# On-Desk Model-Based Study for Evaluating the Effect of Squeezing the Arteries in the Forearm on the Bioimpedance and Pressure of Blood

Authors: Margus Metshein; Paul Annus; Raul Land; Marek Rist; Mart Min; Kristina Lotamõis; Olev Märtens
Journal: Journal of Sensors
 (2023)

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## Abstract

Background. Today, central aortic pressure (CAP) is measured through the invasive procedure of angiography. The only feasible alternative is applanation tonometry, requiring experienced staff to perform reliable measurements. The method of measuring the electrical bioimpedance (EBI) from the wrist gives promising results in estimating the CAP. However, the origin of the EBI data, its quality, and approaches to acquiring the signal are still vague. This study is aimed at determining the dependency of EBI of blood on the diameter, branching, and hindering the blood flow by squeezing the vessel. Methods. An on-desk hydraulic and mechanical pipe system that imitates the arterial tree in the forearm with the modulated flow of saline solution to imitate the pulsating blood was constructed. The setup was verified in the simulation model. The flexible and rigid pipes were squeezed at selected locations of radial and ulnar arteries, and the superficial palmar arc and the pressure with impedance were measured. Results. The multifaceted effect of squeezing the selected locations of arteries in the forearm on the measured EBI and pressure was verified. The effect of arterial stiffening was verified, revealing a very strong inverse correlation of the time-varying impedance (ΔZt) of rigid pipe compared to the measured data of the wrist. Conclusion. To gain the highest magnitude of ΔZt, our research suggests applying pressure on the radial artery and measuring the EBI of the ulnar artery. Our results propose physiology-based suggestions to increase the sensitivity of measured EBI of the pulse wave, constituting a base for designing novel wearable monitoring devices and algorithms for CAP estimation.


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## Body

## 1. Introduction

Cardiovascular diseases (CVDs) are mainly the result of the slow development of circulatory dysfunctions caused by manifold factors. The causes of the development of circulatory dysfunctions causing CVDs can be genetics, age, other chronic diseases, infections, lifestyle, etc. The risks for obesity, smoking, alcohol misuse, sedentary lifestyle, etc., are individual and, in many cases, require smart wearable equipment for unnoticeably monitoring cardiac hemodynamic parameters. To follow, make decisions, and notify the user, intelligent sensors and clever algorithms, capable of assessing the condition of the heart and arterial tree through measuring and processing the electrical properties of pulsating flow of blood, are needed. The mechanical models of the cardiovascular system are appreciated to gain the described knowledge.The cardiovascular system is a complex entity whose exact imitation by on-desk hydraulic and mechanical means is a sophisticated task. To develop instrumentation for monitoring parameters of cardiac hemodynamics, the knowledge of the functioning of arterial tree (gained through electrical and mechanical characterization) is required. The understanding can be produced in two ways: by characterizing the human body (1) or by imitation models that mimic the human body and its compartments (virtual or physical) (2). For instance, we can imitate the blood flow by constructing artificial copies of the arterial system.For characterizing the cardiovascular system, several methods are used, like invasive procedures (e.g., direct blood pressure measurements in the aorta), noninvasive procedures (e.g., peripheral blood pressure measurements), and indirect measurements (e.g., the calculation of arterial pressure wave velocity (PWV) from known distance from the aorta to the radial artery). In practice, pulse and its parameters are detected, among others, also with optical (photoplethysmography [1] and laser Doppler velocimetry [2]), mechanical (ballistocardiography [3], seismocardiography [4], etc.), and electrical methods (electrocardiography, impedance spectroscopy, magnetic induction monitoring [5], etc.).One possibility to evaluate the properties of the human body is the measurement of electrical bioimpedance (EBI). The pulsating volume of arterial blood in the radial and ulnar artery that originates from the heart carries vital information about the circulatory system which is expected to be available in the measured waveform of EBI [6]. EBI is measured by attaching electrodes on the skin surface, applying excitation in the form of low amplitude alternative voltage (or current), and measuring the response.The noninvasively measured value of EBI is composed of the sum of conductivities and resistivities of highly different values caused by the complex content of the forearm (and the human body). If the artery and thus the pulsating volume of blood remain in close vicinity of the electrodes, the contribution of layers of skin, body fat, and blood vessel wall can be expected. Moreover, the proximity of muscles, bones, and tendons, i.e., the matter of different conductivity, influences the measured value of EBI. However, we can expect such an effect to be low as the main contribution comes from the arterial blood.The conductivity of muscular tissue (0.362 S/m at 100 kHz) and tendons (0.389 S/m at 100 kHz) is only twice as lower than that of blood (0.703 S/m at 100 kHz) [7], while the conductivity of wet skin (0.066 S/m at 100 kHz) is ten times worse, and the conductivity of bone (0.021 S/m at 100 kHz) is 33 times worse than that of blood [7].Due to that, the source of the signal is debatable, raising questions about the measured value of the measured impedance (Z). The literature shows simplistically that the pulsating blood in the artery causes the modulation of the measured EBI signal (i.e., the time-varying impedance (ΔZt). However, based on the considerations concerning the volumes of matter of different conductivity in the forearm and calculations presented in [8], the ΔZt cannot purely originate from the pulsating volume of blood in arteries. Most likely, it is a complex phenomenon, mainly originating from the compression of muscular tissue (which contains blood), caused by the pulsating volume of blood in the artery.With the goal of simplicity, the current paper relies on an approach that theZ will emerge from invariable impedance (Zinvar) and ΔZt:
(1)Z=Zinvar+ΔZt.The EBI waveform of the pulsating volume of blood in the radial artery evolves when the pulse wave arrives, increasing and decreasing rhythmically the artery diameter (and the value ofΔZt) (visual representation is available in Figure 1)). A similar effect is expected from the arrival of the pressure wave, causing the time-varying pressure (ΔPt) to change.Figure 1
Principle of determining the time varying impedanceΔZt in the EBI waveform.This research was performed in the frames of developing transfer function (and respective means) for estimating the central aortic pressure (CAP) of blood by measuring the emergingΔZt in the radial artery [9]. In our daily research, knowledge is gained from analyzing the pulse wave signals at the distal radial artery projection area with concurrently measured pressure wave signals during coronary angiography [10]. Today, applanation tonometry is the primary noninvasive method for estimating the CAP [11] instead of the invasive angiography procedure via radial or brachial cannula. Applanation tonometry requires experienced staff to perform reliable measurements, constituting a notable shortfall.Another closely related problem that potentially benefits from this research is lower extremity arterial disease (and its subtypes like claudication and chronic limb-threatening ischemia (CLTI)). In essence, CLTI denotes the blockage of peripheral arteries that results firstly as poor circulation and rest pain and then unhealed wounds, etc., and may end with the need for amputation when untreated. Today, the emphasis is on disease treatment while it should be on early detection. However, arterial pressure monitoring is serving as a solution for preventing the further course of the disease, and the potential solution may be in the measurement of EBI.Several uncertainties arise during the noninvasive detection of pulse waves when using electrical methods, which may ruin the measured data. These are unsteady contact between the electrodes and skin surface, the layers of skin, etc.ΔZt is an important variable, especially in evaluating cardiac hemodynamic parameters with noninvasive means. Due to that, ΔZt values are proportionally low and prone to motion artifact-induced interferences. To construct the waveform of CAP, the pulse wave signal of the highest possible ΔZt is desired to make the transfer function calculation less complex and more exact. The signal is of the highest possible resolution and with a distinguishable curve as the estimation is based on defined points on the waveform [12].The magnification ofΔZt has been reported to be conditionally feasible by the application of external pressure on the radial artery [13]. Yet, the relationship between ΔZt and ΔPt is not so straightforward [14]—mainly due to the complex structure and behavior of the arterial system. Pulse waves can be determined also by measuring the impedance of blood flow in the ulnar artery as in [15]. However, the problem with the ulnar artery is its deeper location in the composition of the forearm, hindering the application of controlled pressure and gained compression. Specifically, the ulnar artery has more interindividual variations and in most cases does not reach the skin layer. Also, it does not lean on a bone (radius) like the radial artery in the forearm.Also, the utilization of focused impedance measurement technique [16] and customized electrode placement strategies [17] has been reported to have the potential for higher ΔZt.


### 1.1. The Aim, Objectives, and Research Questions

The objective of the performed research (and the current paper) was to determine the dependency of the EBI of blood on the diameter of the blood vessel, its bifurcation, and hindering the flow of blood by squeezing the artery. This includes two modalities in the form of the developed system: either flexible (representing normal artery) or a rigid (representing arterial stiffness) tube.The hypothesis for the current work was that by squeezing the artery (i.e., imitating a blockage), the inherent pressure, flow velocity, and hence the measured impedance vary and are manipulable.The flow of pulsating saline solution can be characterized by evaluating the emergingΔZt and ΔPt. The rigid and flexible pipes are squeezed in chosen locations, and the effect of stiffness on the determined ΔZt and ΔPt is evaluated, constituting a novel approach. The data is compared to the previously acquired values of ΔZt and ΔPt [14], measured on the forearm of a single volunteer. The comparison enables us to find the dependency in the dynamics of the flow of saline solution in pipes and blood in the radial artery.The experimentation on the prepared on-desk pipe system was expected to answer the following questions, reflecting the similar properties to arteries in the forearm, which are listed below.(1)
Does the externally applied pressure on the radial artery affectΔZt of blood?(2)
Does the externally applied pressure on the radial artery affectΔPt of blood?(3)
Does there exist a correlation betweenΔZt and ΔPt of blood in radial and ulnar arteries and the superficial palmar arc?We can presume that understanding the principles of measured impedance waveform inception and its possible relation to the development of pressure in the radial artery will provide input for developing tailor-made algorithms and capable wearable monitoring devices.


## 1.1. The Aim, Objectives, and Research Questions

The objective of the performed research (and the current paper) was to determine the dependency of the EBI of blood on the diameter of the blood vessel, its bifurcation, and hindering the flow of blood by squeezing the artery. This includes two modalities in the form of the developed system: either flexible (representing normal artery) or a rigid (representing arterial stiffness) tube.The hypothesis for the current work was that by squeezing the artery (i.e., imitating a blockage), the inherent pressure, flow velocity, and hence the measured impedance vary and are manipulable.The flow of pulsating saline solution can be characterized by evaluating the emergingΔZt and ΔPt. The rigid and flexible pipes are squeezed in chosen locations, and the effect of stiffness on the determined ΔZt and ΔPt is evaluated, constituting a novel approach. The data is compared to the previously acquired values of ΔZt and ΔPt [14], measured on the forearm of a single volunteer. The comparison enables us to find the dependency in the dynamics of the flow of saline solution in pipes and blood in the radial artery.The experimentation on the prepared on-desk pipe system was expected to answer the following questions, reflecting the similar properties to arteries in the forearm, which are listed below.(1)
Does the externally applied pressure on the radial artery affectΔZt of blood?(2)
Does the externally applied pressure on the radial artery affectΔPt of blood?(3)
Does there exist a correlation betweenΔZt and ΔPt of blood in radial and ulnar arteries and the superficial palmar arc?We can presume that understanding the principles of measured impedance waveform inception and its possible relation to the development of pressure in the radial artery will provide input for developing tailor-made algorithms and capable wearable monitoring devices.


## 2. Research Background: Blood Flow Mechanics

The emerging difference with pressure waves must be considered when assessing the blood flow properties in arteries. The blood flow constitutes a “wave” with two distinguishable peaks and decreasing amplitude from the left ventricle to the arterioles. The pressure wave, in turn, also with two peaks—the first one from the peak of blood flow and the second one from the reflection of blood flow at peripheral arteries—has an increasing amplitude [18].The hydraulic and mechanical pipe systems for imitating the principles of the cardiovascular system have been developed and presented in the scientific literature with different goals. However, these systems have mainly been used to circulate the blood of pigs [19], bovines [20], or humans [21] and typically not the isotonic saline solution as an imitation of blood. Secondly, these systems typically study the electrical properties of blood in correlation with its mechanical properties (like velocity [19, 20]) and do not imitate the arteries in the forearm, where the ulnar and radial arteries form a parallel pathway.From fluid mechanics, it is known that the flow velocity in a chosen tube depends on pressure and flow resistance. The flow resistance (R) is dependent on the length (L) and the radius (r) of the tube together with the fluid’s viscosity (η) and is calculated according to Poiseuille’s equation:
(2)R=8ηLπr4.As can be seen, the tube dimensions (especially ther) possess a more important role in applying Poiseuille’s law in determining vascular resistance than the viscosity of blood [22]. Moreover, the arteries are not homogeneous in geometry—their r can change due to physiology [23] and different pathologies. And more importantly, they are not straight, i.e., producing secondary flows, which are the reason for irregularities in shear rate—an important component in the viscosity formation [24]. Fluid mechanics is dominating over the properties of the fluid in the cases of both straight [25] and curved tubes [26].The electrical properties of blood depend mainly on the resistivities of its compartments: erythrocytes and plasma [26]. Also, the physical properties are reported to affect the blood resistivity—for example, with the increase of velocity, the impedance always decreases [21].The blood viscosity changes, depending on the erythrocyte’s rheological properties—reflecting the overall hemodynamic condition [27]. While the maximum arterial blood flow velocity in the aorta is 1 m/s (and decreasing in the following pathway) [28], the increase of impedance from very low (approx. 0.03 m/s) to normal velocities is low, about 1.1% [21]. Interestingly, the impedance changes of blood due to the increase in velocity are claimed to be related to the orientation and shape of erythrocytes [29]; i.e., blood is anisotropic [30].In the current research, we used isotonic saline solution to imitate the arterial blood flow in radial and ulnar arteries for several reasons. The osmotic pressure of the saline solution is like blood plasma as historically been extensively used in diluting the blood (1) [31].The saline solution has highly similar conductive properties to the blood (2). The blood content differs from saline solution in the absence of cellular compartments as the blood is composed of blood cells, mainly erythrocytes, and plasma. However, this can be claimed to have a negligible effect as in current research, as theΔZt is calculated based on the measured signals of EBI and eventually compared based on the sensitivity (RΔZt). In the low-frequency range up to 100 kHz (which is the classical frequency for measurements of EBI), the cell membranes behave more like dielectric material and are therefore of weak complex conductivity (i.e., representing a barrier to charged particles). At higher frequencies, the current passes the cell membrane at different levels; however, the effect on the total measured impedance (modulus, phase, etc.) is negligible.A classical model of arterial three is a single pipe, which is open at one end (to imitate the pulsatile blood from the left ventricle) and closed from the other (to imitate the arterioles where the flow path becomes capillary and becomes venous) [32]. In literature, the vessels are typically imitated by rigid pipes to focus purely on the properties of blood [19, 20]. However, anatomically, the wall of the blood vessels is of varying stiffness (depending on age, blood flow velocity [28], pressure in the circulatory system [33], etc.), and the diameter of the artery is assumably expanding due to the arriving pulse waves. Moreover, we expect the effect of the arterial wall flexibility on ΔZt and ΔPt.The developed physical model depicted the ideal circumstances, where the squeezing effects on the selected arteries are solely mechanical and free of physiological reactions (mainly spasmogenic). The modeling of the presence of muscular tissue, skin, bones, etc., was not part of the current work.However, the layers between the artery and the sensor influence the noninvasive measurements. In the case of pressure measurements, the different conductive properties of the layers between the sensor and object of interest (artery) probably dampen the measured signal (but still deliver the change in its value). This problem is a challenge in applanation tonometry, thoroughly described in [34].The model was focused on imitating the flow of saline solution directly and excluding all the matter that is an issue in noninvasive EBI measurements. As described before, the effect of pulsating volume of saline solution dominates in the determined value ofΔZt. However, a certain (and probably time variable) transfer function applies.


## 3. Devices and Properties

A custom-made step motor-based programmable pulsatile pump generated a pulsating flow of saline solution. The pump was programmed to modulate the flow of saline solution to imitate the pulsating blood from the heart.The impedance spectroscope HF2IS along with the transimpedance amplifier HF2TA of Zurich Instruments AG (Zurich, Switzerland) was utilized to measure the impedance and gather the signal from the pressure sensor. This device is suitable for fulfilling the posed research goals by providing an option of measuring the impedance simultaneously at four excitation frequencies up to 50 MHz in 14-bit resolution. Also, it enables the gathering of signals from two auxiliary connected analog and two digital devices [35].The pressure was monitored by a custom-made sensor (based on manifold absolute pressure sensor of type MPX4250AP of NXP Semiconductors (Austin, TX, USA)), connected to the pipe system. The output of the pressure sensor was saved by the impedance spectroscope through its auxiliary input and shown in voltages (indirectly expressing the pressure).Inherent pressure in the mechanical pipe system was modified by using on-desk clamps (Figure2). Specifically, the distance between the plates of the clamp was decreased and the level of compression increased to reduce the inner diameter of the pipe by enlarging the deformation level (and inherent pressure in the system). The principal drawing of the developed mechanical pulsating system is visible in Figure 3.Figure 2
On-desk clamps for increasing inherent pressure in the pulsating system by compressing the pipe in chosen locations.Figure 3
Principle drawing of the developed mechanical system whose objective is to modulate the saline solution in pipes for imitating the flow of pulsating blood.


## 4. Methods and Measurement Setup

In this research, we implemented the parallel branching of pipes with the option of squeezing both branches (and the outflow) separately (Figures2 and 3). The pipe system was implemented to pump the isotonic saline solution at room temperature through the pipes that imitate the brachial artery, dividing into ulnar and radial arteries and joining again in the superficial palmar arc. We expected that the saline solution passes through both parallel pipes equally as the direction of the flow was towards the container on the floor.We performed the measuring experiments in the cases of two types of pipes (with different physical material properties):(i)
Rigid (nitrile-butadiene rubbers/polyvinyl chloride (NBR/PVC)) (Figure4(a))(ii)
Flexible (PVC) (Figure4(b))Figure 4
Dimensions of rigid (a) and flexible (b) pipes that were used to imitate the arteries in a composed mechanical pulsating system.The rigid NBR/PVC type of pipe was significantly stiffer than the PVC pipe but demonstrated the ability to tolerate the deformation and restored its shape after the clamp removal. The rigid pipe imitated the effect of arterial stiffening.Altogether, seven deformation levels were defined and applied by placing the pipe between the plates of the clamp and reducing the distance with the steps of 0.5 mm. At the deformation level 0, no external pressure was applied. At the 6th deformation level, the pipe passed only the minimum amount of saline solution (i.e., the tube was not completely closed).As the outer diameters of the utilized pipes differ (Figure4), the distances between the plates differ in both cases at a specific level, however providing expectedly comparable deformation onto the pipe (Table 1).Table 1
Unification of the levels of deformation for flexible and rigid pipes.
Def. levelDistance between the plates—flexible pipe (mm)Distance between the plates—flexible pipe (mm)06815.57.525734.56.544653.55.5635The lengths of pipes that imitate brachial, radial, and ulnar arteries and superficial palmar arch can be seen in Figure5.Figure 5
Lengths of pipes and distances between the components in composed mechanical pulsating system.Stainless steel needles (with a length of 20 mm and a diameter of 1 mm) were used as electrodes and pushed through the pipes at equal locations with a gap of 10 mm. The needles were positioned to pervade the pipe through the center to gain maximum contact with the saline solution. In the cases of both types of pipes, the electrodes were always at the branch that imitates the radial artery (Figures3 and 4). The electrodes were connected to an impedance spectroscope by using crocodile clips.The application of external pressure on the ulnar artery, which does not reach the skin layer, is not executable in practice. The technique of application tonometry [10], where pressure is applied on the radial and never on the ulnar artery, confirms this fact. So, in the composed setup of the mechanical system, the electrodes were placed, and impedance was measured only at the radial branch of the pipe. The pressure was applied to the following locations at the composed pipe system (Figures 2, 3, and 5):
(i)
Joint of radial and ulnar branches (representing small arteries in the palm and fingers) (CM1)(ii)
Radial branch (CM2)(iii)
Ulnar branch (CM3)The saline solution, flowing in the pipes, was prepared by dissolving 0.9 g of NaCl in 1 dL of tap water at room temperature. The idea was not to imitate the exact conductivity of human blood as it is a matter of change from individual to individual and depends on several factors (like the size and distribution of erythrocytes [29]), but the close range. The exact conductivity is expected not to influence the dependency between ΔZt and ΔPt and the goals of the current study.We applied a four-electrode configuration which was applied to measure the impedance at the excitation signal of 100 kHz frequency and 500 mV amplitude. We used a single excitation frequency, as the experimentation showed no additional informative outcome in the case of measurements at other defined frequencies for such applications (500 kHz and 1 MHz) [14]. Moreover, 100 kHz is a classical frequency range for EBI measurements of the human body [36].For all the measurement series, we set the pumping rate to 45 beats per minute with a possible maximum pulse amplitude level. At the chosen pumping rate, the flow rate was approximately 17.1 mL per minute. The pressure in the system was not intended to resemble the mean systemic filling pressure of the human body (around 7 mm Hg).We gathered the waveforms ofZand P (length of 30 seconds) with a custom-made LabView program where we performed the initial processing of the signal. The signals were smoothed with a digital Savitzky-Golay filter, as the emerging oscillations in the mechanical pipe system (at approximately 5 Hz) had an interfering effect. Such oscillations were caused by the utilized step motor-based pulsatile pump.ΔZt and ΔPt were calculated based on the gathered waveforms. The goal was to assess the possible conformity between the changes in measured impedance and pressure of saline solution in developed mechanical pipe system at different externally applied compression levels.The explanatory points on the design of the prepared on-desk measurement system can be stated as follows:(i)
The system is a rough representation of the flow path in the arterial tree in the forearm (brachial, radial, and ulnar arteries and superficial palmar arc), which can easily be manipulated through squeezing (which cannot be done in a controlled way in the case of the forearm) and setting electrodes on the preselected spots(ii)
The system is an imitation of the forearm, representing the pumping of arterial blood farther from the heart(iii)
Based on the pulsating volume of saline solution, the evaluation of measured impedance and pressure and through that the assessment of the effect of rigid and flexible pipes in comparison to the radial artery can be performedThe composed system is capable of mimicking the selected piece of arterial tree in the following aspects:(i)
It provides similar flow paths (single pipe (brachial artery) that is branched (through bifurcation) to two parallel pipes (radial and ulnar arteries) and once again joining to a single pipe (superficial palmar arc)(ii)
The flow of saline solution in pipes is pulsating, as the blood in arteries(iii)
It represents two specific conditions of the arterial wall (flexible and rigid) that apply in biological objects (maybe only for a second, but still).


## 5. Measurement Results

Evaluating the gathered waveforms of impedance was performed based on the following approach [14]: ΔZt was calculated based on the determined Zt and Ztinvar.Then, the percentage (RΔZt) of ΔZt from Zt) was found, representing the sensitivity according to
(3)RΔZt=ΔZt×100Zt.Similarly,ΔPt was calculated based on the voltage at the output of the pressure sensor (ΔUt), presented as RΔPt in the following figures. Such an approach is explained by the desire to compare the measured data on the same base regardless of the pulsating volume matter (blood, saline solution, etc.) or material of the pipe (flexible, rigid, arterial wall, etc.).The plates of the clamps were fixed at the desired distance, starting with the undeformed pipe (deformation level 0) and ending with the maximum chosen externally applied pressure (deformation level 6). The measurements were performed equally in both cases of materials of constructed pipe system while the pipes were of equal lengths (Figure5).Three measurements were carried out in the cases of both pipe materials by decreasing the distance between the plates of each clamp separately (in the following order: CM1, CM2, and CM3) from deformation level 0 to 6.ΔZt and ΔPt were measured, and arithmetic means were calculated and represented in percentages (RΔZt and RΔPt) in Figures 6 and 7.Figure 6
RΔZt of the measured impedance of pulsating saline solution in the developed mechanical system with flexible pipes together with RΔPt of detected pressure.Figure 7
RΔZt of the measured impedance of pulsating saline solution in the developed mechanical system with rigid pipes together with RΔPt of detected pressure.Quantitative evaluation can be made based on the values ofΔZt in Ohms in the cases of flexible (Table 2) and rigid (Table 3) pipes. The respective changes at the pressure sensor output (shown in voltages), representing ΔPt, are also shown in comparability reasons in Tables 2 and 3.Table 2
ΔZt and ΔPt of pulsating saline solution in the case of flexible pipe.
Def. levelΔZt (Ω)ΔZt (Ω)ΔZt (Ω)ΔZt (Ω)ΔZt (Ω)ΔZt (Ω)CM1CM2CM3CM1CM2CM300.2900.2560.2671.0240.9230.97710.2940.2960.2660.9570.8070.98820.2970.2460.2660.9970.9250.94830.7840.2410.2700.9180.9310.97440.8740.2840.2660.9130.9261.07250.7770.3990.2480.9300.8550.93662.0370.4500.2513.1760.8290.870Table 3
ΔZt and ΔPt of pulsating saline solution in the case of rigid pipe.
Def. levelΔZt (Ω)ΔZt (Ω)ΔZt (Ω)ΔZt(Ω)ΔZt (Ω)ΔZt (Ω)CM1CM2CM3CM1CM2CM301.6810.4833.9181.0230.8730.97511.8851.2333.5140.9960.8070.99822.0291.4183.7271.0110.9350.95032.0321.3423.1630.9380.9360.96241.2801.5903.0700.9360.9281.06651.5851.3292.1020.9280.8980.93160.6520.8081.0033.1770.9110.934Example waveforms of impedance and pressure of pulsating saline solution in flexible and rigid pipes in the case of deformation level 3 can be seen, respectively, in Figures8 and 9 (squeezed by CM2).Figure 8
Waveforms of impedance (Z) and pressure (shown in voltages (U)) of pulsating saline solution in the developed system of flexible pipe with pressure applied by CM2 at deformation level 3.Figure 9
Waveforms of impedance (Z) and pressure (shown in voltages (U)) of pulsating saline solution in the developed system of rigid pipe with pressure applied by CM2 at deformation level 3.The measured absolute value ofZ of saline solution in both cases of pipe materials remains in the range of 500 Ω. The impedance spectroscope’s accuracy for measuring Z in the interval of 0.1 kΩ–50 kΩ at the excitation signal frequency of 100 kHz is 0.05% [35]. As a result, the smallest possible fraction and resolution of measured Z is about 0.03 Ω (based on the base value of Z (Figure 9))—the value below the change in measured signal is not identifiable. The result is times lower than the calculated values of ΔZt in Tables 2 and 3, acknowledging the results to be valid.However, in the context of the current research and paper, the base value was not the primary concern. The problem was related to the pulse wave shape and magnitude (ΔZt). And this is, in the light of the resolution of the measurement setup/device (considering its internal filters, oversampling, and the additional postprocessing), trustable; moreover, the reproducibility of the pulse waveform is evident (Figures 8 and 9).The range of the results that are higher than 0.5 mV is trustable as for analog auxiliary inputs, the resolution is 16 bits.


## 6. Simulation of Fluid Dynamics in Branched Arterial System of the Forearm

Few published results report the numerical modeling and simulations of arterial trees in human arms. However, these are focused on the effect of the point of bifurcation of the brachial artery to radial and ulnar arteries and the modeling of the flow of arterial blood through the prism of the emergence of blood pressure [37]. The second type of such paper contains the modeling of bifurcation by simple T-junction geometry [38]. Both types of above-described research focus on recirculation, caused by the bifurcation and its effect on the flow velocity.However, dynamic models require much more computational power than static models. At the same time, the number of attributes and tools is reduced, especially in evaluating a wide range of possible properties (like impedance). To our knowledge, modeling of the effect of squeezing on the arterial tree in the forearm at selected spots has not been presented earlier.A simplistic numerical static simulation of blood flow, based on general fluid dynamics, was modeled (as a set of T-junctions). A freeware program Flowsquare4.0 was used—a two-dimensional computational fluid dynamics software [39].Simulation is aimed at evaluating the effect of squeezing on the velocity of flow and pressure in the rough model of an arterial tree in the arm, based on T-junction type of bifurcations. We measured the flow speed and pressure at the same spot—in the middle upper flow path (virtually the radial artery). The measured flow speed values in the relative location of electrodes (Figure3) in the cases of no squeezing and squeezing by CM1-3 are visible in Table 4.Table 4
Flow speed in radial artery model in simulation when squeezing pipe at locations CM1-3.
VariableNo squeezingCM1CM2CM3Flow speed u (m/s)0.08720.08580.08130.0854Secondly, we performed a visual evaluation of the effect of squeezing the artery on the pressure wave based on the simulation results. The color coding shows the emerging pressure, calculated based on the atmospheric pressure (1 Pa). As visible in Figure10, in the case of symmetric flow paths, the pressure is emerging symmetrically in both parallel branches.Figure 10
Formation of pressure in the case of no blockage on the flow path.The same can be recognized in the situation where CM1 is applied, reducing the diameter of the flow path to half of the original size (Figure11). However, the reduced flow path increases the pressure at the convergent bifurcation—however by visual evaluation only marginally close to the divisive bifurcation. The pressure increases near the point of squeezing.Figure 11
Formation of pressure in the case of squeezing CM1.In the case of applying pressure by CM2 or 3, the simulation reveals the effect at each branch of the pipe (Figure12).Figure 12
Formation of pressure in the case of squeezing CM2 (or CM3).Pressure is increasing afore the point of squeezing. By knowing the property of the wall of the vessel, being dependent on a variety of factors, including pressure, its flexibility is expected to increase with increasing pressure (ΔPt), increasing the magnitude of ΔZt.In symbiosis with the flow speed (the faster the flow, the lower the value ofΔZt), the squeezing of the artery, on which we measured the EBI (Table 4), enables us to obtain the highest value of ΔZt.


## 7. Discussion

In this section, the result of experimentation on the composed mechanical pipe system is discussed and compared with the data acquired from the radial artery in the forearm of a single volunteer.


### 7.1. Effect of Squeezing the Pipe in Location CM1

The imitation of arteries in the forearm with a single flexible PVC pipe [14] can be compared to the proposed setup of parallel flexible PVC pipes. We deformed the pipe without an alternative flow path in both setups. At the excitation frequency of 100 kHz, the value of ΔZt increases. The dependence of ΔZt and ΔPt in the cases of flexible and rigid pipes in an enhanced system is more complex.There are visible numerical differences in Tables2 and 3 between the calculated values of ΔZt —being smaller in the case of flexible pipe. This is assumably caused by several aspects. Primarily, the conductance of both pipe materials is different, adding offset to the measured variable. The measured Z of a 10 mm piece of flexible pipe is approximately 100 kΩ while it is about 15 kΩ in the case of rigid pipes. Secondly, unless we used the identical saline solution, the experiments were performed consecutively with the pause for changing the pipes (in the following order flexible (1) and rigid pipe (2)). The dissolved saline crystallizes onto the surfaces, and its consistency with electrical properties varies. Thirdly, as ΔZt is a calculated variable and the exact values of the measured Z and Zinvar depend on the specific measurement, these values vary. The above is the reason for presenting the results in percentages in Figures 6 and 7.The trend ofΔZt in the case of rigid pipe is the same as in the case of flexible pipe—however steeper (Figure 13). Also, ΔPt follows the same trend as in the case of flexible pipe (Figure 14). At the highest deformation level, the value of inherent pressure gains the maximum level, and ΔZt reaches its highest possible value.Figure 13
Trendlines ofΔZt of pulsating saline solution in flexible and rigid pipes at different deformation levels.Figure 14
Trendlines ofΔPt of pulsating saline solution in flexible and rigid pipes at different deformation levels.The measuredΔPt in the case of the enhanced setup with flexible pipes remains on a similar level up to the highest deformation, where the result sharply increases (Figure 14). The above can be explained by the flexible properties of the pipe. With the increase of inherent pressure in the system, ΔZt increases while it is not large enough to increase ΔPt until the highest deformation level.Additionally, the correlation coefficient (r) can give information on the linear relationship between the determined ΔZt and ΔPt. See Table 5 for r in the cases of externally applied pressure on pipes (clamps CM1-CM3) in the composed system.Table 5
Correlation coefficients between the determinedΔZt and ΔPt in the cases of pulsating saline solution in flexible and rigid pipes.
Pipe materialr (CM1) ΔZt/ΔPtr (CM2) ΔZt/ΔPtr (CM3) ΔZt/ΔPtFlexible0.89-0.70.64Rigid0.990.330.41Table5 confirms a very strong correlation (the interpretation bases on the directives for clinical trials [40]) between ΔZt and ΔPt when increasing the external pressure on the pipe (with CM1). This result reveals that when depicting the arterial tree in the forearm as a system with single in and output, the changes in ΔZt follow the changes in ΔPt (and vice versa).


### 7.2. Effect of Squeezing the Pipe in Location CM2

By applying increasing pressure on the flexible radial branch of the pipe,ΔZt is slightly decreasing up to the 3rd deformation level and then starts to increase solidly.The assumption is that by hindering the flow of saline solution, the pressure caused by CM2 is increasing, and the inner diameter of the flexible pipe enlarges slightly with every arriving pulse wave. At the average pressure, the saline solution is still divided between the two branches, directing more flow to the ulnar branch of the pipe. The above is causing a slight decrease inΔZt. At higher deformation levels, the ulnar branch cannot continue passing the flow of saline solution in increasing amounts. As a result, the diameter of the radial branch of the pipe is increasing, resulting in larger values of ΔZt.With the increasing level of deformation of the radial branch of the rigid pipe,ΔZt increases up to the 4th deformation level and then starts to decrease rapidly.The result is reversed compared to the trendline in the case of flexible pipe (Figure13). The reason relates to the inability of rigid pipe to expand. Expectedly, pressure in the radial branch of the pipe increases with squeezing, enabling the increase in ΔZt—while still permitting saline solution to flow. At the same time, flow velocity increases, and the volume of saline solution heading to the ulnar branch of the pipe decreases the value of ΔZt in the radial branch.The calculation ofr indicates the appearing differences in ΔZt and ΔPt when applying pressure with CM2—being inverse in the case of flexible pipe (Table 4). The pressure in the radial branch of the pipe increases (with the increase in diameter) while the detected ΔZt decreases. The rigid pipe cannot expand, and there is no clear correspondence.


### 7.3. Effect of Squeezing the Pipe in Location CM3

When applying external pressure on the ulnar branch of flexible pipe,ΔZt demonstrates only a slight and constant decrease (Figure 6). The decrease of ΔZt in the case of rigid pipe is much steeper (Figure 7), being about four times smaller when comparing the 6th to deformation level of 0.The reason for such a variable, but the confluent trendline slope, is presumably the different material properties of used pipes. When squeezing the ulnar branch of the pipe, the pulsating saline solution is directed to the radial branch of the pipe (whereZ is measured). The diameter of the flexible pipe can increase through expanding, compensating for the otherwise decreasing ΔZt. As the diameter of the rigid pipe cannot enlarge, the decrease of ΔZt is faster. As visible in Figure 14, the trendline of ΔPt is similar for both pipe systems, however slightly increasing in the case of rigid pipe, demonstrating the nonexpanding effect of rigid wall material.The calculatedr of ΔZt and ΔPt (Table 4) shows a moderately strong dependence in the case of flexible pipe and fair dependence in the case of rigid pipes. It is important to notice that in the composed system, the pressure sensor position may not reflect the exact pressure values in each parallel branch of the pipe. Firstly, the on-desk system is not closed (as the cardiovascular system is due to the capillary pressure). Secondly, the pressure sensor is only in a single location in the developed system (brachial branch of pipe) and not duplicated in other branches.In the current research, the emphasis was set on the change inΔZt and ΔPt, i.e., not the absolute values. The pressure caused by the pulsatile pump changes rhythmically in a narrow range. The effect of performed external squeezing in the three chosen locations (Figure 3) is expected to manifest in the sole pressure sensor readings. The above is assumably affected by suppression but is still registrable. Hence, the results can be considered comparable, measured 330 mm away from the location of the pressure sensor.


### 7.4. Comparison of the Effect of Squeezing in the Composed Pipe System and Radial Artery

The comparison of the measuredΔZt of the mechanical pipe system with the measured ΔZt of the radial artery in the forearm of a single volunteer (presented in [14]) can be performed.The implemented pipe system is expected to provide a rough imitation of arteries in the forearm under controllable squeezing, where a saline solution flows through the parallel pathway. Although in the initial research [14], the external pressure on the radial artery was applied in four levels, the squeezing in the enhanced pipe system was increased to seven levels, and the correlation of the results is expected to be attainable (Figure 15).Figure 15
ΔZt of pulsating saline solution in mechanical system with flexible and rigid pipes and pulsating blood in radial artery of a single volunteer.There is no clear correlation between the values ofΔZt, measured during the increasing externally applied pressure in the case of saline solution in flexible pipes and blood in radial artery (Figure 15). See Table 6 for r in the cases of externally applied pressure (clamps CM2) on pipes in the composed system and radial artery in the forearm.Table 6
Correlation coefficients between the determinedΔZt in the cases of pulsating saline solution in both types of pipes and blood in the radial artery.
VariableΔZt flexible pipe/arteryΔZt rigid pipe/arteryr0.06-0.97Concerning the rigid pipe, a very strong reverse relationship between the values ofΔZt during the increasing level of applied pressure can be realized (Table 6). This result leads to the consideration of much more complex properties of the arterial wall that apply in the case of arterial stiffening (explained thoroughly in [30]) that cannot be interpreted fully through the utilization of PVC pipe. If the pressure on the radial artery is applied, its wall stiffens, unlike the wall of the ulnar artery that redirects blood. In the case of rigid pipe, only the saline solution flow speed can increase; i.e., the trend of ΔZt can indeed be reversed. However, the correlation is surprisingly strong. Still, the correlation needs confirmation during research with a large number of samples.We will not discuss the correlation subsequently betweenΔPt in both as the positions of the pressure sensor (and also the results) differ in both setups and are not linearly comparable.


### 7.5. Summary

We can obtain the highest value ofΔZt when applying pressure with CM1, i.e., hindering the flow of saline solution before it flows into the container. However, such application is not feasible in the human forearm where the capillary pressure dictates the conditions.The solution for practical EBI measurement to achieve the maximum value ofΔZt could be to apply pressure on the radial artery while measuring the EBI on the ulnar artery. Based on the presented results, ΔZt of blood in the ulnar artery is increasing. The assumption is that the radial and ulnar arteries operate as a parallel pathway with a compensation mechanism to direct the blood to peripheral arteries in the case of blockage in one pathway.The effect of squeezing the parallel branch of pipe (radial or ulnar artery) in the developed mechanical pipe system is remarkable and emerges notable differences inΔZt and ΔPt between the utilization of flexible or rigid pipes.The effect of the pipe flexibility on the magnitude of measuredΔZt is evident and indicates the property of reduced rigidness to tolerate pulsation. A clear link with the effect of vascular aging on the stiffness of arteries can be noted, which is a reason for the increase of PWV and consequently a cause of heightened systolic blood pressure [28].The resistivity of the blood is claimed to be dependent on the velocity and acceleration due to the reorientation of erythrocytes [22]; i.e., the resistivity will increase during the increase of velocity. However, as the results of current research show, the measured values of EBI are higher in the case of rigid (while the velocity of blood flow is higher) than flexible pipes (see Tables 2 and 3), so such an effect would only increase the difference. Due to that, the conclusions are valid.A significant conclusion can be drawn: a rough mechanical pipe system with pulsating saline solution can principally imitate the pulsating blood in the arterial tree for EBI measurement-based characterization. The inclusion of a parallel branch for mimicking the ulnar artery validates the developed system for imitating and evaluating the dynamics of blood flow in arteries of the forearm for EBI measurements.


## 7.1. Effect of Squeezing the Pipe in Location CM1

The imitation of arteries in the forearm with a single flexible PVC pipe [14] can be compared to the proposed setup of parallel flexible PVC pipes. We deformed the pipe without an alternative flow path in both setups. At the excitation frequency of 100 kHz, the value of ΔZt increases. The dependence of ΔZt and ΔPt in the cases of flexible and rigid pipes in an enhanced system is more complex.There are visible numerical differences in Tables2 and 3 between the calculated values of ΔZt —being smaller in the case of flexible pipe. This is assumably caused by several aspects. Primarily, the conductance of both pipe materials is different, adding offset to the measured variable. The measured Z of a 10 mm piece of flexible pipe is approximately 100 kΩ while it is about 15 kΩ in the case of rigid pipes. Secondly, unless we used the identical saline solution, the experiments were performed consecutively with the pause for changing the pipes (in the following order flexible (1) and rigid pipe (2)). The dissolved saline crystallizes onto the surfaces, and its consistency with electrical properties varies. Thirdly, as ΔZt is a calculated variable and the exact values of the measured Z and Zinvar depend on the specific measurement, these values vary. The above is the reason for presenting the results in percentages in Figures 6 and 7.The trend ofΔZt in the case of rigid pipe is the same as in the case of flexible pipe—however steeper (Figure 13). Also, ΔPt follows the same trend as in the case of flexible pipe (Figure 14). At the highest deformation level, the value of inherent pressure gains the maximum level, and ΔZt reaches its highest possible value.Figure 13
Trendlines ofΔZt of pulsating saline solution in flexible and rigid pipes at different deformation levels.Figure 14
Trendlines ofΔPt of pulsating saline solution in flexible and rigid pipes at different deformation levels.The measuredΔPt in the case of the enhanced setup with flexible pipes remains on a similar level up to the highest deformation, where the result sharply increases (Figure 14). The above can be explained by the flexible properties of the pipe. With the increase of inherent pressure in the system, ΔZt increases while it is not large enough to increase ΔPt until the highest deformation level.Additionally, the correlation coefficient (r) can give information on the linear relationship between the determined ΔZt and ΔPt. See Table 5 for r in the cases of externally applied pressure on pipes (clamps CM1-CM3) in the composed system.Table 5
Correlation coefficients between the determinedΔZt and ΔPt in the cases of pulsating saline solution in flexible and rigid pipes.
Pipe materialr (CM1) ΔZt/ΔPtr (CM2) ΔZt/ΔPtr (CM3) ΔZt/ΔPtFlexible0.89-0.70.64Rigid0.990.330.41Table5 confirms a very strong correlation (the interpretation bases on the directives for clinical trials [40]) between ΔZt and ΔPt when increasing the external pressure on the pipe (with CM1). This result reveals that when depicting the arterial tree in the forearm as a system with single in and output, the changes in ΔZt follow the changes in ΔPt (and vice versa).


## 7.2. Effect of Squeezing the Pipe in Location CM2

By applying increasing pressure on the flexible radial branch of the pipe,ΔZt is slightly decreasing up to the 3rd deformation level and then starts to increase solidly.The assumption is that by hindering the flow of saline solution, the pressure caused by CM2 is increasing, and the inner diameter of the flexible pipe enlarges slightly with every arriving pulse wave. At the average pressure, the saline solution is still divided between the two branches, directing more flow to the ulnar branch of the pipe. The above is causing a slight decrease inΔZt. At higher deformation levels, the ulnar branch cannot continue passing the flow of saline solution in increasing amounts. As a result, the diameter of the radial branch of the pipe is increasing, resulting in larger values of ΔZt.With the increasing level of deformation of the radial branch of the rigid pipe,ΔZt increases up to the 4th deformation level and then starts to decrease rapidly.The result is reversed compared to the trendline in the case of flexible pipe (Figure13). The reason relates to the inability of rigid pipe to expand. Expectedly, pressure in the radial branch of the pipe increases with squeezing, enabling the increase in ΔZt—while still permitting saline solution to flow. At the same time, flow velocity increases, and the volume of saline solution heading to the ulnar branch of the pipe decreases the value of ΔZt in the radial branch.The calculation ofr indicates the appearing differences in ΔZt and ΔPt when applying pressure with CM2—being inverse in the case of flexible pipe (Table 4). The pressure in the radial branch of the pipe increases (with the increase in diameter) while the detected ΔZt decreases. The rigid pipe cannot expand, and there is no clear correspondence.


## 7.3. Effect of Squeezing the Pipe in Location CM3

When applying external pressure on the ulnar branch of flexible pipe,ΔZt demonstrates only a slight and constant decrease (Figure 6). The decrease of ΔZt in the case of rigid pipe is much steeper (Figure 7), being about four times smaller when comparing the 6th to deformation level of 0.The reason for such a variable, but the confluent trendline slope, is presumably the different material properties of used pipes. When squeezing the ulnar branch of the pipe, the pulsating saline solution is directed to the radial branch of the pipe (whereZ is measured). The diameter of the flexible pipe can increase through expanding, compensating for the otherwise decreasing ΔZt. As the diameter of the rigid pipe cannot enlarge, the decrease of ΔZt is faster. As visible in Figure 14, the trendline of ΔPt is similar for both pipe systems, however slightly increasing in the case of rigid pipe, demonstrating the nonexpanding effect of rigid wall material.The calculatedr of ΔZt and ΔPt (Table 4) shows a moderately strong dependence in the case of flexible pipe and fair dependence in the case of rigid pipes. It is important to notice that in the composed system, the pressure sensor position may not reflect the exact pressure values in each parallel branch of the pipe. Firstly, the on-desk system is not closed (as the cardiovascular system is due to the capillary pressure). Secondly, the pressure sensor is only in a single location in the developed system (brachial branch of pipe) and not duplicated in other branches.In the current research, the emphasis was set on the change inΔZt and ΔPt, i.e., not the absolute values. The pressure caused by the pulsatile pump changes rhythmically in a narrow range. The effect of performed external squeezing in the three chosen locations (Figure 3) is expected to manifest in the sole pressure sensor readings. The above is assumably affected by suppression but is still registrable. Hence, the results can be considered comparable, measured 330 mm away from the location of the pressure sensor.


## 7.4. Comparison of the Effect of Squeezing in the Composed Pipe System and Radial Artery

The comparison of the measuredΔZt of the mechanical pipe system with the measured ΔZt of the radial artery in the forearm of a single volunteer (presented in [14]) can be performed.The implemented pipe system is expected to provide a rough imitation of arteries in the forearm under controllable squeezing, where a saline solution flows through the parallel pathway. Although in the initial research [14], the external pressure on the radial artery was applied in four levels, the squeezing in the enhanced pipe system was increased to seven levels, and the correlation of the results is expected to be attainable (Figure 15).Figure 15
ΔZt of pulsating saline solution in mechanical system with flexible and rigid pipes and pulsating blood in radial artery of a single volunteer.There is no clear correlation between the values ofΔZt, measured during the increasing externally applied pressure in the case of saline solution in flexible pipes and blood in radial artery (Figure 15). See Table 6 for r in the cases of externally applied pressure (clamps CM2) on pipes in the composed system and radial artery in the forearm.Table 6
Correlation coefficients between the determinedΔZt in the cases of pulsating saline solution in both types of pipes and blood in the radial artery.
VariableΔZt flexible pipe/arteryΔZt rigid pipe/arteryr0.06-0.97Concerning the rigid pipe, a very strong reverse relationship between the values ofΔZt during the increasing level of applied pressure can be realized (Table 6). This result leads to the consideration of much more complex properties of the arterial wall that apply in the case of arterial stiffening (explained thoroughly in [30]) that cannot be interpreted fully through the utilization of PVC pipe. If the pressure on the radial artery is applied, its wall stiffens, unlike the wall of the ulnar artery that redirects blood. In the case of rigid pipe, only the saline solution flow speed can increase; i.e., the trend of ΔZt can indeed be reversed. However, the correlation is surprisingly strong. Still, the correlation needs confirmation during research with a large number of samples.We will not discuss the correlation subsequently betweenΔPt in both as the positions of the pressure sensor (and also the results) differ in both setups and are not linearly comparable.


## 7.5. Summary

We can obtain the highest value ofΔZt when applying pressure with CM1, i.e., hindering the flow of saline solution before it flows into the container. However, such application is not feasible in the human forearm where the capillary pressure dictates the conditions.The solution for practical EBI measurement to achieve the maximum value ofΔZt could be to apply pressure on the radial artery while measuring the EBI on the ulnar artery. Based on the presented results, ΔZt of blood in the ulnar artery is increasing. The assumption is that the radial and ulnar arteries operate as a parallel pathway with a compensation mechanism to direct the blood to peripheral arteries in the case of blockage in one pathway.The effect of squeezing the parallel branch of pipe (radial or ulnar artery) in the developed mechanical pipe system is remarkable and emerges notable differences inΔZt and ΔPt between the utilization of flexible or rigid pipes.The effect of the pipe flexibility on the magnitude of measuredΔZt is evident and indicates the property of reduced rigidness to tolerate pulsation. A clear link with the effect of vascular aging on the stiffness of arteries can be noted, which is a reason for the increase of PWV and consequently a cause of heightened systolic blood pressure [28].The resistivity of the blood is claimed to be dependent on the velocity and acceleration due to the reorientation of erythrocytes [22]; i.e., the resistivity will increase during the increase of velocity. However, as the results of current research show, the measured values of EBI are higher in the case of rigid (while the velocity of blood flow is higher) than flexible pipes (see Tables 2 and 3), so such an effect would only increase the difference. Due to that, the conclusions are valid.A significant conclusion can be drawn: a rough mechanical pipe system with pulsating saline solution can principally imitate the pulsating blood in the arterial tree for EBI measurement-based characterization. The inclusion of a parallel branch for mimicking the ulnar artery validates the developed system for imitating and evaluating the dynamics of blood flow in arteries of the forearm for EBI measurements.


## 8. Conclusion

Answers to the posed questions in the introductory section are given subsequently.(1)
The increasing pressure on the radial or ulnar artery affectsΔZt of blood in the radial artery. The result depends on the squeezed artery and its flexibility. In the case of flexible pipe, ΔZt decreases up to a certain pressure level and then starts to increase. In the case of rigid pipes, the trend of ΔZt is inverted(2)
The increasing pressure on the radial or ulnar artery affectsΔPt of blood while the result also depends on the flexibility of the flow path. As ΔPt was not measured separately in radial and ulnar branches of the pipe but only in the brachial branch, no individual information of ΔPt is known(3)
A very strong correlation between the measuredΔZt and ΔPtis evident in the case of squeezing CM1 in the cases of both types of pipes. The relation in the cases of radial and ulnar arteries is complex and depends on the squeezed arteryThe simulation result confirms the theoretical base of fluid mechanics through the occurrence of pressure. Squeezing the pipe increases the pressure and reduces the flow speed afore the point of compressing the flow path. Also, afore the point of bifurcation,ΔZt must be measured on the pipe where the pressure is applied, to gain the highest value.This is confirmed by comparing with the practical measurements on the human forearm, revealing the absence of linear correlation with the on-desk experiment. However, a very strong inverse correlation ofΔZt in the case of rigid pipes was determined. The result indicates the properties of the arterial wall and the possible effect of arterial stiffening through aging.Based on the research results, the suggestion for gaining the highest magnitude ofΔZt is to compress the radial artery and measure the impedance of the ulnar artery.


## 9. Limitations and Perspectives of the Work

There are certain limitations in the presented research that require consideration. We used isotonic saline solution to imitate blood in the on-desk model. However, while the concentration of the saline solution can be adjusted, the utilization of blood will be considered in further research to increase the complexity of the measured impedance spectrum.In the on-desk model, tubes of different material properties were used to imitate the arteries. Arteries (and blood vessels in general) have a complex character, depending highly on the physiology of the whole body, including psychology—imitation is exceptionally complicated. The utilization of blood vessels will be considered in the future.The saline solution flows in the on-desk model freely towards the floor (earth)—the capillary pressure is imitated solely by atmospheric pressure. In the circulatory system, the capillary pressure (and venous pressure) is higher than atmospheric pressure [41]. We assume that the capillary pressure affects the measured values of pressure (and impedance); however, the exact influence is the subject of determination. So, the measurement results presented in the current paper are comparable for both types of tubes in the chosen framework. Still, the free-flowing end of the system towards the ground must be replaced with a valve, to imitate the properties of capillary pressure (not just the atmospheric pressure).While the current research focuses on amplitudes ofΔZtand ΔPt, the ultimate goal is to extract the hemodynamic feature points. The impedance cardiogram that enables the evaluation of the heart is a high-valued source of information. Moreover, the information is available in all the arteries. For this, modulating the flow of saline solution based on the true cardiac profile of blood flow is needed. Such an experiment will require a complex step motor-based pulsating control system and hardware.An implementation is needed in the next generation of the pulsating mechanical system (to achieve additional information on hemodynamic parameters of arterial tree): the addition of flowmeters into each pipe branch. The additional flowmeters help to verify the expected increase in velocity of saline solution in the rigid pipe.



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*Source: 5710835-2023-03-11.xml*