A Novel in-situ Dynamic Mechanical Analysis for Human Plantar Soft Tissue: The Device Design, Definition of Characteristics, Test Protocol, and Preliminary Results

doi:10.21203/rs.3.rs-3729145/v1

The in-situ mechanical characterization of elastomers is not highly regarded due to the existence of a well-established set of sample-based standard tests for research and industry. However, there are certain situations or materials, like biological soft tissue, where an in-situ approach is necessary due to the impossibility of sampling from a living body. We have developed a dynamic mechanical analysis (DMA)-like device to approach in-vivo and in-situ multidimensional stress-strain properties of human plantar soft tissues. This work elucidates the operational mechanism of the novel measurement, with the definition of a new set of moduli, test standardization and protocol. Exploratory results of a volunteer’s living plantar, silica rubber samples are presented with well preciseness and consistence as expected.

Biophysics

plantar soft tissue

in-vivo

in-situ

dynamic mechanical analysis

biomechanical characterization

The plantar soft tissue, located between the dermis and bones of foot, is a critical composite material integrated of fat and specific connective tissue [1] to cushion shock, absorb impact [2, 3], and protect against excessive local stress [4] for our daily locomotion and weight-bearing activities. Given the feature of shape recovery and energy dispersion, biological soft tissue is generally taken as elastomer in the field of biomaterials and biomechanics; and artificially synthesized elastomers of moduli in the MPa range can be easily tuned to match well with the mechanical properties of soft tissues [5]. Thereafter, the characterization of mechanical properties of soft tissue is a key content in the field of clinical medicine, biomedical engineering, and bionic materials [6, 7].

The stress-strain mechanical test methods for industrial elastomer are therefore applied onto biological soft tissues [8], usually with cadaveric specimens [9], whereas live specimens are strictly impossible, and even experiments targeting animal organs are difficult to achieve and require very strict conditions and ethical permission. However, the obvious difference between ex-vivo specimen and living tissue in the biochemical state and mechanical properties makes it controversial and lack of feasible cross check.

Current material characterizations of living tissues are mainly carried by ultrasound and imaging due to their non-invasive feature [10–12]. However, imaging methods are subject to exposure and have strict limitations on the number of measurements and irradiation time. Moreover, these indirect methods can only provide discrete stress-strain data, which makes the construction of constitutive equation difficult.

Over the past decades, dynamic mechanical analysis (DMA) has become a standard tool for materials research to approach the periodic strain-stress behavior, elasticity, and viscosity [13, 14]. A number of DMA tests were reported on ex-vivo cadaveric specimens, whereas the defects are obvious [15]. In recent years, some researches have adopted in-vivo indentation tests via a single pulse to access the force-displacement and stress-relaxation curves [16], and achieve half of the periodic dynamic stress-strain correspondence. Yet continuous and full-periodic mechanical measurements on living tissues, as an ideal methodology, has not been reported in the field.

In-situ and In-vivo mechanical tests on plantar soft tissue, if being made feasible, are not only of importance in precise measurement comparing to the cadaveric tests, but also implies significant potentials in clinics and healthcare. The variations in the soft tissue's mechanical characteristics at different plantar locations may indicate health or even pathological issues. For instance, the soft tissue stiffening under the metatarsal heads may lead to foot ulcers in diabetics [17] and metatarsalgia in the elderly [18]; It has also been demonstrated that altered mechanical properties of the heel pad may result in shock-induced injuries such as heel pain and Achilles tendinitis [19]; Since soft tissue properties vary remarkably across different plantar regions [20], the real-time monitoring on the material properties on the living plantar are necessary as a clinical examine [21], whereas ex-vivo test has no way to be useful in this mean.

During daily activities, the planter soft tissue bears mechanical loads and land forces in various dimensions: i.e., pressure acting normal to the land and shear stress acting tangential to the plantar surface [22]. For various orthopedic or systemic diseases, it can be of great interest to learn the effects of different forms of stress onto the human foot. However, while so far vertical pressure has been widely reported, and there are very few studies on shear and torque [23]. One probable reason may be the lack of available device and methodology for the shear and torque measurements, especially in-vivo and in-situ [24].

In response to the above concerns, we have invented a device based on the principle of DMA to measure the in-vivo and in-situ material properties of soft tissue, especially for plantar. The engineering verification of the design has been done in simulation, and consistent theoretical results has been achieved to certify its capability to measure the periodic strain-stress behavior, and analyze the material properties in a continuous fashion [25–27]. In this manuscript, the mechanical design and working principle of the in-situ dynamic mechanical analysis (DMA)-like device is described in details (section II), the characteristics, i.e., a set of moduli, for soft tissue in this newly-invented test are defined (section III), the sample standardization and calibration is carried out with the help of finite element analysis (FEA), as a common tool in biomechanics [28, 29] (section IV), the test protocol on living plantar is settled (section V), and finally, the primary results of testing on a living planter, a silica rubber mimic foot, and a silica rubber brick sample have been delivered as examples (section VI).

The application of periodical stress-strain onto plantar and the corresponding monitoring mainly involves sinusoidal motion of detector and its effective adhesion onto the subject, with precise add-on of force and distance sensor. As demonstrated in Fig. 1, three stress-strain detecting units of tensile, shear, and torque are arranged in a supporting framework, with a cover lid to place the foot and three holes on it can subject the test-points of the plantar to the detector head. Moreover, a vacuum suction cup is set onto the head to firmly bound the plantar, and enables the reciprocal motion of soft tissue. The mechanical structure design of the three detection units can be simplified as sine mechanism, as shown in Fig. 2–4.

The mechanical design of vertical reciprocal motion can be simplified as the crank slider mechanism, as shown in Fig. 2. By rotating the disk, along with the eccentrically mounted tie rods, the shaft makes reciprocating linear motion vertically under the limitation of the linear bearing. The force sensor and probe head are mounted sequentially on the shaft, while the displacement sensor is mounted on a fixed plate. One thing shall be addressed here, although the displacement is determined by the mechanical structure, e.g., the size of rotary disk, the eccentrical radius and the length of rod and so on, depending on the stiffness of testee subject, and inevitable errors, the actual strain happens on the subject may not be the set of displacement, which are observed many times in our following practice, therefore an independent displacement sensor is necessary. And this difference will be discussed in the results section. The mechanism of shearing motion can also be simplified as the crank slider, only that in a horizontal way, as shown in Fig. 3.

The horizontal torsion motion can be realized by crank rocker mechanism, as shown in Fig. 4. With the rotary of disk, the slider mounted eccentrically on the disk through the bearings rotates and drives the lead rail to swing cyclically. The torque sensor connected to the torsion axle monitors the oscillation via a synchronous belt. And torsional deformation is recorded by the angle transducer.

Moreover, each unit is equipped with a set of lifting mechanisms, allowing the detector to automatically rise during testing. After touching the plantar, the appropriate height is determined based on a default stress threshold, and the mechanism is fixed at that initial position. Then vacuum is applied to adhere the soft tissue. This is to avoid subjective force errors caused by testee actively adjusting the height of the foot to match the probe. As shown in Fig. 5, the mechanical principle is a nut-screw rotation, with a self-locking brake motor to keep the zero-position unchanged during the reciprocating test.

To ensure non-destructive and non-invasive binding, a vacuum composite suction cup is designed for the detector joint during the inspection (Fig. 6). The suction cup is composed of a rigid inner core and an elastic skirt edge. The upper surface of cup is designed with support ribs to ensure a stable and flat contact onto the tissue, and avoid shape change of the testing tissue. Also, this design can increase adherence intensity by lower the contact area with the same vacuum degree. Our practice verified that this design can firmly adhere the soft tissue under particular testing condition. The vacuum is provided by a regular laboratory oil pump with degree to be sufficient for the suction without the uncomfortable feeling reported by testees.

In classical material mechanics, moduli are conducted by the relative change of stress (force) and strain (size change), e.g., the Young’s modulus of tensile/compression is defined as E = σ /ε =(ΔF/A)/(ΔL/L), where involves the original shape (L). However, while the strain here is a rigorous definition with exact shape and measures of the test sample, and the determination of these parameters is trivial in common material test, the testee we are dealing with in the new in-situ test has mere measures on shape and size (even if we can do exact measurements in some cases), either for biological tissue or inorganic object. Because the test is applied on a small area of the outer surface of a relatively large sample, the strain is obviously not only the shape change of the cylinder behind the suction area, therefore the original size L of this cylinder is regardless of the “modulus” interested in the present case, as the area marked out by the orange rectangle in Fig. 7. Figure 7a is the FEA simulation of the in-situ tensile on a silica rubber brick sample. Although we have determined the effective strain depth is ~ 5cm in this case of brick sample [27], it is still mysterious to approach the shape and size of an “equivalent cylinder”. And for biological tissue, the dilemma is more complicated, the original shape and size of soft tissue is extremely difficult to be measured, and it almost differs in every individual case. Although we can somehow measure the thickness of plantar tissue, i.e., the distance from skin to the lower end of calcaneus, as the area marked in Fig. 7b, when the detector drives the motion of the suction area, it is easy to image that the whole plantar tissue around (without clear boundary) involves in the shapes change, and even worse the confinement of skin plays crucial role in the stress response, it is meaningless to define the original L here.

On the other hand, it is not unreasonable to doubt if this parameter is necessary in biomechanical characterization. Since we have exactly measurable force (or stress with area) and displacement (strain), given the L temporarily undefined, we may firstly define a series of “apparent moduli” analog to classical moduli: Similar to the classical Young’s modulus, we define the tensile/compression combined modulus as

$$\begin{array}{c}{H}_{TC}=\frac{{F}_{TC}/A}{\varDelta L/L}\#1\end{array}$$

where F_TC is the force of both push and pull, A is the area of suction, L is the “original” length, and note the ΔL is the displacement of up and down.

Then the new shear modulus is defined as

$$\begin{array}{c}{H}_{S}=\frac{{F}_{S}/A}{\varDelta x/L}\#2\end{array}$$

where F_S is the force of shearing of two directions, and note the Δx is the displacement of tissue sheared to both sides. Due to the relationship between shear and torsion, we have the applied torque T (in the unit of Nm) as

$$\begin{array}{c}T=\frac{{J}_{T}}{L}{H}_{S}\phi \#3\end{array}$$

where φ is the angle of twist in radians, and J_T is the torsion constant in the unit of m⁴, although it firmly depends on the shape of object, and is complicated to determine for irregular shapes, fortunately we can simply derive it, without knowing the exact form in the means of geometry, from Eqs. 2 and 3:

$$\begin{array}{c}{J}_{T}=\frac{TA\varDelta x}{{F}_{S}\phi }\#4\end{array}$$

Then we have the analog torsion modulus (or torsional rigidity analog to classical definition) in the unit of Nm²

$$\begin{array}{c}{H}_{t}=\frac{TA\varDelta x}{{F}_{S}\phi }{H}_{S}\#5\end{array}$$

Note that in the real test of plantar, there are two modes of shearing test (longitudinal and transverse), and correspondingly two moduli H_LS and H_TS, the H_S in Eq. 5 is taken as (H_LS + H_TS)/2 in practice.

Here the only undetermined variable is L, but whatever it may be, it does not affect the parallel comparison between the moduli in the same category among the tests. The definition can certainly fulfil our current needs to measure and examine the plantar tissue as a healthy indicator, by considering the shape and size are also part of the “eigen” tissue properties to be reflected by the stress-strain behavior, the term “apparent moduli” objectively characterize the properties of a particular tissue. In this way, we may set a nominal value of L to balance the dimension of equations. Currently this parameter is set to be 10mm.

In the future research, with a large number of testing data, we expect to employ machine learning to figure out the underlying correlations and establish a reliable relationship between newly-defined analog moduli H and classical moduli G with a so-called “equivalent length” L. (This work is currently in progress in our group, since it is not a main concern in this work, we hope the results will be reported in near feature).

The main idea of the in-situ test is a compromise for the strong limit of living tissues, as the test conditions such as force, frequency, temperature and so on are strictly confined within a tiny window. However, as a characterization itself, the determination of test limits requires samples beyond the coverage. Note that, the force and torque sensors employed in the instrument are mature industrial products and their calibration is trivial. The general procedure here is to correct the operational or systematic error.

On the other hand, a series of standard samples for calibration and correction is a must for a standardized characterization, while obviously the living tissue cannot serve this role, in either concern of standard materials or availability. In this work, the silicon rubber (SR) is selected to approximate the heel pad tissue. With present knowledge of the living tissue, the grade of SR is chosen as the tensile modulus of 0.518MPa, compressive modulus of 1.228MPa, elongation at break of 363.4%, hardness of 18 (shore A), and density of 1.086g/cm³.

We employ a SR brick measuring 10×10×5cm³ to test as a reference because the shape of a mimic foot cannot be a standard form of samples and lacks systematical comparability. A metal box covers the brick to act as the frame holder and give a rigorous confinement. In our earlier work [27], with the help of FEA, an ignorable boundary condition was sought to determine the shape and size of the brick sample in order to guarantee that the size is large enough to reflect the eigne properties of the elastomer regardless of the impact of size or boundary morphology. For the silica rubber employed in this case, that boundary was determined to be 5×5×2.5cm³, thereby the current size is doubled to ensure the sufficiency.

It should be noted that here the size and material property of “standard” brick sample are merely artificial choice. Since our research focused the biological soft tissue, especially the plantar, we select this grade of silica rubber for a standard sample. Nevertheless, this in-situ DMA method can also be expected to apply to the research of other soft matters, and depends on the objects it is meant to measure, the standard sample for calibration is a free choice. The basic principle is a reproducible elastomer to calibrate the machine, with sufficient size and regular shape to avoid the geometrical effect, and there is no necessity to rule a universal “standard” sample.

A volunteer participant (female, age: 30–35 year., height: 165-170cm, weight: 65-70kg, body mass index (BMI): 24–25) (the personal info is reported in interval to protect privacy) has taken the test and been reported in this manuscript. The criteria for participant selection excluded any with acute or chronic pain, active disease states that could affect soft tissue stiffness, thickness, and any history of foot surgery two years prior to the experiment. The participant is fully informed and signed the consent before trials. The Ethical Review Committee of Huashan Hospital, Fudan University (HIRB) approves the ethical review (see the supplemental materials).

Due to the significant heterogeneity of plantar, the shearing along different direction is quite considerable, which also accords to the functionality of plantar. Thus, as mentioned above, in practice we take two modes of shearing test in longitudinal and transverse directions, that is, the direction from heel to toe, and vertical to the foot. In this way, the tests in four directions were carried out respectively at five spots on plantar tissue that are considered to be critical in bear-loading or prone to ulceration and, including the three spots on the forefoot (the first, second, and fifth metatarsal heads), the midpoint on the lateral edge of the arch, and the centre of the heel [30], as shown in Fig. 8.

Participant is asked to provide a series of clinical information of gender, age, height, weight, foot length, foot width, foot health, shoe-wearing habits, daily average steps, and exercise habits before each test. During the test, the volunteer sequentially places five test positions on the detectors of three stress-strain detecting units (tensile/compression, shear, and torsion) for the corresponding test. To ensure the data accuracy, each test is repeated three times, that is, 45 tests in total for one testee.

In this work, the amplitude of reciprocal and shearing test is set to be ± 2mm, the twist range of torsion test is set to be ± 14°. The amplitude is chosen by observing the regular motion of healthy plantar pad, and the frequency is determined by an empirical upper limit of human foot usage in common sense, and higher frequency may cause noticeably discomfort on testee [31]. It is important to note that the displacement in real test is not exact the setup value (± 2mm or ± 14°), due to the test conditions and characteristics of testee, the difference could be unignorable, therefore the strain must also be preciously measured to calculate the moduli. The reciprocal motion is processed for 10 seconds. In practice, the oscillation begins at a lower frequency and reaches its set frequency after 1 second. Typically, it takes around 2 seconds for the signal to become stable, so we take the data after t = 4 seconds to calculate the average force and errors. The test conditions on mimic foot model and brick sample are similar.

Furthermore, as silica rubber of particular grade is utilized to prepare the “standard sample” in this research, we have prepared a SR foot model with the same grade for test, as a reference comparison to the living plantar. The model is extracted and rebuilt from CT scan of real foot. The bones are 3D-printed with PLA resin. The general test gesture, the foot and mimic foot model positioning, and a direct view of detection are shown in Fig. 9. The videos of tests on living foot and SR mimic foot are attached in supplementary materials as a visual presentation of the test.

The living test results on the volunteer’s plantar soft tissue are presented in Fig. 10. There are 20 subfigures classified by four types of stress-strain behaviors (tensile/compression (Fig10. a-e), longitudinal shear (Fig10. f-j), transverse shear (Fig10. k-o), and torsion (Fig10. p-t)) on five spots (M1, M2, M5, E and H). In all the four types of tests, we intendedly reverse the directions of displacement and force to present a peak-to-valley view for a clear observation. In the results of tensile/compression, the peak in the force curve represents the compression (push up) with a valley on the displacement, and vice versa. In shear and torsion, the stress is symmetrical thus the direction is trivial. For a better demonstration, the sixty periods of signals of three trials (twenty periods in one trial) are overlapped to be cloud curves and the average of each are presented as solid line in Fig. 10.

It can be observed that the periodic signals behave stable in amplitude and extremum, which confirms the preciousness of the device and method. Since the stability of test quite depends on the cooperation of the testee, the results are much more stable within in one trial, whereas the signal overlap of different trials may sometime generate noticeable noise, e.g., the Fig. 9 c and e, though the deviations are still in acceptable range.

The same tests have also been done on the five spots of the SR mimic foot model and brick sample described in section 4. The measured force, strain and calculated moduli are summarized in Table 1. The data are found to be generally consistent and reasonable. The displacements (strain) in each test mode are stable respectively with acceptable deviations. It is observed that the stress and strain are mutually correlated, for example the five T/C tests on living plantar roughly presents negative relation between force and strain, i.e., higher force is paired with smaller strain. This agrees with our common sense that if a subject is “hard” to deform, it costs larger force and less deformation. Given that the H_TC of various spots are significantly different, the small deviations on strains confirms the preciousness of the machine and test method. On the other hand, the H_TC of mimic foot model are relatively more consistent, that also can be expectable since the mimic model is more homogenous with uniform material and texture. And the higher moduli of mimic model imply the grade of SR employed here maybe slightly “stiffer” to mimic the plantar tissue, at least for this individual case. Furthermore, the SR brick sample presents even larger force, smaller strain and higher modulus in every category, which reflects the effects of size and shape, and it again imprints the necessity of sample standardization and calibration discussed in section 4.

Table 1. The results of tests on living heel and inorganic samples.

	Tensile/Compress Force (N)	Displacement (mm)	Analog T/C Modulus H_TC (MPa)	Longitudinal Shear Force (N)	Displacement (mm)	Analog Shear Modulus H_LS (MPa)	Transverse Shear Force (N)	Displacement (mm)	Analog shear modulus H_TS (MPa)	Torque (Nm)	Displacement (degree)	Analog Torsion modulus H_t (Nmm²)
H	16.1092	3.4894	0.1470	22.7591	3.7650	0.1591	17.7480	3.7191	0.1256	0.3671	27.2828	7792.8316
E	9.9179	3.6807	0.0858	24.0483	3.7574	0.1684	14.7859	3.7626	0.1034	0.4648	26.6395	10233.7153
M1	10.1403	3.6345	0.0889	20.1704	3.7600	0.1412	15.5846	3.7262	0.1101	0.3103	27.5882	6519.0184
M2	12.8173	3.5763	0.1141	18.3603	3.7700	0.1282	18.1256	3.6963	0.1290	0.3563	27.2923	7477.6902
M5	5.7805	3.7253	0.0494	15.7581	3.7647	0.1102	10.7590	3.8090	0.0743	0.4457	26.6985	9755.8493
mimic foot H	17.7531	3.1848	0.1775	24.2747	3.6560	0.1747	9.8051	3.7595	0.0686	0.5379	26.2163	12348.3490
mimic foot E	17.4398	3.1041	0.1789	29.2398	3.6457	0.2111	20.4914	3.6184	0.1490	0.4493	26.9436	9714.7592
mimic foot M1	15.2842	3.1077	0.1566	34.5190	3.6361	0.2498	21.7866	3.7111	0.1545	0.2312	27.9804	4857.7139
mimic foot M2	19.4164	3.0625	0.2019	30.6189	3.6434	0.2212	22.4072	3.6397	0.1620	0.7944	24.6478	18751.1222
mimic foot M5	17.7670	3.1079	0.1821	28.3611	3.6354	0.2053	20.6922	3.6236	0.1503	0.6130	25.6889	13882.1904
SR brick sample*	23.0096	3.0253	0.2422	40.3724	3.6145	0.2939	/	/	/	1.3636	21.1032	37023.3077

*The brick sample is homogeneous in horizontal thus the shear direction is regardless

Moreover, several interesting observations on the data can induce some intuitive conclusions. For the T/C test, the M2 and H spot have the higher modulus, whereas these two are considered to be most load-bearing spots on the plantar, therefore the fact that they have better material property accords well to our expectation. And the H spot is even higher than M2 while the heel has less bearing area than forefoot. In the two modes of shearing test, only spot E presents large difference in longitudinal and transverse, which obviously relates to its heterogeneity in geometry, and the longitudinal is much larger, whereas the foot arc bears shearing along this direction during daily walking, and shearing in the other direction is rare. Another impressive value the H_t on the M5, which is much larger than other spots. Torsion is a rarely mentioned stress in the study of foot and plantar mechanics, and there is none published report on this topic to the best of authors’ knowledge. However, it is also a common daily experience, that when we turn around during walking, we usually start exerting force from the outer part of the forefoot, that is the M5.

Though these intuitive observations are still far away from scientific hypothesis and facts, which relies on the establishment of a big dataset to make sound conclusions, and these results measured could also possibly be due to the individual features, rather than common properties of human plantar, further investigations based on a large number of participants tested are necessary to find general laws. Better still, the agreements of above findings to our common sense are good encouragements on this novel in-situ DMA method. Since this manuscript is mainly to demonstrate our newly-invented device and establish the methodology, we are not going to further analyze the data and their correlations to the foot health. Future work in depth will be reported based on a decent number of tests with a collection of sufficient data, and is in progress in our group.

This study is expected to establish a new standard method, which is inspired by the DMA in classical material science to obtain periodical strain-stress behavior to analyze the viscoelasticity of elastomer, especially the plantar soft tissue. The main novelty is to overcome the difficulty of in-situ characterization on the mechanical properties of biological soft tissues. via fixing soft tissues by vacuum suction cups to measure the living tissue, and obtain in-vivo mechanical properties of living plantar tissues. Three types of mechanism: tensile/compression, shear, and torsion are designed and four modes of tests are applied on five particular chosen spots on the living plantar. The results show good preciousness and consistence, and several interesting intuitive correlations are observed in the volunteer and mimic sample tests data, which well encourages the subsequent systematic researches in the future. This in-situ DMA methodology is expected to have important potential value in biomechanical theory, clinical diagnosis and footcare engineering application.

Additionally, this new technique is also expected to make critical contributions to the finite element analysis (FEA), which is a common tool in biomechanical analysis, but always being accused by the lack of the material parameters in reality [28], by providing the direct realistic material properties, and a golden standard to check the simulation. Hopefully more complex anisotropy finite element models of foot can be built with the foundation of the data measured by the device.

A set of “moduli” similar to the classical modulus are defined with measurable strain and stress. With incorporating the characteristic length as an internal part of the “apparent property” of subject, we found it is practical to setup a nominal original length, as 10mm in this work, to make parallel comparison among the test results. However, the possibility and necessity to determine an effective “equivalent length” L to characterize the “eigen property” of subject, especially for those of complex shape and size, remained to be a challenge. Furthermore, it is an intrigued question that if there exists firm relationship between the newly defined modulus and the classical modulus. These uncertainties are hoped to be answered in the future research on a large number of tests and collection of data on various living testees and inorganic samples, with the help of machine learning.

Author Contributions:

X.M. supervised and coordinated project; R.H. and J.Z. designed research; L.W., L.T. and R.H. performed main research; X.N. analyzed data; and R.H. and L.W. wrote the paper.

Acknowledgement

This work is financially supported by the National Key Research and Development Program China (2022YFC2009500), the Medical Engineering Fund of Fudan University (YG2021-005, YG2022-008), the Fudan-Yiwu Fund (FYX-23-102), and the TZI-ZJU Industrial Program (2022ZSS09, 2023CLG01, 2023CLG01PT). The authors sincerely appreciate Ms. Ren Huang for graphical artwork.

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Usain Bolt's world record for the 100-meter sprint is 9.58 seconds, taking approximately 41 steps, that is about four steps per second, i.e., two single plantar landings. Therefore, 2Hz can be considered the upper limit of human foot usage under full load conditions.

The authors declare no competing interests.

Supplementary materials not available with this version.

A Novel in-situ Dynamic Mechanical Analysis for Human Plantar Soft Tissue: The Device Design, Definition of Characteristics, Test Protocol, and Preliminary Results

Status:

Version 1

Abstract

Figures

1. Introduction

2. Device Design

3. Definition of Characteristics

4. Standard Sample and Calibration

5. Test Protocol

6. Preliminary Results and Discussion

7. Conclusion and Perspective

Declarations

Author Contributions:

Acknowledgement

References

Additional Declarations

Status:

Version 1