Automated Classification and Identification of Liver Dysfunction Using a New Class of Shape Descriptors

Copyright © IFAC Theory and Application of Digital Control New Delhi , India 1982

AUTOMATED CLASSIFICATION AND IDENTIFICATION OF LIVER DYSFUNCTION USING A NEW CLASS OF SHAPE DESCRIPTORS T. Prasad*, A. M. K. Badreldin* and M. A. Ismail** ·Faculty of Engineering, University of Waterloo, Waterloo, Ontario, Canada "Department of Computer Science and Engineering, University of Petroleum and Minerals, Dhahran, Saudi Arabia

Abstract. Different shapes or patterns for the decay of a radioactive tracer in the blood and the uptake of the same tracer by the liver may be recorded in most experiments using a digital multiprobe system. Procedures for the analysis, recognition and classification of these shapes for diagnostic and prognostic purposes are explained in this paper utilizing a newly developed algorithm for shape description in a multidimensional space in conjunction with a pattern classification system. Test results of the system on a group of patients containing several classes of liver dysfunction are also included. Keywords. Biomedical; Computer Applications; Medical Information Processing; Medical Systems; ~attern Recognition. INTRODUCTION Monitoring different mechanisms involved in hepatic uptake, conjugation and biliary excretion of radioactive tracers such as radioactive rose-bengal, sulfobromophthalein (BSP) , etc., provide one of the most sensitive and reliable indices for the evaluation of liver function. Appropriately designed experiments using such tracers may yield information of particular importance both from the clinical as well as the physiological point of view. Usually any tracer enters the hepatic sinusoids bound to protein, crosses the space of Disse, is taken up by the hepatocytes for temporary storage and is excreted into the bile. Hepatocyte uptake depends on the status of microcirculation, the integrity of the liver cells, and the saturation of their uptake and storage sites. Protein carriers, identified as Y and Z proteins, facilitate the transport of these tracers across hepatocyte membrane. Once within the cell, the tracer may undergo conjugation in the reticulum, or directly enter the Golgi apparatus for excretion in the biliary network. The classic approach for assessing liver cell function using dyes has been to determine the serum level of the dye in a single sample obtained 20 to 45 minutes after administration. This approach may lead to an erroneous interpretation. The test is much more sensitive, reliable and selective if the initial removal capacity is assessed by obtaining specimens at 5-minute intervals for a total of at least 20 to 30 minutes. This approach is recommended for persons in whom subclinical liver disease is suspected. One of the most reliable tests for differentiation between hepatitis and biliary atresia is the rose-bengal test (Rosenthal, 1969). 653

The fluorescent dye rose-bengal, the potassium or sodium salt of tetrachlorotetraiodoflurescein, was first reported as a useful agent in the determination of the functional state of the liver by G. D. Delprat in 1923. It was believed that rose-bengal dye was removed entirely from the blood stream by the liver parenchymal cells and excreted into the bile where there was virtually complete recovery in the stool. Rose-bengal, which was used in clorometric tests, received little publicity until 1954 when G. V. Taplin combined rose-bengal (RARB). With this new agent, extensive evaluation as to what the body does with rose-bengal was made possible. Using rabbits, Taplin showed that the phagocytic Kupffer cells play no part in the uptake of rose-bengal. With further testing, he showed that rose-bengal is neither obsorbed from the gut nor from the bowel (Rosenthal, 1969). Indicating the excellent tracing characteristics of RARB, other experiments have shown that rose-bengal does not combine with red blood cells while in the blood stream (Biorek and co-workers, 1960), and that although rose-bengal binds itself to albumin, this does not affect the catabolism of albumin, and thus does not upset normal physiology (Bocci, 1961). There is little uptake of rose-bengal into extravascular space; the liver begins extracting rose-bengal into the bile within a few minutes after injection into the blood stream. Als,o , rose-bengal is not decomposed by the liver (Biorek, 1960), although recent studies seem to indicate that there is a continuous dissociation of 131 1 with rose-bengal and that some urinary excretion may be in the form of free 131 1 (Freeman and co-workers, 1968). Furthermore, although rose-bengal consists of several components, it has been determined

654

T. Prasad, A. M. K. Badreldin and M. A. Ismail

that the blood disappearance curve is not due to the biological situation. RARB has thus proved to be a very good tracing agent and provides a popular test of biliary function. The external patterns of 131I-rose-bengal and studies of appearance of radioactivity in feces make this radioisotopic form of the dye particularly useful in the differential diagnosis of liver dysfunction. RARB also may be used in liver scanning. Visualization of the liver by radionuclide imaging is dependent upon physiologic processes involving the hepatocytes and Kupffer cells. The hepatocytes which comprise about 60% of the mass of the liver have the ability to selectively accumulate and excrete material from the blood. This process is used to evaluate hepatobiliary function when iodinated rose-bengal is administered to the patient. The hepatocytes selectively accumulate and excrete RARB. A normal liver accumulates and then excretes most of the dose into the intestinal tract. via the biliary system. with only 5% or less recovered in the urine. RARB is retained in the liver in cases of intrahepatic or extrahepatic obstruction. As a result of conjugation of the rose-bengal with reflux into the blood. activity may be seen in the kidneys in such patients and the recovery in the urine may be as much as 35 to 40%. Serial scans are of value to determine the p.a tency of the biliary system and the degree of obstruction (Bockus. 1976). In studying the biliary kinetics. much attention was directed to the analysis of the liver uptake-excretion curves. Scintillation counters over the hepatic region and over the head (to represent the activity in the blood. considering the head to be a large pool for the blood) are usually used to measure the activity in both the liver and blood. The curves obtained for every patient may be considered as characteristic "patterns" and they correlate with the state of the patient. Several techniques. including some based on mathematical modelling. have been utilized to study the hepatobiliary system. using kinetics of this tracer (Ismail and others. 1980; Truco and co-workers. 1966; Waxman and others. 1972; Cars on and Jones. 1979; Saffer and co-workers. 1976). In this paper we show how shape descriptors can be utilized effectively to extract useful information from the uptake-excretion curves associated with RARB without the need to model the hepatobiliary system mathematically. In this context. a new technique for the analysis of such patterns. based on their shapes. is described. and the applicability of the proposed algorithm to practical data is demonstrated. DERIVATION OF SHAPE DESCRIPTORS The technique described here is a newly developed algorithm that can handle any pattern whether this pattern is a single-valued function or a general overlapping loop in two or

more dimensions (Badreldin. 1980; Badreldin and co-workers. 1980). We start the formulation with considering the general case of an n-dimensional closed curve r in an orthogonal system with parametric representation

z(R,) = ( x

(1)

(R,). x

(2)

(R,) ••••• x

(n») (,0

where R, is the arc length with reference to a starting point

x

(2) Xo

o

'

•••

,

The arc length is given by: k E

j=l (n) (n» 2 ) 1/2 + . . . + ( x j +1- X j where k is the point number, k = 1,2, .••• N. with N denoting the number of points on the curve (Fig. 1).

x

-0

~l

Fig. 1 Every x(i)of the n-coordinates (x(l), x(2) .••• x(n» can be expressed as a function of arc length. if the curve r is traced. As an example. let us consider the description of the rectangular shape given in Fig. 2(a). The two coordinates Xl and x can be expanded 2 as functions of the·cumulative arc length as shown in Fig. 2(b). Each of these functions is then expanded in Fourier series.

Automated Classification and Identification of Liver Dysfunction

655

then the coefficients [a{i), b{i)] cannot be m m used since they contain no information regarding these characteristics. In other words, we are seeking some shape descriptors that are invariant under translation, rotation and changes in the starting point, properties that are not satisfied by the ordinary coefficients [a{i), b{i)]. m m

'ol

In order to get an expression for the curve r using formula (2), a vector representation ~ is used so that

z

=

(4)

~ is the unit vector in the xCi) -

where (0)

direction.

Fig. 2

Substituting equation (2) into (4), In general, if we have a clo~i~ loop in ndemensions, the coordinate ~ (i), defined as the i-th coordinate, can ~e expressed as:

~i)

(R.)

CS) (2)

i

1, 2, ... , n,

k

1, 2, ••• , N.

sin (2llmi ) L k

Let us define the following quantities:

where, M ~ number of coefficients in the Fourier expansion, and L

~

total length of the trajectory.

The coefficients a{i) a{i) and b{i) can be o 'm m evaluated numerically from the following approximate relations: a

a

(i) 0

(i) m

N

a b

{ L ~i»/N

(2) 12 II + a 0

a (I)

a

-0

0

+... +

a

en) 0

I -n

m

en) a (I) (2) I + am 12 + .•. + a m -n m II

m

b (2) ben) I b (I) 12 + ... + m -n m II + m

(6)

k=l N

21lm (i) 2 ( L cos (Lik» ~ k=l

IN

(3)

Substituting equations (6) into (S), we get M

b (i) m

N

2 ( L k=l

21lm (i) sin{Lik» ~

IN

+ L

{a cos m=l-nl

= a

-0

+ b where N

number of points and m = 1,2, .•• ,M.

Formula (2) can be used for the reconstruction of the curve. It can be shown that if information concerning the absolute position or rotational orientation of the curve is needed,

-nl

(7)

sin (2llmi )} L

k

where k = 1, 2, .•. , N The vectors a

-nl

( 2) {a (1) , am '

m

•• _,

a (n)} and m

656

~

T. Prasad, A. M. K. Badreldin and M. A. Ismail

{b~l), b~2), ••• , b~n)}

=

where m = 1, 2, •.• , M can be represented in magnitude and direction using n-dimensional spherical coordinate transformations. In other words, a and b can be represented in n-dimensions-Wy a ~itude and (n-l) angles giving the direction of every vector in the space. Thus the representation takes the form: ( I a I, Cl , Cl , . , . , Cl 1) and m

1

n-

2

( Ib I, B , B , ••• , B 1)' m

1

n-

2

These magni tudes

can be evaluated from:

la

m

1= (

n (i) 2)1/2 r (a ) , m=1,2, ••. ,M i=l m

In this study, the uptake of RARB by the liver and its decay in the blood were measured for two hours in sixteen subjects. Five of these subjects were normal, six were cirrhotic and five patients were having obstructive jaundice. As a first step in this analysis it was assumed that the two outputs, one representing the percentage activity in the blood and the other representing the activity in the liver, can be drawn against each other in a plane. Having three identified groups in our sample, the average characteristic curves for each group are shown in Fig. 4. These curves are considered

( 8)

1.0

and n (i) 2 ( r(b i=l m

») 1/2 , m=1,2, •.. ,M

Ib mI

(9)

Therefore, we have M magnitudes for the a's and the same number of magnitudes for the b's. It can be shown that the coefficients A given by m

1.0

Fig. 4. A

m

(la

2

I

m

+ Ib mI

2 1/2

)

,

m=1,2, ••• ,M

(10)

represent a new class of shape descriptors, that are invariant with respect to translation, rotation and changes in the starting point. Other types of descriptors that are also invariant with respect to size or dilation are derived elsewhere (Badrelden, 1980). DESCRIPTION, IDENTIFICATION AND CLASSIFICATION OF THE UPTAKEEXCRETION CURVES The algorithm developed in the preceding section may be applied with efficiency to describe the uptake-excretion curves. As mentioned before, usually we have two curves representing the radioactivity in the blood and the liver respectively. Typical curves in a normal case are given in Fig. 3.

Average characteristic curves for all groups N: Normal, C: Cirrhosis, IHO: Intrahepatic Obstruction and EHO: Extrahepatic Obstruction.

to be patterns in two dimensions, and the shape descriptors were calculated for each patient. Thus, every patient now has a vector of shape descriptors that are derived from his two original data curves. Based on these descriptors, any patient may be assigned the appropriate class utilizing any suitable classification algorithm (Duda and Hart, 1973; Tou and Gonzalez, 1974). Consideration of the first two shape descriptors for every patient in the sample leads to the scatter diagram shown in Fig. 5 which shows clearly how powerful the proposed algorithm is for the classification of patients into different groups. A

0.20 0.16 100%

0.12

..'" ..... "'> ..... ..., .... ...... .,." '" .. '"

0.08

,', : 0 \

~ ....O_}IHO 0.04

c u

u 0

o ....

o 1 0

Fig. 3.

time(min.)

Schematic showing the radioactivity in both blood and liver (in percentage of an initial dose).

Fig. 5.

o

N

,,;

VI N

,,;

,.,o ,,;

1

Scatter diagram showing the clustering of members of each group utilizing the first two shape descriptors Al and A2 for every patient.

Automated Classification and Identification of Liver Dysfunction The proposed algorithm offers an alternative to the mathematical modelling approaches usually adopted in such cases. It can be looked at also as an automatic data reduction method or feature extraction technique that is sensitive to the variations in the shapes of these signals, which one usually looks for in diagnosis, prognosis or monitoring. The proposed methodology offers an automatic approach for the classification and identification of liver dysfunction. CONCLUSION This paper presents a new approach for automatic description, identification and classification of liver dysfunction based on the dynamics of radioactive rose bengal as a tracer, utilizing a newly developed class of shape descriptors. These descriptors are very sensitive to the variations in the uptake-excretion curves, leading to features of potential importance in differential diagnosis of liver dysfunction, and consequently in both prognosis and monitoring. The effectiveness of the proposed methodology is demonstrated using real life data. It is envisaged that the methodology explored in this paper will find extensive applications in the study of physiological processes, with potential benefit to biomedical and health care sys terns • ACKNOWLEDGEMENTS The supports extended by NSERC (National Science & Engineering Research Council) of Canada and the University of Petroleum and Minerals, Dhahran, Saudi Arabia, for this research are gratefully acknowledged. REFERENCES Badreldin, Amira M.K. (1980). Shape Descriptors for Multidimensional Curves and Trajectories. M.A.Sc. theses, University of Waterloo, Waterloo, Ontario, Canada. Badreldin, A.M.K., Wong, A.K.C., Prasad, T. and Ismail, M.A. (1980). Shape Descriptors for n-dimensional Curves and Trajectories. Proc. IEEE Int. Conf. on Cybernetics and Society, Boston, Ma., October 8-10, 1980, pp. 713-717. Biorek, G., Gardell, S., Carlberger, G. and Meurman, L. (1960). Excretion of Rose Bengal in Bile. Nature, 185, 847. Bocci, V. (1961). Distributi~and Fate of Rose Bengal. Nature, 189, 584. Bockus, H.L. (Ed.)(1976). -castroenterology, vol. 3: The Liver, Gallbladder, Bile Ducts and Pancreas. W. B. Saunders Co., Toronto. Carson, E. R. and Jones, E. A. (1979). Use of Kinetic Analysis and Mathematical Modeling in the study of Metabolic Pathways in Vivo. New England J. Med., 300, Two parts, 18, 1016-1027 and 19, 10781086.

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Duda, R. and Hart, P. (1973). Pattern Classification and Scene Analysis. John Wiley and Sons, New York. Freeman, L., Kay, C. and Derman, A. (1968). Renal Excretion of Radioiodonated Rose Bengal - A Pitfall in the Interpretation of Rose Bengal Abdominal Scans. J. Nuclear Med.,~ 227. --Ismail, M. A., Prasad, T., Quintana, V. H. and Badreldin, A.M.K. (1980). Deterministic versus Stochastic Models in Studying Hepatobiliary Kinetics. Proc 11th Annual Pittsburgh Conf. on Modeling and Simulation, Pittsburgh, Pa., May 1-2, pp. 81-82. Rosenthal, L. (1969). Application of Radioiodinated Rose Bengal and Colloidal Radiogold in the Detection of Hepatobiliary Disease. Warren H. Green, Inc., St. Louis, Missouri, U.S.A. Saffer, S. I., Mize, C. E., Bhat, U. N. and Szygenda, S. A. (1976). Use of Nonlinear Programming and Stochastic Modeling in the Medical Evaluation of Normal-Abnormal Liver Function. IEEE Trans. Biomed. Eng., vol. BUE-23 , 200-207. Tou, J. T. and Gonzalez, R. C. (1974). Pattern Recognition Principles. Addison-Wesley Pub. Co., Inc., Reading, Massachusetts. Waxman, A. D., Leins, P. E. and Siernsen,J. K. (1972). In Vivo Dynamic Studies of Hypatocyte Function: A Computer Method for the Interpretation of Rose Bengal Kinetics. Comput. & Biomed. Res., S, 1-13.