Recognition of Traditional Chinese Medicine Sphygmograms Using the System Identification Approach

Copyright © IFAC Identification and System Parameter Estimation 1982 . Washington D.C .. CSA 1982

RECOGNITION OF TRADITIONAL CHINESE MEDICINE SPHYGMOGRAMS USING THE SYSTEM IDENTIFICATION APPROACH Z.-F. Zhang, R.-J. Ma and Y.-J. Feng Department of Automatic Con tro l, B eijing Institute of Technology, Beijing, China

Ab8tract. PickiRg IIp the chAracterilltic values of tradi tional Chinese Medicine sphygaogrus using the systeM identification approach is considered in this paper. The successive approxiaation Method to deter.ine the pulse graph's estiaated paraaeters, siailar to the relaxation algoritha, is investigated. Several typical pulses, the chronic nephritia and acute urethri tis abnoraal pulse graph before and after cure, soae cases of the finger plethysaograas of the healthy and the hyper-tensive before and after exercise, as well as the sphygaogr_s of about 50 pregnant wOllen, are given. These results indicate, that by identifying the pulse's type, diagnosing a disease and forecasting a fetus sex is possible. Keywords. Identification; linear systeM; relaxation algorithM; parameter estiaation; bioaedical; lIodelling; data processing. INTRODUCTI(J( The s phygJftograas is one of the iaportant basis in traditional Chinese Medicine for diagnosing a disease. It has been used over several thousand years. However, the tradi,· tional Methed of feeling the pulse through the fingers ia very aubjective and the resul t sOIletiaes variell froa person to person. Several kinds of apparatus for aeasuring and rec ording the s phygaogrUII, have been developed in China since the 1960' s. Those ins tru.ents transfora the beat of the pulse into an electric signal by using a sensor, and record it. In this paper, the sphygJIogrus were recorded by Type M'IT-A apparatus produced by Tianjin Institute of Medical Instruaents and provided by Tianjin Pulse Co~dition Research Cooperation Group. The recorded typical sphygaograas consist of three parts: the .ain wave, the pre-dicrotic wave and the dicrotic wave (Fig. 1). Many achieve.ents in the field of sphygJIogr&a recognition and their use in disease diagnosis have been aade in Chinese aedical circles. They hope to discover chAracterilltic values in the curves, which aay reveal distinguishing features. So far, the aethod used in aedicine follows the electrocardiograa aethod, i. e., direc tly aeasuring the geoaetric sises of the curves, &I!I ahovn by the &nl;lea ~C, £T, .d and the altitudes I h , I , I , ete. in Fig. 1. However, due to the c 8;.-

y

r

T

fIIain Wave

Fig. 1.

Predicrotic Wave

Dicrotic Wave

Typical tarqy pulse figure METHODOLOGY

Although identifying the sphygaograM is a problea of pattern recognition, in order to transfora the geOllletric characteristics of the pulses' figures into nUMerical ones, we atteapted to resolve this problea with the systea identification lIethod, i.e., the systea aodelling and paraaeter estiaating approach. We rega,rd the pulse condition y( t) &8 a dynaaic response of the 2nd order linear continuous systea S, under input function u(t). Consider the pulse condition data y(t) which satisfies the following 2nd order differential equation,

y

plex foras of several sphygaogrus, difficuloio ties arise when studying thea. In fact, a standardized aeasureaent .ethod, suitable for dilltinguishing several typical pulse ri~rea, does nat yet exist.

"() t y. () '"1 y(t) • ----u(t) t y t + ~ t + i:T.r ~

122 3

t~

'tT!

(1)

Z.-F . Zhang , R.- J . Ma and Y.-J . Feng

1224

where Tt -- time constant. which shows the increase in impulse response speed; T - tiae constant. which shows the Cl decrease in iapulse response speed. Usually, Tt < Tq • and sOlletbes the s phygnlo~_ satiBfies T « T • t q

The characteristic equation of differential eqnation (1) is D2 +- 1

Tt

D+

--1--

=0

(2)

TtTq

There are two re a1. roots. when T ~ 4T t' and a P!lir of eonjugate c_plex roota. when T<4T q

t

.1

u( t)

l/\ u( t)

2nd Order

~

~inear Systo

I

y( t) •

~ y( t)

t

Fig. 2. Regarding the pulse condition as a dynamic response of 2nd order linear systea It is possible to lIIake the sphYgMograM discrete with a unifora sampling interva14T. Returning to the corresponding Eq.(I), we have the difference equation

T

t

=-

T ::q

( R)

In(-a2' 41.T ] n(-a2)

In(-a/+(ZCAt ~.\2 2., -a&J

FrOll (6) and (7), Tt~Tl :l nd T :::::T2 , when T1«T2. So, Eq. (4)-\.9) can be ased to obtain tfle estiaates .1't and "?q ,of t he tim e_ Qonsta.nt Tt and Tq • provided estimates of ~1 :l nd ~2 have been obtained. The approach of paraMeter e=(a, ,az • b) Tes t i _ mation, which is based on the d i screte dynamic systeM method used here. differs fr om the general parameter estimation met.hod by the unknown sequence{ukl. However,we know t his a.inly consists of impulses. The i mpulse, i n the sense of lIIedical mechanism. may be re g~ rd as systole of the left ventricJe. The relaxation algoritha of the generalized least squares method(see,for example,Goodwi n and Payne, 1977) , was the basis for this. A successive apprcxiaation algorithm. wh i ch attempts to estilllate {Ukf along with 1), i s now presented. Specifically. one might use the fol l owing algorithlll: Stage 1. For t he first time. se t{u kl as a unit illpulse and obtai n the r ou~h l eas t square estiaate for 8=(a1.a2.b) • Denote the estimated e by ~(l)=(a (1) a (1 ) b(l))T 1 '2' . Stage 2. Fora u (l)"(Yk+l-al(l)y -a

(I),

k-l k=2.3.····· · ,N-l

k

k

(1)

2

)!b(l)

(10)

=0 ana using -e(1) and h }. calculate {uk ( l)l by k (10) • S~e 3. Due to the sphygm~alll systea itself being a lowpass filter, d~scretization error in Yk' will lead to {u k (l)J which has a s trong high-frequency oscillation.Therefore, a s uit a ble smoothi~ process is necessary. Stage 4. In{ut<'~' which has been subj ected to a smoothing process, the ampli tude which is less than 1~ unit May be omitted. and the other willbe reserved, i .e., let u

where

Yk= y(k4T) u k- u(k.4T) {lA-J stochastic disturbance sequence arishing fro. observation and dis~ cretion.

The relation between the coefficients of difference equation (3) ai' a 2 , b and the tiae constants of the continuous aodel Tt' Tq may be deterained as follows 1 If (

fk'" Uk(l)

4,)2 ""2

+ a ", 0, then the characteristic 2 equation (2) has two real roots: 1 z -In( 1 ~Dl =- -Tl ~T al 1 1 D K--=-ln(--t 2 T2 AT 2

and T -t

J ( ~2 ) + a ) 2 2

(4)

a 2 + a ) (..:.1) 2 2

( 5)

I

TIT2 1 =--Dl +D 2 Tl+T2

1 T = = Tl + T q TtDI D2 2 (~)2 If + a < 0, then 2 2

u

k

=0

S~e

(6) (7)

if

uk(l)~

0.1, k=2.3 .. ···:,N-l

if u (l)< 0.1 k

5. With the obta.ined{u i. return to

Stage 1. and repeat the abov~ calculati on to (2 ) (3) obtain estimates of 9 ,e , .. .... . In general, owing thatiEklis co] ored noi se and unnecessary in the estillla t e of the parameter of noise sequence itself. empl oying an instrulllental variable Method (Goodwin and Payae.1977) to evaluate the parallleter i s ' appropriate. The specific stages are as follows: Stage 1. Obtain an estimate of

'"aLs

by the

122 5

Recognition of Trad i t i ona l Ch i nese Medicine Sphygmogr ams

TABLE 2 Results of Paraaeter EBti.ation of a Slippery Pu18e

recursive least square• • ethed, ebtainiYkl by '" {11) Yk '" ~T 9£s x k' k=l ,2 .. ····· ,N where xk R (Yk-1, Yk-2, Uk_l)T Stage 2. UBe the followi~ recursive a~ori­ tha8 to obtain an 1J'lltrUllenta.l variable estiaate of ~IV (see SBderstrija, Ljun~ and Guetavsson,1978). ~ ( T ~ ~+1 .. ~ + ~+1 YN+1 - xN+l~)

~

(12) ( I)

(14) ~

0:

(15)

,)T ( /\YN-l' " YN-2' uN_ 1

~

= (YN-l' YN- 2 , ~_I)T (16) The above al~oritha ls 8i.ilar to the recur8ive instruMental variable .ethod as ~iven by Goodwin and Payne(1977). But here,{Yk.is evalua ted before the event using (11) and based on ~IS to~ether. Then, the resulting estimation differs fro. the r.ecursive instrumental variable method, and more closely approaches the ta8truaental variable estiaate with

( 17) Toe esti.ation result and algoritha convergence is checked by the total square SUII of a one-step prediction error N-l T ~ ~ ( 18) Q =1: (y - x El k=l k+l k+l k The calculated results fro. much of the sphygJIIO~aJlS' data indicated that i t is possible to obtain ~ood paraaeter esti.atioA results by following the above approxi.ation aethod and the instrUllental variable algarithas.

L 1 2 4 5 7 8

,..

al

1.8786 1.8867 1.8676 1.8669 1.8578 1.85/37

b

'"a2

Q

~ethod

-0.8912 0.008)37 13).077 -0.8994 0.008260 2.3535 1.880) -0.8827 0.008534 -0.88)2 0.008646 1.7710 -0.8752 0.008785 1.7543 1.7161 -0.8767 0.008804

RLS IV

RLS IV RIS IV

Tq , K=Tq/4T t , Ua :: S~PCb, Uk), etc., which reflect the distinguishing features of a sphy~ot;raa. The characteri8tic roots are two real nu.bers, when K~ 1; and a pair of conjugate cOlllplexes, when K < 1. FORTRAN pr~aa HPC-5 consiets of abeut ~50 stateaents for accOllplishing the above calculations, including RLS,IV,and GRAPH{ print graph ) subpr~aas. A nUllber of typical pulses proces8ing results are shown in Fi~. ). Tardy pulse. Four beats to one c ye 1 e of respiration, 70-80 ti.es per minute. Tt =0.0204sl Tq=0.287s1 K=).777 Slippery pulse. Like pebbles rollin~ in a basin. Tt20.076sl Tq.. o.o68s1 K=0.225 Hollow pulse. Superficial, soft and hollow, like an onion stalk. Tt=0.0314s1 Tq=0.05/32s1 Ko:O.463 Taut pulse. Like a treaulous ausical string. Tt=0.0198s, Tq=0.275s; K-3.475

A calculated result of a noraal tardy pulee sphy~~.. (Fig.)a) is sh~n in Table 1. TABLE 1 L 1

2 4 5 7 8

"a1

1.7324 1.7246 1.6723 1.(#)7 1.6n70 1.6005

Results ef P~aaeter Eatiaation of NOTlllal Tardy Pu18e

,..

-O.~goo

-0.7321 -0.6819 -0.6545 -0.6288 -0.61)0

1, 0.01754 0.01818 0.019)2 0.02022 0.02106 0.02165

,..

to parameter estiaations e and{uk}' we can obtain the following quantities: Tt,

Accordin~

Slippery Pu18e

Q Method )7.242 RLS 8.264 IV 6.236 RLS 5.526 IV 5.)05 RLS 5.012 IV

A calculated result of a slippery pu18e sphy~~am (Fig.)b) is shown in Table 2. Execute the Recursive Least Square(RLS) es tiaati on , when the integer variable L=I,4,71 execute Instruaental Variable(IV) estiaat1on,when 12,5,8; and execute the approxiaation algaritha fre. Stage 2 to Stage 4, Le., calculate {ukl and correct it, when L=),6. S(JIIE RESULTS

( a) Tardy Pulse

Fig.).

SOMe typical pulses

Of the three kinds of typical pulsesltardyCIL taut(II) ,and slippery(IlI), the proce8si~ re8ults (aean values) of soae casei!! are 8hown ia Table 3, which roughly deteraine nu.erical features for the above pulsee. The above-mentioned features can also be shown thro~h the processing re8ults of the cOllparison of sOlle cases of illness before and after cure.

Z.- F. Zhang , R.-J . Ma and Y.- J . Feng

1226

TABLE 3

Paraaeters COIIparison of SOIIe Tvpieal Pulses

NUJlber Type of cases I II

III

8 5 7

K

3.34 2.18 0.68

Tt(s) 0.0383 0.0363 0.0512

Tq{s) 0.403 0.302 0.142

U. 0.782 1.914 1.661

Table 4, iJldica.tes 7 ca.ses ef chronic nephritis pulse before and after cure. All of the. include taut coaposition (bout 3 cases, slippery-taut 2 cases cl tardy-taut 2 cases). But after cure, all of the. include tardy cOlllposition( tardy 5 cases, taut-tardy 1 case and slippery-tardy 1 case). The results also indicates that the value Ua descends noticeably. TABLE 4

Coaparison of Chronic Nephritis Pulses Before and After Cure

Before Cure After Cure

K

Tt{s)

1..584

0.0447 0.0448

2.921

Tq{s) 0.273 0.336

Ua

TABLE 5 Compari s on of Acute Urethritis Pulses Before and After Cure

Before Cure After Cure

Tt(s)

Tq(s)

0.456 2.682

0.0624 0.0396

0.1014 0.3484

TABLE 6

The COIIparison of the FingerPlethysmogr&as' Paraaeters, Before and After Exercise Before Exercise AfterEJ(erc ise Ty Uss Uss Ty

Healthy 8 cases Hypertensive 10 cases

16.15

5.49

8.5f)

9.69

16.22

5.08

15.15

4.81

Parameters Ty versus Uss for the above 18 cases are shown in Fig. 4, before exercise, there are hayen't obviously difference between the healthy and the hypertensive person, but after exercise, they are differ grea tly. T

1.615 0.730

Table 5, indicated that two cases of acute urethritis pulaes, before cure,are slippery, but after cure becOlle tardy. The values of K and Tq increase but value Um obviously descends.

K

The comparison of the processing results for soae cases of the finger-plethysaograas of heal thy and the hypertensive before and after exercise are shown in Table 6.

Y

Healthy

•

40

6

•

30 20

Hypertensiye

A .A

.A

/0

A

.6 •

A

U

m

1.29 0.54

A

~L-

THE PROCESSING RESULTS OF THE FINGER PLETHY3MCX::RAM

__

/

~

____________

By finger-plethyaaogrca, it is possible to assist distinguish between the person is healthy and hypertensive, when physical exalIination.

____

ro

2

(a) The finger-plethysa~a~ is aeasured frOll the end of the finger using the photoelectric sensor and the fora of the finger-plethys.ograa soaething like the sphygaograa.

~

~

~

_____

JO

Before exercise

Ty

40

10 20

Discretize the finger-plethYSllograa and treat with Prograa HPC-5. We select the characteristic quantities Ty and Uss Tt Ty = ---y-.T;;:"f--

where Tf is the cycle of the finger-plethysmograa, Ym is the aaxiaUJI altitude of the plethysaograa, Tt and {u k } are the tiae constant and the ricti tious input sequence respectively, which are obtained by the above systea identification method.

fO

(b)

After exercise

Fig. 4. Procesaint; results of 18 cases before and after exercise

Recognition of Traditional Chinese Medic ine Sphygmograms

h of the feaale is aale.

ATTF1IPI' TO FORFI!AST 'mE FE'IUS SEX In this part, we will introduce sOlle re~ul ts abaut the atteMpt to forecast the fetus sex by IItudyi~ sphy~~aaa af pregnant wOllen. the fetus sex through the feel ef pullle, MM ree orded in Ohi-nese anc ien t aedical literature about one thousand years ~o. "Effective Prescription for Woaen", for instance,is an ancient aedical book published and edited by Chen Zhi-P'lin~ in the So~ Dynasty(A.D. 960-1279). Foreeastin~

In recent years, auch attention has been paid to forecasti~ a fetus' sex. Dr.Zhan~ Li-Rung and her co lle~es of the Tianjin Central Hospi tal of Gynecol~y and Obstetrics have been developing a research pr~aa on sphyga~aJlls of pregnant wOlllen, since 1978. The following, is a suaaary of sOlle of their ex peri enc es •

bi~er

1227

than that of the

Quantity K It reflects the ratio of descent and ascent speed of the sphygaouam, and hence K- Tq/4Tt. The value K of the feaale is bi~er than that of the aale, in ~eneral, because there is a "taut" cOllposi tion in the feaale pulse. Quantity p p i t 2/T, where t2 is the distance between the firat and second peak values of the evaluated fictitious input function f U k }, and T is the cardiac cycle. In ~eneral, value p of the fe_ale is saaller than that of the aale. h =2A K ,"0.436 t 2/T=0.491

h "'3.6

K =1.976 t 2/T=0. 169

They observed 150 cases in 1979, analyzing sphyga~amatic characteristics thro~h their eyes, experiences and judgment. The average rate of success through such forecastin~ was 83.1%, and the rate of success in forecasti~ was 9Jt (for females) and 79.5% (for aales) in 200 cases in 1980, as shown in Table 7. (a) Slippery-Taut Pulse (felllale)

TABLE 7 The Tianjin Central Heepital of Gynecolo~y and Obstetrics Forecasting the Fetus Sex 200 Cases in 1980 Male Female

Sex Sphy~ouam Foreca.stin~

Noraal

Fig. 5.

N~per

47 cas"'s % 140.jl

52 02.lJib

Failure

31% 6 0

Fetus Sex

Total

Number of Cases

116

84

Female Male

Success Rate

79.:JIo 93.0%

Forecastin~

S phyglll~aJI

26

This aan-made processing method was dependent on the operator's experiences. Even for the saae sphy~~aa, the results usually turned out to be contrary or equivocal. The systMl identification aethod was evaluate the data. Froa 170 cases of castin~ success as shown in Table 7, of pre~ant wOllen' sphy~ouaas(Fi~. processed with PrOUaa HR:-5.

used to fore50 cases 5) were

Through evaluation and analysis, we discovered that sOlle quantities differ greatly between distinct fetus sexes. Quantity h Width at 70% of aaxiaua altitude Ya in the sphy~~am Yk (aee Fi~. 5). Value

SOIIe noraal pre~nant 11 011 ens , sphy~ouaas

The above evaluated results(aean values) for 50 cases of pre~nant W0lIl ens , sphy~OU&JIs are shown in Table 8.

Nuaber of 45 cases Siailar % 39% COIIIplica tion 12 Reason not Clear 12

Success

(b) FrequentSlippery Pulse (lIIale)

TABLE 8 COIIPUtation Reaul ts of the ParaJlleters of Pregnant WOIIIens' Sphwot;raas(average of 50 cases) h

I(

4.01 2.29

1.31 0.715

p=t 2/T 0.171 0.363

To iaprove the quantity of identification, throu~h evaluation and analysis, a new statistical paraaetar F(K,p), is created, which is a function of paraaeters K andp. Paraaeter F(K,p) versus h for the above 50 caa.a ar.e shown in Fi~. 6, where si~ "." and "." represent a processing resu l t with a fe..le and a aale fetus pulse respectively. In F~. 6, the lo~arithaic coordinate systea is used, 80 that si~ "." and "~" lIIay be coneentzated in a suitable field on the coordiftate plane as shown in the fi~e. Thus, it can be seen that the processin~ results for pre~ant woaen's pulse sphy~o­ ~raaa can predict the sex of the fetus by checki~ whether the point of paraaeters

Z.- F . Zhang , R.- J . Ma and Y.-J. Feng

1228

(h, F~ is in the upper or lower shown in Fi~. 6. 1.0

F( K ,p)

0·9 0.8

" ", - ... , " JI

I

11 11

I

0 .7 0.6

,,,

0 ·5

,

I

If

\ It \

I I

If

." It

11

,

J(

re~ion

as

Feaale

Ix

Male REFEREliCFS

I '11 11 11 II! . . -_ J," ". .... ,, / -- -'"

I

:

\

0·3

JIlt

xJl

\

IC '_-,"

I ".. I"

,

\

I

I

I.

I

. . .

\

,

0.2

Beijin~

I

It

It

0 .4

I

If

,,-

I

.....

h

0.1 '--------------~--~~~~_7~ f 2 3 4 S 6 78910 Fi~.

6.

InsturJllent, Tianjin Centr.l H06pi tal of and Obstetrics, The PLA No.271 H06pi tal and Research Institute ef Spacefli~ht Medical En~ineerin~. We also thank the chancellor of Tianjin Medical Institute, Prof. Wu Xian-Zhon~ for energetic support.

GJnecol~y

Proeessin~ results of .50 cases pre~a.!'It woaens' sphYI9lOU&J\s

CONCLUSIONS The discussions conducted in this paper lead to the conclusions that by usin~ the systeM identification approach, it is possible to assist in identifyin~ a pulse type, di&«nosin~ a disease and forec&8ti~ the fetus' sex. So far, the research of sphYI9lOUaJIs is at an exploratory st.&«e. These results are only preliainary. ACKNOWLEDGE2'!ENT This work has been supported by Beiji~ Research Institute of Medical Apparatus and

Minitary Areas Hospital (1981). The observation of 266 cases sphYI9I~aas (Technical Report). Bekey, G.A. and J.E.W. Beneken (1978). Identification of biological systeas : a survey. Autoaatica, 14, 41-47. Fukunaga, K. (1972). Introduction to Statistical Pattern Recognition. Acadelllic Press, New York. Chap. 10-11. Goodwin, G.C. and R.L. Payne (1977). _Dynaaic Systelll Identification, ExperiMent Desi!n and Data Analysis. Acadeaic Press, New York. Chap.7, pp. 175-192. Ma, R.J. and Y.J. Fen~ (1980). Sphy~o~ms identification prilllary exploration. Congress on Control Theory and Applications, Guilin, China. SOdenrtrf:., T., L. Ljun~, and 1. Gustavsson (1978). A theoretical analysis of recursive identification method. AutOMatica, 14, 231-244. Tianjin Garrison COIIIJland Hospital (1980). The observation of chronic nephritis and acute urethri tis abnona) pulse ~aph before and after cure(Technica) Report). Wu, S.M. and S.M. Pandit (1979). Tillle Series and S tea Anal is: Modellin and A 1ications. In ~anuscript form • Zhan~, L.R. and others (1980). Analysis of sphy~~aas in 1137 WOMen. J. Chinese Gynecologyand Obstetrics, 12, 156-158. Zhan~, L.R. and others (1981). 3.50 cases clinical analysis forecastin~ fetus sex by sphYgBlograllls. (To be published).