sensors Article

Development of a Tonometric Sensor with a Decoupled Circular Array for Precisely Measuring Radial Artery Pulse Min-Ho Jun † , Young-Min Kim † , Jang-Han Bae, Chang Jin Jung, Jung-Hee Cho and Young Ju Jeon * KM Fundamental Research Division, Korea Institute of Oriental Medicine (KIOM), Daejeon 305-811, Korea; [email protected] (M.-H.J.); [email protected] (Y.-M.K.); [email protected] (J.-H.B.); [email protected] (C.J.J.); [email protected] (J.-H.C.) * Correspondence: [email protected]; Tel.: +82-42-868-9306 (ext. 306); Fax: +82-42-868-9480 † These authors contributed equally to this work. Academic Editor: Vittorio M. N. Passaro Received: 9 March 2016; Accepted: 23 May 2016; Published: 26 May 2016

Abstract: The radial artery pulse is one of the major diagnostic indices used clinically in both Eastern and Western medicine. One of the prominent methods for measuring the radial artery pulse is the piezoresistive sensor array. Independence among channels and an appropriate sensor arrangement are important for effectively assessing the spatial-temporal information of the pulse. This study developed a circular-type seven-channel piezoresistive sensor array using face-down bonding (FDB) as one of the sensor combination methods. The three-layered housing structure that included independent pressure sensor units using the FDB method not only enabled elimination of the crosstalk among channels, but also allowed various array patterns to be created for effective pulse measurement. The sensors were arranged in a circular-type arrangement such that they could estimate the direction of the radial artery and precisely measure the pulse wave. The performance of the fabricated sensor array was validated by evaluating the sensor sensitivity per channel, and the possibility of estimating the blood vessel direction was demonstrated through a radial artery pulse simulator. We expect the proposed sensor to allow accurate extraction of the pulse indices for pulse diagnosis. Keywords: pressure sensor; radial artery pulse; piezoresistive sensor; tonometric sensor; face-down bonding (FDB); decoupled circular array

1. Introduction The radial artery pulse has long been one of the major diagnostic methods in both Eastern and Western medicine [1–3]. Two thousand years ago, the Greek medical scientist Galen classified pulse waves and used them for clinical diagnoses, and his diagnosis theory remained in use until the medieval era. Since the invention of the sphygmogram in 1863, it has been possible to measure pulse waves to utilize various variables, such as blood pressure (BP) and augmentation index (AIx), and it is widely used in clinics [4–7]. Currently, there are many requests to develop objective and scientific equipment for precisely measuring pulse waves on radial arteries [8–10]. The shape characteristics of the pulse reflect the condition of the cardiovascular system, such as the elasticity and viscosity of the arterial wall, compliance, and the resistance of the blood flow. In Eastern medicine, traditional doctors analyze not only the temporal, but also the spatial, characteristics of the pulse wave on the left and right radial arteries to diagnose diseases and discern the effectiveness of treatments [11,12]. These doctors have been using their fingers to measure the detailed shape of pulse waves, although the diagnosis result can Sensors 2016, 16, 768; doi:10.3390/s16060768

www.mdpi.com/journal/sensors

Sensors 2016, 16, 768

2 of 12

be highly dependent on the senses of the doctors. The detailed shape characteristics of the pulse wave are difficult to obtain using general-purpose measurement systems. Measuring the spatial-temporal characteristics of the pulse wave with various conditions of applying pressure to the radial artery provides more useful information for diagnosis than conventional measurement methods. Therefore, an advanced measurement system needs to be developed for measuring the detailed properties of the cardiovascular system and for accurate diagnoses in Eastern medical clinics. Various types of sensing elements for effective pulse measurements, such as piezoelectric, piezoresistive, capacitive, and hall sensors, have been steadily developed. These elements have their own advantages in terms of their measurement principle; however, they have problems that must be overcome for precisely measuring pulse waves on radial arteries. The pulse sensor that uses piezoelectric elements is limited to obtaining static information, which means the applied pressure on the radial artery. The acquisition of static information is important for precisely measuring pulse waves because the shape of the pulse changes according to the applied pressure [13]. Hall sensors measure changes in the magnetic field generated by the movement of permanent magnets due to pulsation of the radial artery. Although hall sensors have the advantage of measuring dynamic information of pulse waves in a small area, these sensors are not suitable for measuring static data [14]. Pulse-taking platforms that use a capacitive tactile sensor array (Pressure Profile System Company, Los Angeles, CA, USA) can measure pulse length and width using 3-D pulse wave data obtained through a 3 ˆ 4 array of capacitive sensors. However, the signal interference among channels has yet to be solved, and the low sensitivity (over 0.5 mmHg in the full sensing range of 300 mmHg) makes observing subtle changes in the pressure pulse waveform difficult [15]. The piezoresistive sensor is the prominent method for precisely measuring radial artery pulses because it can acquire both static and dynamic information of pulse waves with high sensitivity. The piezoresistive sensor requires a temperature compensation for signals changed by the heat conducted from the skin. A study by Yoo et al. [16] developed a pulse sensor that includes a temperature sensor to compensate the output signals according to temperature changes. The crosstalk among channels of a sensor array is an important issue for measuring both the temporal and spatial information of the pulse wave for pulse diagnosis. Various types of sensor arrays, including piezoresistive sensors, contain crosstalk, and it decreases the measurement accuracy of each channel. Therefore, sensors need to be designed that minimize crosstalk among channels. In this study, we developed an advanced sensor for precisely measuring pulse waves on radial arteries and a method for improving its performance. A circular-type pulse sensor array with seven piezoresistive sensors was developed using a fabrication method with face-down bonding (FDB). Crosstalk among channels was eliminated by the sensor design, which can transmit pressure for each channel independently. By using a stick pad as an insulator, the sensor can only obtain the signals regardless of temperature changes. In addition, a method for estimating the direction of the radial artery was proposed to provide the proper direction for the sensor pressure and to improve the measurement accuracy. The sensitivity and coefficient of variance (CV) of the proposed sensor were assessed experimentally, and the performance of the method for estimating artery direction was evaluated using a radial artery pulse simulator. The estimation of artery direction facilitates more accurate analysis for the spatial information of the pulse, such as depth, width, and force. 2. Design and Experimental Section 2.1. FDB-Type Pressure Sensor for Radial Pulse (PSRP) 2.1.1. The Structure and Assembly of PSRP A gauge-type silicon pressure sensor (US9173, Unisense, Hsinchu, Taiwan) was used to measure the pulse pressure of the radial artery. This sensor was integrated with the PCB by FDB, and it was covered with a silicone rubber mold. Independent pressure sensor units (IPUs) were composed of PCB, core pressure sensor, and silicone rubber mold, as shown in Figure 1. The core sensor was connected

Sensors 2016, 16, 768

3 of 12

to the PCB by a solder bump. This process increases the durability of the sensor, and it improves the degree of 2016, integration of the sensor due to the wireless device. Sensors 16, 768 3 of 12 Sensors 2016, 16, 768

3 of 12

Figure 1. Independent pressuresensor sensorunit unit(IPU) (IPU) size: size: 2.5 2.52.5 mm × 2.7 Figure 1. Independent pressure 2.5mm mm× ˆ mm ˆ mm. 2.7 mm. Independent sensorThe unitPSRP (IPU)has size:three 2.5 mm × 2.5 the mm first × 2.7 layer mm. consists of a Figure 2 Figure shows1.the structure pressure of the PSRP. layers:

Figure 2 shows the structure of the PSRP. The PSRP has three layers: the first layer consists of a stick pad for delivering the pulse of the radial artery to the IPU, as well as the cap on the stick pad. stick padFigure for delivering the pulse ofofthe radial artery to the IPU, as wellthe as first the cap on the stick 2 shows the structure PSRP. The PSRP has three layers: consists apad. Each stick pad is mounted on an IPUthe and protrudes externally through the hole inlayer the outer caseofof Eachstick stick pad is mounted on an IPU and protrudes externally through the hole in the outer case pad for delivering the pulse of the radial artery to the IPU, as well as the cap on the stick pad. the PSRP. This structure enables the crosstalk between IPUs to be eliminated because the radial artery of Each pad is mounted on an IPU and protrudes through thethe hole in thesurface outer case of the PSRP. This structure the crosstalk between IPUs to be eliminated because the radial artery pulsestick is transmitted toenables the IPU individually. The capexternally was used to broaden contact of the the PSRP. This structure enables the crosstalk between IPUs to be eliminated because the radial artery pulse is transmitted the IPU individually. The cap was used to contact surface of the skin. This sensor to has the structural advantage of minimizing thebroaden effect ofthe temperature changes transmitted the IPU against individually. The cap was used toeffect broaden the contact the skin.pulse Thisissensor haspad thetoinsulates structural advantage of minimizing thesecond of temperature changes because because the stick heat from the skin. The layer is the IPU, surface and theof third skin. This sensor hasconnector the structural advantage of The minimizing effect of temperature changes layer pad consists of the PCBfrom and pogo pins for connecting the IPU and theand PCB.the There is alayer the stick insulates against heat the skin. second the layer is the IPU, third because the stick pad insulates against heat from the skin. The second layer is the IPU, and the third groove obtain a precise connection between the consists of for thealignment connectortoPCB and pogo pins for connecting thepogo IPUpins andand the IPUs. PCB.Figure There 3isshows a groove layer consists process of the connector PCB and pins connecting the IPU aand the PCB. There a the assembly this PSRP. Thispogo sensor is for cost effective because malfunctioning IPUis is for alignment to obtain afor precise connection between the pogo pins and IPUs. Figure 3 shows the groove for alignment to obtain a precise connection between the pogo pins and IPUs. Figure 3 shows simply replaced with a new one rather than replacing the entire PSRP. assembly process for this PSRP. This sensor is cost effective because a malfunctioning IPU is simply the assembly process for this PSRP. This sensor is cost effective because a malfunctioning IPU is replaced with a newwith onearather than replacing the entire simply replaced new one rather than replacing thePSRP. entire PSRP.

Figure 2. PSRP structure. Figure 2. PSRP structure.

Figure 2. PSRP structure.

Sensors 2016, 16, 768

4 of 12

Sensors 2016, 16, 768

4 of 12

Sensors 2016, 16, 768

4 of 12

Figure 3. PSRP assembly process. Figure 3. 3. PSRP Figure PSRPassembly assemblyprocess. process.

Figure 4 shows the dimensions of the developed PSRP. IPUs are placed at 0.5 mm gaps, and the Figure 4 shows the dimensions of the developed PSRP. IPUs are placed at 0.5 mm gaps, and the diameter of 4the first layer, which consists seven IPUs, stick pads, caps,atis0.5 10.12 Figure shows the dimensions of theof developed PSRP. IPUs areand placed mmmm. gaps,The andIPUs the diameter of the first layer, which consists of seven IPUs, stick pads, and caps, is 10.12 mm. The IPUs can precisely measure parallel and vertical pulse information of the radial artery because seven IPUs diameter of the first layer, which consists of seven IPUs, stick pads, and caps, is 10.12 mm. The IPUs can can precisely measure parallel and vertical pulse information of the radial artery because seven IPUs werewere placed in in aparallel circular shown ininof Figure experimental results also precisely measure andarrangement, vertical pulseas the radial artery because seven IPUs placed a circular arrangement, asinformation shown Figure 4. 4. TheThe experimental results also were demonstrated thatthat the developed PSRP was suitable structure assessing spatial characteristics placed in a circular arrangement, as shown inaaFigure 4.structure The experimental results also demonstrated that demonstrated the developed PSRP was suitable forfor assessing the the spatial characteristics of the pulse wave. of the pulse wave. the developed PSRP was a suitable structure for assessing the spatial characteristics of the pulse wave.

Figure 4. PSRP Dimensions (unit: mm).

2.1.2. PSRP Evaluation

Figure 4. 4. PSRP Dimensions (unit: (unit: mm). Figure PSRP Dimensions mm).

The PSRP evaluation system can apply a force of seven steps on each channel to evaluate the

2.1.2. PSRP 2.1.2. PSRP Evaluation Evaluation characteristics of the PSRP. The system consists of three parts: an actuator that applies force on each channel using a motor, ansystem electronic scale (CUX4200H, Seongnam-si, Korea) that can The PSRP PSRP evaluation ofCAS, seven steps on on each each channel tomeasure evaluate the the The evaluation system can can apply apply aa force force of seven steps channel to evaluate the mass applied to the channel, and a controller that controls motor movements according to the characteristics of the PSRP. The system consists of three parts: an actuator that applies force on each characteristics of the PSRP. The system consists of three parts: an actuator that applies force on each inputusing from athe electronic scale through serial communication. Figure 5 presents a diagram of measure the channel motor, anelectronic electronic scale (CUX4200H, CAS, Seongnam-si, Korea) channel using a motor, an scale (CUX4200H, CAS, Seongnam-si, Korea) thatthat cancan measure the sensor assessment system.

the mass applied to channel, the channel, a controller that controls movements according the mass applied to the and aand controller that controls motormotor movements according to the to input input from the electronic scale through serial communication. Figure 5 presents a diagram of the from the electronic scale through serial communication. Figure 5 presents a diagram of the sensor sensor assessment assessment system.system.

to each channel until the target force is reached. The sensor signals are stored in a PC via a DAQ (NI-USB6218, National Instruments, Austin, TX, USA). The seven-step force was sequentially applied, and the sensor signals and output from the electronic scale were saved. The sensor assessment system repeated this process three times. Considering the contact area (3.61 mm2) of the cap connected with each channel, a target force of 10 gf is equivalent to a pressure of Sensors203.76 2016, 16, 768 mmHg. The sensitivity was evaluated using each channel output signal. From the three5 of 12 repeated measurements, the repeatability was calculated employing the coefficient of variance (CV).

Sensors 2016, 16, 768

5 of 12

The evaluation system automatically applies force (i.e., 0 gf, 5 gf, 10 gf, 15 gf, 20 gf, 25 gf, and 30 gf) to each channel until the target force is reached. The sensor signals are stored in a PC via a DAQ (NI-USB6218, National Instruments, Austin, TX, USA). The seven-step force was sequentially applied, and the sensor signals and output from the electronic scale were saved. The sensor assessment system repeated this process three times. Considering the contact area (3.61 mm2) of the cap connected with each channel, a target force of 10 gf is equivalent to a pressure of 203.76 mmHg. The sensitivity was evaluated using each channel output signal. From the three repeated measurements, the repeatability was calculated employing the coefficient of variance (CV).

Figure 5. Schematic diagram of the sensor assessment system.

Figure 5. Schematic diagram of the sensor assessment system.

2.2. Method for Estimating Blood Vessel Direction

The evaluation system applies force (i.e., 0 gf,and 5 gf, 10 gf, 15 among gf, 20 gf, 25 gf, and The developed PSRPautomatically is less influenced by skin temperature interference channels, 30 gf)and to each channel until the target force is reached. The sensor signals are stored in a PC via a DAQ it is suitable for estimating the blood vessel direction due to the circular-shaped arrangement. (NI-USB6218, Nationala schematic Instruments, Austin, TX, USA).for The seven-step sequentially applied, Figure 6 presents diagram of the method estimating the force bloodwas vessel direction using PSRP on the radialand artery. Whenfrom a channel is at the center it has aThe high-amplitude signal, and and the sensor signals output the electronic scale artery, were saved. sensor assessment system 2 ) of the signal becomesthree smaller as a Considering channel is far from the center. develop method forconnected estimatingwith repeated this process times. the contact areaTo(3.61 mmthe the cap the direction of theforce radialof artery, the blood vesselmmHg. directionThe wassensitivity performed was each channel, a target 10 gfan isexperiment equivalentfor tofinding a pressure of 203.76 using a pulse wave simulator (Victor Pulse, Tellyes Scientific Inc., Tianjin, China). evaluated using each channel output signal. From the three repeated measurements, the repeatability was calculated employing the coefficient of variance (CV). Figure 5. Schematic diagram of the sensor assessment system.

2.2. Method for Estimating Blood Vessel Direction 2.2. Method for Estimating Blood Vessel Direction

The developed PSRP is less influenced by skin temperature and interference among channels, and The developed PSRP is less influenced by skin temperature and interference among channels, it is suitable for estimating the blood vessel direction due to the circular-shaped arrangement. Figure 6 and it is suitable for estimating the blood vessel direction due to the circular-shaped arrangement. presents a schematic diagram of the method for estimating the blood vessel direction using PSRP on Figure 6 presents a schematic diagram of the method for estimating the blood vessel direction using the radial artery. channel is at the center it has a high-amplitude signal, and theand signal PSRP on theWhen radial aartery. When a channel is atartery, the center artery, it has a high-amplitude signal, becomes as a channel is as fara from theiscenter. Tothe develop methodthe formethod estimating the direction thesmaller signal becomes smaller channel far from center.the To develop for estimating of the radial artery,ofan for the blood vessel wasdirection performed using a pulse the direction theexperiment radial artery, anfinding experiment for finding thedirection blood vessel was performed using a pulse wavePulse, simulator (Victor Pulse, Tellyes Scientific Inc., Tianjin, China). wave simulator (Victor Tellyes Scientific Inc., Tianjin, China).

Figure 6. Schematic diagram for estimating blood vessel direction using PSRP.

Figure 6. Schematic diagram for estimating blood vessel direction using PSRP.

Figure 6. Schematic diagram for estimating blood vessel direction using PSRP.

Sensors 2016, 16, 768 Sensors 2016, 16, 768

6 of 12 6 of 12

The output signals from the experiment were collected using the following process. The PSRP, The output signals from the experiment were type collected using the following process. PSRP,angle. which has seven channels arrayed in a circular arrangement, is rotated at a The certain Sensors 2016, 16, 768 6 of 12 which has seven channels arrayed in a circular type arrangement, is rotated at a certain angle. The The output signals of the PSRP were obtained as the channels that are applied with a predetermined output signals of the PSRP were obtained as the channels that are applied with a predetermined force. The output fromvessel the experiment were collected using following process. Thesignals. PSRP, The force. The direction of signals the blood was estimated through thethe analysis of the output Thewhich direction of the blood vessel was estimated through the analysis is of the output signals. The signals hasthrough seven channels arrayed in a circular type arrangement, at aparts: certainapplied angle. The signals obtained the channels were pre-amplified and dividedrotated into two pressure obtained channels pre-amplified andthat divided into two applied pressure output through signals ofthe the PSRP werewere obtained as the channels are applied withparts: a predetermined force. signals and and pulse waveform signals, asasshown Figure 7.The Theapplied applied pressure signals and the pulse signals pulse signals, shownin inthrough Figure 7. pressure pulse The direction ofwaveform the blood vessel was estimated the analysis of the outputsignals signals.and Thethe signals waveform signals can be obtained by passing the input signals through a low pass filter and band waveform canthe bechannels obtainedwere by passing the input through a low pass filter and band pass obtainedsignals through pre-amplified andsignals divided into two parts: applied pressure filter,pass respectively. filter,and respectively. signals pulse waveform signals, as shown in Figure 7. The applied pressure signals and the pulse waveform signals can be obtained by passing the input signals through a low pass filter and band pass filter, respectively.

Figure 7. Flow chart dataacquisition acquisition of and pulse waveform. Figure 7. Flow chart ofofdata of applied appliedpressure pressure and pulse waveform. Figurea 7. Flow chart ofmodel data acquisition of applied pressurevessel and pulse waveform. blood vessel Figure 8 shows geometrical of the PSRP and blood for estimating

Figure 8 shows a geometrical model of the PSRP and blood vessel for estimating blood vessel direction through sensor rotation. Figure 8a depicts the entire circular-type sensor and the channel Figure 8sensor shows rotation. a geometrical model the PSRP bloodcircular-type vessel for estimating blood vessel direction through 8aofdepicts theand entire sensor and the number of each channel. Figure Figure 8b presents a geometrical model for the moving distance of channel the direction through sensor rotation. Figure 8a depicts the entire circular-type sensor and the channel number of each channel. Figure 8b presents a geometrical model for the moving distance channels from the x-axis when the channels that are in a straight line (i.e., two, four, and six) areof the number of each channel. Figure 8b presents a geometrical model for the moving distance of the channels from the x-axis the channels are8cindepicts a straight line (i.e.,and two, four, and six) are rotated around channelwhen four clockwise (CW).that Figure the direction amplitude of the channels from the x-axis when the channels that are in a straight line (i.e., two, four, and six) are various forces applied to the radial artery (assumed to8c bedepicts a circular shape). The is reduced byof the rotated around channel four clockwise (CW). Figure depicts the direction and amplitude rotated around channel four clockwise (CW). Figure 8c the direction andforce amplitude of the thevarious geometric shape and force direction as the channels are moved from the x-axis by the rotation various forces applied to the radial artery (assumed to be a circular shape). The force is reduced forces applied to the radial artery (assumed to be a circular shape). The force is reduced byof by the PSRP. the geometric and force direction thechannels channels are thethe x-axis by the of the geometric shapeshape and force direction asas the aremoved movedfrom from x-axis byrotation the rotation of the PSRP. the PSRP.

Figure 8. PSRP model and artery model pushed by channels: (a) PSRP of the decoupled circular type Figure 8. PSRP model and artery model pushed by channels: (a) PSRP of the decoupled circular type

with rotation (Ɵ), (b) location channels around channel and (c) the circular load on type Figure 8.with PSRP model and arterychange modelof pushed byrotated channels: (a) PSRP of four, the decoupled rotation (Ɵ), (b) location change of channels rotated around channel four, and (c) the load on vessel wall pushed by channels. with arterial rotation (θ), (b) location change of channels rotated around channel four, and (c) the load on arterial vessel wall pushed by channels. arterial vessel wall pushed by channels. In other words, when the PSRP four),the thechannels channelsabove above In other words, when the PSRProtates rotatesaround aroundits itscenter center point point (channel (channel four), andand below channel four move from the x-axis as much as the rotation angle. When the channel applies below channel four move from the x-axis as much as the rotation angle. When the channel applies In other words, whenvessel the PSRP rotates around its center pointcenter (channel four), the channels above pressure to the lowest wall of the the vessel, vessel,the theforce forcethat that pressure to the lowest vessel wallatatthe thedistance distancemoved moved from from the the center of and below channel four is move from the x-axis to as much asLaw. the rotation angle. When the channel applies thethe channel receives decreased channel receives is decreasedaccording according toHooke’s Hooke’s Law. pressure to the lowest vessel wall at the distance moved from the center of the vessel, the, ,where force that Assuming that the blood vessel is circular (with the of a circle: circle: where Assuming that the blood vessel is circular (with the equation equation r r the channel receives is decreased according to Hooke’s Law. is the radius of a circle) and that the output values of the channel are proportional to the height is the radius of a circle) and that the output values of the channel proportional to the height

Assuming that the blood vessel is circular (with the equation of a circle: x2 ` y2 “ r2 , where r is the radius of a circle) and that the output values of the channel are proportional to the height difference from the center of the blood vessel (by Hooke’s Law, F = kx, where k is a constant), the normalized expression of the force (Py ) obtained at the channel is in the following form:

Sensors 2016, 16, 768

7 of 12

! ) Py “ F pyq ¨ sinϕ ´ F pyq ¨ cos2 ϕ ¨ sinϕ

(1)

Sensors 2016, 16, 768

7 of 12

Here, F pyq is the correlation between the height of the channel and the applied force, ymin is the heightdifference at whichfrom F pyqthe becomes 0, the andblood ymax vessel is the (by height at which is klocated at the center center of Hooke’s Law,the F = channel kx, where is a constant), the of the blood vessel.expression F pyq can of bethe expressed follows: normalized force ( )as obtained at the channel is in the following form:







F pyq “ k¨ pymax ´ ymin q



(1)

(2)

is Here, is the correlation between the height of the channel and the applied force, at whichconstant. becomes 0, and is the heightisatatwhich the channel locatedvessel, at the and wherethe k height is the spring F pyq is 1 when the channel the center of theisblood of the blood vessel. canatbeyexpressed as follows: F pyq center is 0 when the channel is located of the channel that applies pressure to the min . The location

blood vessel’s wall (x, y, and angle (ϕ)) is obtained (2) and k ∙ by the following, using the equation of a circle trigonometric functions: where k is the spring constant. is 1 when the channel is at the center of the blood vessel, and is 0 when the channel is located at b. The location of the channel ythat applies pressure to the 2 ´1 x “angle( l¨ sinθ,))yis“obtained r2 ´ by pl¨ the sinθq , ϕ “ tan blood vessel’s wall (x, y, and following, usingxthe equation of a circle and trigonometric functions:

(3)

The obtained force F pyq and angle (ϕ) are substituted into Equation (1) to obtain the pressure (3) ∙ , ∙ , applied by the channel according to location. Finally, the equation for normalized pressure (Py ) accordingThe to PSRP rotation beangle expressed obtained force (θ) can and ( ) areas: substituted into Equation (1) to obtain the pressure applied by the channel to location. Finally, the equation for normalized pressure ( ) b # according b 2 ´pl ¨ sinθ q2 r according to PSRP rotation ( ) 2can be expressed as: 2 ´1

Py “



k¨ p

r ´ pl¨ sinθq ´ ymin q¨ sinptan



ˆb ∙



2

r2 ´ pl¨ sinθq ´ ymin q

¨ ∙







b

∙ ¨ cos2 ptan´1

∙b

¨ sinptan´1

q ´k

l ¨ sinθ



r2 ´pl ¨ sinθ q2 q l ¨ sinθ

+





r2 ´pl ¨ sinθ q2 q l ¨ sinθ

(4) (4)



An experimental set-up was established to confirm the possibility of estimating the blood vessel’s experimental set-up9a.was established to confirm thewas possibility thepulse bloodwave direction,An as shown in Figure First, the produced PSRP locatedofonestimating top of the vessel’s direction, as shown in Figure 9a. First, the produced PSRP was located on top of the pulse simulator of the radial artery, which generates pulse waves, and signals were obtained by repeatedly wave simulator of the radial artery, which generates pulse waves, and signals were obtained by applying pressure and rotation. A DC motor was used to control the desired pressure applied by repeatedly applying pressure and rotation. A DC motor was used to control the desired pressure the output channel 4 of inchannel the PSRP, the rotation angle was manually controlled using a appliedsignal by theof output signal 4 inand the PSRP, and the rotation angle was manually controlled scaledusing rulera on the outer case of the PSRP and a compact structured light laser (3D PRO Laser Mini™ , scaled ruler on the outer case of the PSRP and a compact structured light laser (3D PRO Laser ProPhotonix, Salem, NH,Salem, USA).NH, USA). Mini™, ProPhotonix,

(a)

(b)

Figure 9. (a) Experimental set-up and (b) experimental sequence for estimating blood vessel direction.

Figure 9. (a) Experimental set-up and (b) experimental sequence for estimating blood vessel direction.

As shown in Figure 9b, channel four, located in the center of the PSRP, was placed at the center

As shown FigureWe 9b,assumed channelthat four, located in was the center PSRP, was placed at the center of the bloodinvessel. channel four placed of on the center of the artery when pulse onlyWe received fromthat channel fourfour and was signals from on other channels were absent. Thepulse of thesignals bloodwere vessel. assumed channel placed center of the artery when

Sensors 2016, 16, 768

8 of 12

applied pressure was controlled by the motor such that the output voltage of the channel four signal reached 5 V, which is the target output voltage. The experimental sequence and method for Sensors 2016, 16, 768 8 of 12 estimating blood vessel direction in the artery model in the simulator is shown in Figure 10. The signals from each channel were obtained for more than 20 s (sampling rate: 200 samples/s). After acquisition was complete, the PSRP was lifted, rotated by 5°, were and then applied again. signalssignal were only received from channel four and signals from other channels absent. The applied This process the experiment repeated untilthe theoutput degreevoltage of rotation reached 60°four because thereached degree pressure wasofcontrolled by thewas motor such that of the channel signal gap between channels 60°. The obtained were separated signals and 5 V, which is the target is output voltage. The signals experimental sequence into and applied method pressure for estimating blood pulse waveform signals for analysis to the PSRP sensor rotation. vessel direction in the artery model according in the simulator is shown in Figure 10.

Figure 10. Experimental sequence for estimating blood vessel direction on the artery model in the simulator. Figure 10. Experimental sequence for estimating blood vessel direction on the artery model in the simulator.

3. Results and Discussion

The signals from eachSensor channel were obtained for more than 20 s (sampling rate: 200 samples/s). 3.1. Characteristics of PSRP After signal acquisition was complete, the PSRP was lifted, rotated by 5˝ , and then applied again. evaluate theexperiment developed was sensor, the coefficient variance (CV) forreached experiments that were This To process of the repeated until the of degree of rotation 60˝ because the ˝ repeated three times was calculated, and the sensitivity per channel was obtained by increasing the degree gap between channels is 60 . The obtained signals were separated into applied pressure signals applied force by seven stages. sensitivity was calculated using therotation. output signals of the sensors, and pulse waveform signals forThe analysis according to the PSRP sensor and the repeatability was evaluated using the CV of the five sensors, as shown in Table 1. The average 3. Resultsof and sensitivity theDiscussion five sensors was 0.327 (V/gf), and the average CV was 0.62%. In detail, the sensitivity corresponds to 0.016 V per 1 mmHg because a force of 10 gf is equivalent to a pressure of 203.760 mmHg. 3.1. Characteristics of the PSRP Sensor sensor system has a variation of 0.245 mmHg to measure 40 mmHg. Considering the CV, developed Moreover, it implies 40 mmHg, which is acoefficient typical pulse pressure,(CV) can be into 2200 To evaluate thethat developed sensor, the of variance fordigitized experiments thatlevels were because system is 0.3 mV considering the supply voltagewas (±10obtained V) and the A/D repeatedthe three timesresolution was calculated, and the sensitivity per channel by 16-bit increasing converter. The sensitivity variation and system resolution of the fabricated PSRPs are suitable for the applied force by seven stages. The sensitivity was calculated using the output signals of the detecting various pulse contours forevaluated radial pulse diagnosis. sensors, and the repeatability was using the CV of the five sensors, as shown in Table 1. The average sensitivity of the five sensors was 0.327 (V/gf), and the average CV was 0.62%. In detail, Table 1. Sensor sensitivity. the sensitivity corresponds to 0.016 V per 1 mmHg because a force of 10 gf is equivalent to a pressure of 203.760 mmHg. Considering the CV, the developed sensor system a variation of 0.245 CH7 mmHg Sensor CH1 CH2 CH3 CH4 has CH5 CH6 to measure 40Sensitivity mmHg. Moreover, it implies that 40 mmHg, which is a typical pulse pressure, can be (V/gf) 0.32294 0.37252 0.36359 0.35303 0.32533 0.31089 0.32765 Sensor #1 digitized into 2200CV levels the system resolution is 0.30.48756 mV considering supply0.88291 voltage (%) because 0.57954 0.03916 0.73674 0.05013 the 3.05291 (˘10 V) and the 16-bit A/D converter. The sensitivity variation and system resolution of the fabricated Sensitivity (V/gf) 0.32178 0.32949 0.33023 0.35977 0.35673 0.3545 0.34215 Sensorare #2suitable for detecting various pulse contours for radial pulse diagnosis. PSRPs CV (%) 2.38609 0.22454 0.40759 0.04822 0.08609 0.06177 0.13737

Sensitivity (V/gf) 0.32415 0.32455 0.3523 0.36408 0.32426 0.348 3.2. Experimental Result for Estimating Blood 0.35095 Vessel Direction Sensor #3 CV (%) 0.22802 0.177 0.05883 0.07506 0.45001 0.21664 0.24718 The signal obtained(V/gf) by the0.33615 sensor was divided into an0.31423 applied pressure a pulse Sensitivity 0.32551 0.25834 0.30729 signal 0.3162and 0.3162 Sensor #4 waveform signal. CV The(%) applied pressure according was1.08301 calculated by the 0.22001 signal, 0.05361 0.31644to sensor 0.45993rotation, 0.43231 0.15042 average valueSensitivity of the applied pressure signals obtained for 20 s. The peak value of the pulse waveform, (V/gf) 0.33256 0.30244 0.28766 0.33387 0.29701 0.27744 0.29768 Sensor #5to sensor rotation, was calculated from the average waveform, after deriving the average according CV (%) 2.69237 0.43782 1.07538 2.37248 0.82258 0.07627 0.13191 waveform from the obtained pulse waveform signals as shown in Figure 11. Theoretical values were 2 R mean and standard deviation are 0.999168 and 0.000931, respectively. calculated by substituting the information on the sensor location and the blood vessel geometry of the simulator into the theoretical equation in the experiment for estimating the blood vessel direction. Figure 12 is a graph of the normalized applied pressure, according to sensor rotation, which was

Sensors 2016, 16, 768

9 of 12

obtained through the experiment. The black dotted line in Figure 12 shows the theoretical values of the applied pressure signals calculated using the theoretical equation. The generally positive match between the experimental values and the theoretical values shows that the equation is adequate for expressing the force according to sensor rotation. Sensors 2016, 16, 768

9 of 12

Table 1. Sensor sensitivity.

3.2. Experimental Result for Estimating Blood Vessel Direction Sensor

CH1

CH2

CH3

CH4

CH5

CH6

CH7

The signal obtained by the sensor was divided into an applied pressure signal and a pulse Sensitivity (V/gf) 0.32294 0.37252 0.36359 0.35303 0.32533 0.31089 0.32765 Sensor #1 signal. The applied pressure signal, according to sensor rotation, was calculated by the waveform CV (%) 0.57954 0.03916 0.73674 0.48756 0.05013 3.05291 0.88291 average value of the applied pressure signals obtained for 20 s. The peak value of the pulse waveform, Sensitivity (V/gf) 0.32178 0.32949 0.33023 0.35977 0.35673 0.3545 0.34215 Sensor #2 to sensor rotation, was calculated from the average waveform, after deriving the average according CV (%) 2.38609 0.22454 0.40759 0.04822 0.08609 0.06177 0.13737 waveform from the obtained pulse waveform signals as shown in Figure 11. Theoretical values were Sensitivity (V/gf) 0.32415 0.35095 0.32455 0.3523 0.36408 0.32426 0.348 Sensor #3 by substituting the information on the sensor location and the blood vessel geometry of calculated CV (%) 0.22802 0.177 0.05883 0.07506 0.45001 0.21664 0.24718 the simulator into the theoretical equation in the experiment for estimating the blood vessel direction. Sensitivity (V/gf) 0.33615 0.32551 0.25834 0.31423 0.30729 0.3162 0.3162 Sensor12 #4 is a graph of the normalized applied pressure, according to sensor rotation, which was Figure CV (%) 0.22001 0.05361 0.31644 0.45993 0.43231 1.08301 0.15042 obtained through the experiment. The black dotted line in Figure 12 shows the theoretical values of Sensitivity (V/gf) 0.33256 0.30244 0.28766 0.33387 0.29701 0.27744 0.29768 Sensor #5 pressure signals calculated using the theoretical equation. The generally positive match the applied CV (%) 2.69237 0.43782 1.07538 2.37248 0.82258 0.07627 0.13191 between the experimental values and the theoretical values shows that the equation is adequate for 2 R mean and standard deviation are 0.999168 and 0.000931, respectively. expressing the force according to sensor rotation.

Figure 11.11. Average waveform of the of pulse from eachfrom channel according PSRP rotation. Figure Average waveform thesignal pulseobtained signal obtained each channel toaccording to PSRP rotation.

If the fabricated PSRP is used to measure pulse waves on the radial arteries of the body, then the blood vessel direction cannot be estimated using the applied pressure signals because the blood If the fabricated PSRP is used to measure pulse waves on the radial arteries of the body, then vessel is under the skin. Hence, the blood vessel direction needs to be estimated from the pulse the blood vessel direction cannot be estimated using the applied pressure signals because the blood waveform signal. To determine whether it is possible to estimate the blood vessel direction from the vessel is under the skin. Hence, the blood vessel direction needs to be estimated from the pulse pulse waveform signal, the pulse waveform signals obtained from the experiment were compared waveform signal. To determine whether it is possible to estimate the blood vessel direction from the with the theoretical value. Figure 13 depicts the peak value of the average waveform, according to sensor rotation, by deriving the average waveform from the pulse waveform signal. The black dotted line represents the values calculated from the theoretical equation. Compared with the pulse waveform signals, it has greater fluctuation and error than the applied pressure signal. The signal amplitude, according to sensor rotation, however, tends to follow the theoretical values. For instance, at 0°, where channels two, four, and six pressure the blood vessel in a straight line, the pulse

Sensors 2016, 16, 768

10 of 12

pulse waveform signal, the pulse waveform signals obtained from the experiment were compared with the theoretical value. Figure 13 depicts the peak value of the average waveform, according to sensor rotation, by deriving the average waveform from the pulse waveform signal. The black dotted line represents the values calculated from the theoretical equation. Compared with the pulse waveform signals, it has greater fluctuation and error than the applied pressure signal. The signal amplitude, according to sensor rotation, however, tends to follow the theoretical values. For instance, at 0˝ , where channels two, four, and six pressure the blood vessel in a straight line, the pulse waveform signal ˝ is high2016, in all Sensors 16, three 768 channels. When the sensor is rotated by approximately 30 , the pulse waveform 10 of 12 ˝ signals appear only on channel four. At 60 of rotation, the signal amplitudes are the highest in Sensors 2016, 16, 768 10 of 12 channels three, four, and five. Thissensor resultrotation. shows that theonpulse waveform signal of each channel channel fluctuates according to the Based this result, the possibility of estimating fluctuates according to the sensor rotation. Based this result, Additionally, the possibilityin ofthe estimating the blood the bloodfluctuates vessel direction byto sensor rotation wasonconfirmed. applied pressure channel according the sensor rotation. Based on this result, the possibility of estimating vessel direction by sensor rotation wasvalue confirmed. Additionally, in the applied pressure signal graph signal graph (Figure 12), the output of the signals from channels two and six becomes 0 at the blood vessel direction by sensor rotation was confirmed. Additionally, in the applied pressure (Figure 12), the output value of the signals from channels two and six becomes 0 at approximately 30˝ approximately 30° of sensor valuechannels of channels five becomes signal graph (Figure 12), therotation, output whereas value of the thepressure signals from twothree and and six becomes 0 at of sensor rotation, whereas the value ofby channels three between and five becomes 0 at approximately 0approximately at approximately 35°. This is pressure an error caused the interval channels and 30° of sensor rotation, whereas the pressure value of channels threetwo andand five four becomes ˝ . This is an error caused by the interval between channels two and four and between four and six, 35 between four and six, being mm smaller thanbythe and four four and 0 at approximately 35°. This0.4 is an error caused theintervals intervalbetween betweenchannels channelsthree two and and being 0.4 five. mm smaller than the intervals between channels three and four and four and five. four and between four and six, being 0.4 mm smaller than the intervals between channels three and four and four and five.

Figure 12. 12. Normalized to sensor sensor Figure Normalized output output signal signal for for pressure pressure value value of of each each sensor sensor channel channel with with respect respect to rotation from from 00°˝ to 60°. ˝. rotation to 60 Figure 12. Normalized output signal for pressure value of each sensor channel with respect to sensor rotation from 0° to 60°.

Figure 13. Normalized peak value of pulse wave signal for each sensor channel with respect to sensor rotation from 0° to 60°. Figure 13. 13. Normalized peak value value of of pulse pulse wave wave signal signal for for each with respect respect to to sensor sensor Figure Normalized peak each sensor sensor channel channel with rotation from from 00° to 60 60°. ˝ to ˝. rotation The errors in the signal are generated by the unevenness and the deformation of the simulator

bloodThe vessel by the applied The other reason is the clearance the stick pads on the errors in the signalpressure. are generated by the unevenness and the between deformation of the simulator IPU and the outer case holes. The cap of the PSRP sensor does not hold uniform intervals between blood vessel by the applied pressure. The other reason is the clearance between the stick pads on the the padsouter when applying pressure, the sensors pressure in an unwanted IPUstick and the case holes. The cap ofand the PSRP sensorapply does not hold uniform intervalsdirection. between Therefore, it is not easy to precisely estimate vessel direction within 10°unwanted due to errors in the the stick pads when applying pressure, andthe theblood sensors apply pressure in an direction. measuring signal. Due to the unevenness or deformation of the blood vessel not being within Therefore, it is not easy to precisely estimate the blood vessel direction within 10° due to errors in the the range of control, minimization of the clearance between the stick pad and the outer case hole is measuring signal. Due to the unevenness or deformation of the blood vessel not being within the

Sensors 2016, 16, 768

11 of 12

The errors in the signal are generated by the unevenness and the deformation of the simulator blood vessel by the applied pressure. The other reason is the clearance between the stick pads on the IPU and the outer case holes. The cap of the PSRP sensor does not hold uniform intervals between the stick pads when applying pressure, and the sensors apply pressure in an unwanted direction. Therefore, it is not easy to precisely estimate the blood vessel direction within 10˝ due to errors in the measuring signal. Due to the unevenness or deformation of the blood vessel not being within the range of control, minimization of the clearance between the stick pad and the outer case hole is required through precise assembly of the stick pad and the sensor housing case. In addition, the performance of the sensor can be improved when the contact surface between the IPU and the stick pad is flatter. A pulse waveform that does not consider blood vessel direction can become a dominant source of error when calculating the diagnostic index using the amplitude of the pulse wave, such as AIx or pulse power [17,18]. Accurate and precise measurement of the pulse waveform is particularly important in the pulse diagnosis for Eastern medicine. The pulse sensor array must be laid 90˝ to the longitudinal direction of the blood vessel to accurately estimate the pulse width or length. Since the structure of the radial artery is anatomically covered by the skin layer, however, the amplitude of the pulsation needs to be compensated for when estimating the blood vessel direction. As shown in the experimental results, depending on the direction of the blood flow, an error occurs at a maximum of 10 ˘ 0.45 (%) from the reference point of 0˝ according to degree. The estimation of blood vessel direction allows the pulse width to be measured more precisely, and the developed sensor can measure the pulse width and blood vessel direction within an error of 10˝ . Using the fabricated sensor allows automatic determination of the direction in which the pulse sensor is laid, as it approximately infers the blood vessel direction through function approximation after measuring the pulse peak by rotating the sensor from 0 to 60˝ . 4. Conclusions and Outlook This study developed a circular seven-channel piezoresistive sensor array using sensors assembled by the FDB method. The fabricated sensor was designed such that the pressure delivery path of each channel is independent to remove crosstalk among channels. By comparing the signal obtained from the circular-type PSRP sensor, it was possible to more precisely measure the pulse waveform by more effectively estimating the path of the radial artery. The fabricated sensor was confirmed to guarantee repeatability on sensitivity through its variance error of 0.62%, on average. The applied pressure value and peak value of the pulse waveform according to the blood vessel direction was observed using the pulse simulator to investigate the distortion effects of the blood vessel direction on the pulse waveform measurement. The results showed that it was similar to the theoretical model of pulse waveform change due to blood vessel direction and the relative difference in rotation angle (θ) of the pulse sensor. Applying pressure to the blood vessel in a certain direction when the radial artery is not visible is one of the essential factors for obtaining more precise pulse waveforms. The fabricated sensor allows improvement of the reliability of the pulse measurement because the PSRP sensor can be measured in the same direction of the blood vessel whenever measuring the pulse wave. Moreover, it is expected to improve the diagnostic precision of pulse indices that use the change in pulse amplitude, such as AIx, pulse width, and pulse power, which have high clinical usage in Eastern and Western medicine. Studies on computational methods that estimate the blood vessel direction and compensate for the pulse wave error using the approximation model of the blood vessel direction that we developed are required as follow-up investigations. Moreover, additional analysis on the factors that cause measurement errors (e.g., structural modification of the radial artery according to the applied pressure, mechanical errors in the production process of the pulse sensor, deformation noise during applied pressure to the radial artery due to soft tissue characteristics of the blood vessel and the skin layer) need to be conducted. Finally, the possibility of practical utilization of the fabricated sensor needs to be studied by actually applying the sensor in clinics.

Sensors 2016, 16, 768

12 of 12

Acknowledgments: This work was supported by a grant (K16022) from the Korea Institute of Oriental Medicine (KIOM), funded by the Korean government. Author Contributions: M.-H. J. and Y.-M. K. wrote the manuscript and designed and conducted experiments for sensor’s characteristics. J.-H. B. analyzed the signal data as he made the computer program to collect and analyze the pulse signal. C. J. J. and J.-H. C. installed the experimental set-up and conducted the experiments with M.-H. J. and Y.-M. K. Y.-J. J. conceived the structure of FDB sensor and contributed to writing and revising the manuscript. Conflicts of Interest: The authors declare no conflict of interest.

References 1. 2. 3. 4. 5.

6. 7.

8. 9. 10. 11. 12. 13. 14. 15.

16. 17. 18.

Nichols, W.W.; O’Rourke, M.F. McDonald’s Blood Flow in Arteries: Theoretical, Experimental and Clinical Principles, 5th ed.; Hodder Arnold: London, UK, 2005. Westerhof, N.; Stergiopulos, N.; Noble, M.I.M. Snapshots of Hemodynamics: An Aid for Clinical Research and Graduate Education, 2nd ed.; Springer Science & Business Media: New York, NY, USA, 2010. Ryu, H.H.; Lee, S.W.; Lee, J.; Lee., Y.; Kim, J.Y. Analysis of physical quantification of pulse types by pulse diagnosis. Korean J. Oriental Physiol. Pathol. 2007, 21, 1381–1387. Nichols, W.W. Clinical measurement of arterial stiffness obtained from noninvasive pressure waveforms. Am. J. Hypertens. 2005, 18, 3S–10S. [CrossRef] [PubMed] Kohara, K.; Tabara, Y.; Oshiumi, A.; Miyawaki, Y.; Kobayashi, T.; Miki, T. Radial augmentation index: A useful and easily obtainable parameter for vascular aging. Am. J. Hypertens. 2005, 18, 11S–14S. [CrossRef] [PubMed] Weber, T.; Auer, J.; O’Rourke, M.F.; Kvas, E.; Lassnig, E.; Berent, R.; Eber, B. Arterial stiffness, wave reflections, and the risk of coronary artery disease. Circulation 2004, 109, 184–189. [CrossRef] [PubMed] Jeon, Y.J.; Kim, J.U.; Lee, H.J.; Ryu, H.H.; Lee, Y.J.; Kim, J.Y. A clinical study of the pulse wave characteristics at the three pulse diagnosis positions of chon, gwan and cheok. Evid. Based Complement. Altern. Med. 2011. [CrossRef] [PubMed] Kim, H.; Kim, J.Y.; Park, Y.-J.; Park, Y.-B. Development of pulse diagnostic devices in Korea. Integr. Med. Res. 2013, 2, 7–17. [CrossRef] Alastruey, J.; Passerini, T.; Formaggia, L.; Peiró, J. Physical determining factors of the arterial pulse waveform: Theoretical analysis and calculation using the 1-D formulation. J. Eng. Math. 2012, 77, 19–37. [CrossRef] Zuo, W.; Wang, P.; Zhang, D. Comparison of Three Different Types of Wrist Pulse Signals by Their Physical Meanings and Diagnosis Performance. IEEE J. Biomed. Health Inform. 2016, 20, 119–127. [CrossRef] [PubMed] Wang, Y.Y.L.; Chiu, W.B.; Jan, M.Y.; Bau, J.G.; Li, S.P.; Wang, W.K. Analysis of transverse wave as a propagation mode for the pressure pulse in large arteries. J. Appl. Phys. 2007, 102, 064702. [CrossRef] Bae, J.H.; Jeon, Y.J.; Kim, J.Y.; Kim, J.U. New assessment model of pulse depth based on sensor displacement in pulse diagnostic devices. Evid. Based Complement. Altern. Med. 2013. [CrossRef] [PubMed] Liu, S.H.; Tyan, C.C. Quantitative analysis of sensor for pressure waveform measurement. Biomed. Eng. Online 2010, 9, 6. [CrossRef] [PubMed] Lee, S.S.; Nam, D.H.; Hong, Y.S.; Lee, W.B.; Son, I.H.; Kim, K.H.; Choi, J.G. Measurement of blood pressure using an arterial pulsimeter equipped with a Hall device. Sensors 2011, 11, 1784–1793. [CrossRef] [PubMed] Hu, C.-S.; Chung, Y.-F.; Yeh, C.-C.; Luo, C.H. Temporal and spatial properties of arterial pulsation measurement using pressure sensor array. Evid. Based Complement. Altern. Med. 2012, 2012, 745127. [CrossRef] [PubMed] Yoo, S.K.; Shin, K.Y.; Lee, T.B.; Jin, S.O.; Kim, J.U. Development of a radial pulse tonometric (RPT) sensor with a temperature compensation mechanism. Sensors 2013, 13, 611–625. [CrossRef] [PubMed] Kim, J.U.; Jeon, Y.J.; Kim, Y.M.; Lee, H.J.; Kim, J.Y. Novel diagnostic model for the deficient and excess pulse qualities. Evid. Based Complement. Altern. Med. 2012, 2012, 563958. [CrossRef] [PubMed] Kim, J.U.; Jeon, Y.J.; Lee, Y.J.; Kim, K.H.; Kim, J.Y. Novel diagnostic algorithm for the floating and sunken pulse qualities and its clinical test. Evid. Based Complement. Altern. Med. 2011, 2011, 813427. [CrossRef] [PubMed] © 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

Development of a Tonometric Sensor with a Decoupled Circular Array for Precisely Measuring Radial Artery Pulse.

The radial artery pulse is one of the major diagnostic indices used clinically in both Eastern and Western medicine. One of the prominent methods for ...
5MB Sizes 0 Downloads 9 Views