CONTROL OF THE BICEPS ACTIVITY WITH THE SIMPLE ULTRASOUND PROBE Timofey Krit, Shamil Asfandiyarov, Mariya Begicheva, and Valery Andreev Moscow State University, Faculty of Physics, Moscow, Russia email: [email protected] Yuly Kamalov The Russian National Research Center of Surgery named after B.V. Petrovsky e-mail: [email protected]

Since human muscles, particularly biceps, have an anisotropic structure associated with fibrous struc- ture, it is important to study the muscle taking into account its anisotropy. We constructed a simple ultrasonic shaker to control the activity of the biceps. The device performs non-invasive control of the biceps state from the surface. A certain frequency of the tissue displacement caused by the vibrat- ing indenter is chosen to excite shear waves inside the biceps. The displacement of the tissue then can be registered by means of the ultrasonic signal emitted from the probe that is firmly connected to the indenting surface. Both speed and frequency of the shear waves are smaller than the same properties of the ultrasound. The device is a rectangular ultrasonic probe attached to the front part of the movable vibrator plate. The vibrator with the help of the movable plate, leaning the front part of the bicep, excites shear waves in it. An ultrasound probe monitors the propagation of shear waves in the muscle in real time. Two-channel signal generator connected to the operating computer powers both the vi- brator and the ultrasonic probe. Registration of ultrasound pulses received by the piezoelectric ele- ment is performed using an oscilloscope also connected to a computer. Thus, power signals are formed and evaluation is implemented in specially developed software. The probe has a form of an elongated rectangle which makes it possible to register the shear waves excited in two polarizations: along and perpendicular to the muscle fibers and measure the shear elasticity of the muscle taking into account its anisotropy. Measurements of biceps shear elasticity are carried out at various loads: static and variable. The processes of biceps relaxation are investigated. This will help to develop a method that will determine the effect of muscle load on its growth and damage. Keywords: biceps, elasticity, shear wave, ultrasonic imaging

1. Introduction As the name of the biceps brachii muscle implies, it has two heads and is located on the arm. The muscle is commonly referred to as simply the biceps. Both heads attach on the scapula. The long head arises from the supraglenoid tubercle and runs over the head of the humerus and out of the joint capsule to descend through the intertubercular (bicipital) groove to join with the short head that has come from the coracoid process. Because tendons of both heads cross the shoulder joint anteriorly, the biceps assist in shoulder flexion. However, its main function is at the elbow [1]. Functionality of the biceps is ex- tremely important, since it determines the ability to flex the arm at the elbow joint, which, of course, is

1 ICSV26, Montreal, 7-11 July 2019 important in the day-to-day functioning of the body, and when applying special loads. Advances in the experimental study of viscoelastic properties of muscles [2] in recent years are associated with the emer- gence of methods of elastography based on the use of shear waves [3]. Ultrasonic elastography is a new technology with many potential applications. It is highly effective in diagnostics due to its ability to recognize and qualify various pathologies of tissues or tissue-mimicking materials [4]. In this paper, the elastography method was used to evaluate the normal physiological pa- rameters of the biceps brachii for further practical application of elastography in clinical studies. Modern medical ultrasound is performed mainly using the echo-pulse approach and the brightness mode of display (B-mode) [5]. The basic principles of visualization in B-mode today are almost the same as several decades ago. The approach is to send small ultrasonic pulses from an ultrasonic probe into the body. Since ultrasonic waves penetrate into the tissues of the body with different acoustic impedances, some of them are reflected back to the probe (echoes), and some continue to penetrate deeper. Echoes resulting from the reflection of a series of consecutive pulses are processed and combined to generate an image. Thus, the ultrasonic probe works both as a transducer (generating sound waves), and as a receiver (recording sound waves). The ultrasonic pulse is actually quite short, but since it passes along a straight path, it is often called an ultrasonic beam. The direction of propagation of ultrasound along the line of the beam is called the axial direction, and the direction in the image plane perpendicular to the axial direction is called the lateral direction. Usually only a small part of the ultrasonic pulse is returned as a reflected echo after reaching the surface of the body tissue, and the rest of the pulse continues to propa- gate along the beam line to a greater depth in the tissue. Measurements in the B-mode give only qualita- tive ideas about the state of the tissue, and the result of these measurements is not always accurate. There are more accurate methods of non-invasive diagnosis, based on the fact that the presence of heterogene- ities in the tissues and various pathological changes has a strong effect on their shear elasticity. Shear waves cannot penetrate at all depths necessary for non-invasive medical diagnostics of biolog- ical tissues. Thus, longitudinal ultrasonic waves are used for excitation and detection of shear waves in the investigated region to which the shear waves cannot propagate from the surface. Acoustic pulse-wave elastography was particularly popular among the methods based on the excitation of the shear waves with the ultrasound. In this paper, the acoustical radiation force impulse (ARFI) method is used, which was implemented in clinical devices since early 2000s [6]. Quantitative estimation of shear wave velocity is realized on the basis of well-known algorithm of excitation and registration of shear wave in tissue [7]. ARFI imaging technology consists in mechanical excitation of tissue using short acoustic impulses (push- ing pulses) in the region of interest chosen by the researcher [8]. The pushing pulses excite shear waves that propagate in the region of interest, perpendicular to the acoustic pushing pulse. Shear waves cause localized micron displacements of the tissue. The pushing pulse is several hundred cycles long and differs in voltage from the B-mode pulse consisting of a short number of cycles. At the same time, imaging waves are generated. These waves are less intensive than the push impulse (1:100). Wave detection is used to determine the position of the shear wave in the tissue at each time point. The moment of interac- tion between the shear waves and the imaging waves indicates the period of time elapsed between the generation of shear waves and their complete passage through the region of interest. Writing the shear wave front in several places and comparing these measurements with the current time, we can determine the value of the shear wave velocity. The harder the area inside the tissue, the greater the velocity of the shear wave that propagates through this area. Currently, ARFI technology is successfully used for non-invasive medical diagnostics of liver, kidney and other viscera [9]. The tissues studied with the help of this technology usually possess isotropy of the shear modulus. As the result, the shear wave propagating in any direction has the same velocity, i.e. the wave velocity measured in such tissues has the same value in any direction. The values of the velocities differ only in regions of shear modulus inhomogeneity, which correspond to the areas of location of pathological changes in tissues. ARFI technology is implemented in several models of ultrasonic scan- ners capable of generating short-range acoustic radiation forces. The action of such forces on the tissue

2 ICSV26, Montreal, 7-11 July 2019 ICSV26, Montreal, 7-11 July 2019 causes the localized small (1-10 μm) displacements inside the tissue. The response of the tissue to the acting radiation force is registered with conventional pulses that form the image in the B mode. Two- dimensional images of tissue displacement are created by repeating this process along several lines of the image. As a result of cross-correlation processing of images obtained in the B-mode, the tissue dis- placement is monitored at different times. Thus, the shear wave velocity in the tissue is determined.

2. Wave propagation through the anisotropic medium In the ARFI method shear waves are generated in a fixed region of 1 x 0.5 cm in size, called ROI (region of interest). This area can be observed on a grey-scale image of the tissue in B-mode. Short focused acoustic pulses, which duration is 3-5 ms and a repetition frequency is 5-10 kHz, propagate along the scanning beam (Fig. 1) and cause shear forces in the tissue (exactly in ROI), the magnitude of which depends on how the tissue weakens impulse (of course, the main contribution is absorption) and pulse intensity. In turn, shear forces cause shear waves that propagate perpendicular to the scanning beam, far from the original excitation region. Therefore, if the tissue density does not change, softer tissues exposed to a given radiation force move farther than stiffer tissues, and, having a lower shear modulus, more slowly reach their peak displacement (on the order of tens microns) and return to their original state more slowly in comparison with more rigid tissues. Together with the focused pulses, a sequence of detection pulses is continuously emitted parallel to the scanning beam in order to track the propagation of the shear wave. The detecting pulses intercept the shear wave front at several predefined locations and, by fixing the time of arrival of the signal from these points, one can obtain the time at which the tissue reaches its peak displacement and the relaxation time. From these data, shear wave propagation velocity is quantified, and then, the stiffness of the tissue. Such information can be displayed by ARFI systems or as a map reflecting spatial differences in the stiffness of the tissue, or, as most often, quantitatively: the elasticity of the tissue is then represented by the shear wave speed (Shear Wave Velocity or SWV), usually measured in meters per second. The dynamics of anisotropic media, including elastic waves in such media, is described by a system of equations

22 uuim 2 = iklm (1) t  xkj  x

In this equation, U i stands for the displacement vector of an element of a continuous elastic medium,

iklm is the 4th-rank tensor of the elastic moduli. Generally, the number of independent elastic moduli is 21. For structures with hexagonal symmetry, the number of independent elastic moduli is 5 (A, B, C, D, F) [10]:

xxxx== yyyy A , xyxy = B , xxyy =−AB2 , xxzz== yyzz C , xzxz== yzyz D , zzzz = F . The tensor components are written in the Cartesian coordinate system. The z axis is directed along the muscle fiber (Fig. 1). The muscle mechanical properties are assumed to be invariant under rotation about this axis [11].

y x Fiber direction z

Figure 1: The direction of the axes according to the fiber direction in the model.

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We search for a solution of the system of differential equations (1), in the form of the monochromatic waves

ui= u i0 exp() − i t + ikl x l (2) with a constant amplitude u i0 . The substitution of the form (2) in (1) results in

2 ui=  iklm k k k l u m .

Considering uui=  im m we can transform the previous expression into the system of equations

2 ( im−=  iklmk k k l) u m 0 (3) of three variables u x , u y , u z . System (3) has non-zero solutions only when its determinant turns to zero:

2 det  im−=  iklmkk k l 0 (4) This equation determines the dependence of the frequency of the wave on the wave vector; it is called the dispersion relation. The solutions of the dispersion relation (4) are three frequency- independent wave velocities. We choose the coordinate system so that the wave vector k belongs to the xz plane. Thus, kkx = sin , k y = 0 , kkz = cos , where  is the angle between the vector k and axis z. Then the solu- tions of equation (4) are as follows 2 2 2 2 1 =+k( Bsin D cos  ) , 1 1 2 2 2 2 2 2 2 2 2 2 2 . 2,3 = k Asin+ F cos  + D (()() A − Dsin  + F − D cos ) + 4()CD + sin cos  2   In this work, when measurements were conducted, the shear wave polarization was not taken into account, since it was believed that there are only two directions of propagation:  = 0 and  =90 . When the wave vector is directed along the z axis (the wave propagates along the muscle fibers,  = 0), one of the equation roots corresponds to the longitudinal wave, the other two roots are the same and refer to transverse waves: F D c2 = , cc22==. l  tt12 In case the wave vector is directed along the x axis (the wave propagates across the muscle fibers,  =90 ), then all velocities are different: A B D c2 = , c2 = , c2 = . l  t1  t2  That is the difference between the anisotropic medium and the isotropic one. The only longitudinal wave and two shear waves exist in an isotropic medium, and the velocities of the shear waves would coincide. In the general case, for an arbitrary inclination of the wave vector to the z axis, it is not possible to separate the longitudinal and transverse waves. However, the anisotropic properties of the medium change radically when the propagation velocities of longitudinal waves significantly exceed the shear wave velocities. Such media, in which shear elastic

4 ICSV26, Montreal, 7-11 July 2019 ICSV26, Montreal, 7-11 July 2019 moduli are much smaller than those associated with the compressibility of the material, are called soft solids. An example of such a medium is muscle tissue. It is shown in [12]that in the "soft solids" that the modules A, C, F have to be of the same order as 2 2 cl , and the other two modules B, D have to be much smaller and to be of the same order as ct . Since the shear wave velocity in the muscle is 2 orders of magnitude smaller than the velocity of the longitu- dinal wave, this condition is obviously satisfied. Then the velocities will be expressed as follows: A BD D c2 = , c2 =+sin2  cos2 , c2 = . l  t1  t2  This means three waves can propagate in the muscle tissues: one longitudinal and two transverse. The speed of the first transverse wave is independent of the direction (this is a wave propagating along the fibers), and the speed of the second transverse wave depends on the direction (this is a wave propagating across the muscle fibers).

3. Quantification of the sonoelastograms The study was conducted in the laboratory of ultrasound diagnostics of the Russian National Research Center of Surgery named after B.V. Petrovsky by the experienced doctor with ultrasound diagnostic equipment. The volunteers were chosen among the employees and students of the Faculty of Physics of Moscow State University. All the volunteers were healthy without muscle injuries. The ultrasound diag- nostic system of the expert level Siemens ACUSON S2000 was used with a standard diagnostic probe. The strained condition of the biceps arm muscle was achieved by applying certain loads. The method for creating the load was the following. We took special weight plates commonly used for barbells or dumbbells by the lifters. Four plates each of 1 kg and one plate of 5 kg were used. The combination of certain plates, made it possible to form loads of 1, 2, 3, 4 and 5 kg. Each load created a strained state in the biceps muscle of the volunteer. Before the measurements, each volunteer was at rest for 10-15 minutes, so that no physical activity, even potential, could affect the results. The initial position of the volunteer was the following: sitting on the couch opposite the doctor, the arm was bent at the elbow joint and had a rigid support under the elbow joint. The angle between the bones of the shoulder and forearm was 90°. In this case, both forearm and shoulder were located in a plane perpendicular to the support plane and both at an angle of 45° to the support. The volunteer’s wrist was parallel to the support and the palm was up. Further, the biceps were loaded with the weight plates. The plates were stacked on the palm forming a pile [13]. The experiment that we carried out in order to measure the average value of shear wave velocity in the biceps for various configurations was recently reported [14]. The method of the shear wave excitation was proposed two decades ago by professor Rudenko from Moscow University. The original algorithm assumes that the shear wave is excited by the focused ultrasound beam. The displacement of the particles in the medium is registered by several imaging pulses. The shear modulus in an isotropic media is the same in all direc- tions. The value of the shear modulus can be determined from the shear wave velocity [15]. We con- firmed in the experiment that the biceps anisotropy could be measured as the shear wave velocities are measured for different directions of wave propagation, as it was previously proposed [16]. The ARFI mode, available in the ACUSON S2000 system, is implemented as a Virtual Touch ™ function. This function allows obtaining sonoelastograms, similar to those that can be obtained with conventional sonoelastography. First of all, this mode is used to characterize and visualize damage in tissues. The algorithm that is realized for sonoelastograms in ACUSON S2000 let the investigator obtain qualitive distribution of the shear wave velocity only. It means that the investigator can determine more or less rigid regions only, but can not obtain the exact value of the wave velocity in a certain region. In order to obtain the exact value, the investigator has to use quantitative algorithm that is also available in

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ACUSON 2000 and that we have discussed in our previous work [14]. In this work we created the algo- rithm for evaluation of the sonoelastogram in order to estimate the values of the wave velocities on it. We applied the standard greyscale evaluation tool to calculate the matrix from the image. Then the matrix was multiplied by a shear modulus that was calculated from the value obtained from the quantitative algorithm. We assumed that this value determined the shear modulus in the center of the rectangle. The sonoelastograms are presented on Fig. 2. Both were measured by positioning the probe along the fibers, since we have shown [14] that the change in the elasticity of the biceps is well pronounced only for the measurements when the probe position is longitudinal. The numbers stand for shear moduli in kPa.

a b Figure 2: Measured sonoelastograms (a) under a load of 1 kg; (b) 1 minute after removal of this load. The num- bers stand for shear moduli in kPa. Volunteer’s profile: man, 22 y.o., BMI 25.06. The results we obtained in the sonoelastograms quantification together with the algorithm of the wave velocity estimation [14] would be the ground for the handheld equipment we create to diagnose the bi- ceps.

4. A handheld equipment for biceps activity control

4.1 Overview of the algorithm The essence of the method is the excitation of the shear wave in the tissue and registration of displace- ments caused by its propagation inside the tissue. The displacements would be registered applying ultra- sonic imaging. There are two commonly used methods of shear stress visualisation in elastography: cor- relation processing of echographic images and Doppler method of visualization of shear strains. We use Doppler ultrasound to estimate tissue deformations, since its implementation is easier and less expensive [17]. The basic theoretical expressions for the method of biological tissue elastography based on Doppler visualization of the forced harmonic vibrations field in the tissue are given in [18]. In particular, the vibrational velocity at studied tissue point can be restored. By the restored time dependences of the vi- brational velocities at two points located nearby, it is possible to determine the shear wave velocity in the medium and calculate the shear modulus in the area between the points under study.

4.2 The equipment for biceps activity control The description of the ultrasound Doppler method [17] was used as a reference point for the creation of the device for investigation of the shear elasticity in biceps. We constructed the experimental setup that operates according to the algorithm. The vibrator excites a low-frequency shear wave (about 100 Hz) inside the biceps. Imaging ultrasonic pulses at a fundamental frequency of 2.5 MHz with a duration of several wavelengths are excited with the ultrasonic probe. The probe is firmly mounted on front sur- face of the moving vibrator plate, which has the shape of an elongated rectangle, and receives reflected pulses.

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The recording of the pulse signal reflected from the propagating shear wave lasts for several seconds. The received signal is processed in the computer and the shear modulus in the studied area is estimated. It is possible to measure shear elasticity along and across the muscle fibers by change of the orientation of the vibrating plate with respect to the direction of the muscle fibers. The block diagram of the constructed experimental setup is shown on Fig. 3. The waveform generator powers the ultrasonic probe which forms the ultrasound signal. The probe is mounted on the vibrator which oscillates with low frequency.

Figure 3: The block diagram of the constructed experimental setup. A digital oscilloscope records the signal emitted from the probe and the reflected peaks acquired with the probe. A computer (PC) is used to operate the waveform generator and to process the signals collected from the oscilloscope.

5. Conclusion We constructed a simple model of the diagnostic ultrasonic shaker. The shaker will be tested with the reference to the results obtained from the experiments in the clinic. The device is able to perform non- invasive control of the biceps state from the surface. It is a handheld equipment based on the acoustoe- lastic effect [19] that can be simply used by the consumer. The significance of the suggested algorithm from the scientific point of view is that it can be useful for the measurements that are necessary for creation an appropriate viscoelastic model of the biceps [4]. The most likely application of the algorithm is development of a method that will determine the effect of muscle load on its growth and damage.

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