fast Fourier Transform (FFT). According to Figure 12a, the magnetic field signal is obtained through differential measurements between adjacent SAWS units with different material compositions. The midpoint between the two SAWS units involved in the differential measurement is chosen as the recording point for the signal. After converting the differential signal to a magnetic signal, a two-dimensional MCG is obtained.

Generally, measuring different physical signals requires distinct measurement materials, modules, and sensing logic. The MP-SAWS can selectively output different physical quantities without changing the measurement devices. This design inherently offers high integration. Moreover, due to its small size, the device has the potential for further integration into medical devices.

5. Conclusions

This paper presents a multi-parameter sensor based on SAWS. Finite element analysis models were established for both the SAWS component and the magnetostrictive material component. Specific dimensions and structures were designed for the MP-SAWS model. The resonant modes of the MP-SAWS model were studied. Frequency-domain analysis was conducted on the SAWS component. The characteristic curves, including admittance curves, S11 parameter curves, and mechanical quality factor curves, were analyzed. The resonant frequency was found to be 1.8852 GHz, with an anti-resonant frequency of 1.9610 GHz. The peak values of the admittance curve and S11 parameter curve occurred at the resonant and anti-resonant frequencies, and the mechanical quality factor reached ${10}^{21}$. Unidirectional magnetic field analysis was performed on the magnetostrictive component, revealing various relationships between the magnetic field, magnetostrictive length, inter-material stress, and SAWS resonant frequency. To ensure the accuracy and noise resistance of finite element simulations, electrode-voltage boosting was performed through noise testing. Thermal and stress analyses were also conducted, demonstrating the sensing capabilities of MP-SAWS to temperature and stress. Under stress, the offset of the MP-SAWS resonant frequency showed a discernible inverse correlation with stress changes. Similarly, the offset of the MP-SAWS resonant frequency showed an inverse correlation with temperature changes. The obtained sensing relationship between stress and temperature provides support for medical diagnosis and treatment while also allowing for the calibration of magnetic field sensing results in various magnetic field-testing environments. Multi-parameter measurements were realized via the control variable method. The device’s sensitivities to stress, temperature, and magnetic field were 10.426 kHz/MPa, 68.211 kHz/K, and 0.171 Hz/μT, respectively. By coupling the magnetostrictive material with the SAWS, the sensor can be used for magnetic field measurements. During magnetic field scanning, the resonant frequency of the MP-SAWS decreased as the magnetic flux increased, and the sensing curve exhibited a non-linear relationship. When mapping the MCG, a constant static magnetic field was set, and the sensing curve was simplified to a linear relationship. The simulation model was validated by comparing the simulated MCG data of healthy individuals and patients with existing database data. The results showed that the designed magnetic field sensor and the obtained sensing relationship could accurately sense the MCG with good performance.

However, current MP-SAWS models exhibit certain limitations. In practical applications, an array of the MP-SAWS is planned to be used in a signal detection system, but due to computational constraints, the actual array simulation model of MP-SAWS has not been constructed. Furthermore, specific design and data processing algorithms are required for the construction of a two-dimensional MCG. In two-dimensional simulations, the impact of multi-directional magnetic fields on the device should be considered to better replicate real-world scenarios. The differential algorithm proposed in this paper should also be tested in practice. AI tools may be needed to assist in adjusting numerical weights for generating two-dimensional MCG.

In future research and work, the device fabrication processes and manufacturing of MP-SAWS will be specifically studied based on the simulation results presented herein. Furthermore, to obtain better data in practical testing, future designs will focus on enhancing the sensitivity of cardiac magnetic field measurements.

By comparing the test data with the simulation data, more information about the sensing performance of MP-SAWS can be obtained, providing data support for the advancement of SAWS and sensor research fields and exploring more applications of MP-SAWS.