An attempt to analyze locomotion of leukemia cells by computer image processing

Compur. Biul. Med. Vol. 9, pp. 331-344. 0 Pergamon Press Ltd. 1979. Printed in Great Britain.

AN ATTEMPT OF LEUKEMIA

OOIO-4825/79/1001-0331

SOZ.oO/O

TO ANALYZE LOCOMOTION CELLS BY COMPUTER IMAGE PROCESSINGt

K. LEWANDOWSKA, J. DOR~~ZEWSKI Department

of Biophysics

and Biomathematics, Marymoncka 99,01-813

Medical Center of Postgraduate Warszawa, Poland

Education,

and G. Division

HAEMMERLI

and P. STRXULI

of Cancer Research, Institute of Pathology, University Birchstrasse 95, 8050 Ziirich, Switzerland

(Received

8 September

1978; in revised form

15 February

of Ziirich,

1979)

Abstract - Phase contrast photographs of locomotive leukemia cells from a time lapse film were analyzed by an image processing computer system. Various structural and directional parameters were chosen to characterize dislocation and shape changes of a moving cell. A correlation could be established between the cellular image seen in time lapse films and the numerical shape configuration based on automated image analysis. It seems, therefore, that the parameters chosen represent a basis for further evaluation of the quantitative model of cellular locomotion. Image processing microcinematography

computer system Cell locomotion

L 5222 leukemia Digital image Cell shape analysis

cells

Time lapse

INTRODUCTION Many biological phenomena are connected with the ability of cells to move. We have, for instance, good indirect (histological) evidence for the involvement of cell motility in penetration and spread of cancer [ 11. Direct (cinematographic) evidence is sparse [2] due to the technical difficulties of visualizing cell motility in the living animal. In vitro models are therefore indispensable. As a first step in this direction, we have recorded by time lapse cinematography the behavior of leukemia cells in culture chambers [3,4]. So far, our method of determining cell motility mainly consisted in preparing cell contour drawings at identical time intervals from time lapse film sequences. From these drawings, the pathways of locomotive cells, their speed and the changes of their shape could be determined. However, it was felt that the complex phenomenon of cellular motility demands an evaluation by a method that yields more objective and precise results. For this reason, a computer image processing system was chosen. A similar approach has been described for the recognition and pairing of chromosomes [S], for the identification of cell cycle phases [6], for the determination of sperm cell velocities [7], also for the analysis of macrophage and fibroblast motility [S]. In this communication, the methodology ofan attempt at a computerized evaluation ofthe locomotory activity of leukemic cells is presented. Based on time lapse films of L 5222 rat leukemia cells, several quantitative parameters were chosen for the determination of pathway, speed and shape changes of locomotive cells. It seems that the selected parameters adequately and, in a quantitative way represent the cellular images produced by microcinematography. We, therefore, believe that this automated processing system provides a basis for a detailed and objective analysis of cellular motility.

t This study was performed within the E.O.R.T.C. Cell Surface Project Group. The study was supported by grant No. 10.4of the Polish Academy of Sciences, by the Swiss Cancer League Credit No. For.Ak.75 (5) and by the Ziirich Cancer League. 331

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K. LEWANDOWSKA, J. DOROSZEWSKI,G. HAEMMERLIand P. STR~ULI

PRESENTATION

OF

THE

CELL

MODEL

The cells used for the computer analysis originate from the transplantable unclassifiable leukemia L 5222, propagated by either iv. or i.p. injection into inbred BD IX rats [9]. Details of the motile behavior of L5222 were described elsewhere [lo]. To summarize : L 5222 cells readily attach to a glass substrate. When they are attached, they do not flatten but stay spherical and display three types of motility: surface motility, on spot motility, and locomotion. Surface motility, performed during a resting state in which the cells have assumed a round configuration, is inconspicuous in time lapse films. It can be better visualized by SEM [ll]. When the cells are engaged in either on spot motility or in locomotion, they are polarized by the extension of one major projection. During on spot motility, this extension is used for fastening the cells to the substrate or to other cells and is then called a “foot”. If the cell proceeds from on spot motility to locomotion, the foot trails at the end of the locomotive cell and becomes the “tail”. During locomotion, small cytoplasmic extensions are rapidly extended and retracted from the anterior part while the tail remains rather rigid. Changes in direction occur infrequently and are carried out by bending of the cell body into the new direction. The speed of locomoting cells varies between 1 and 7 pm min- I.

COMPUTER

IMAGE

PROCESSING

SYSTEM

The computer analysis was performed on a Polish computer image processing system CPO-2/K-202 [12,13]. The CPO-2 system consists of a TV camera that introduces the picture, a digital converter and a memory. It is connected to the minicomputer K-202. The whole digitized picture, consisting of 512 x 512 points in 16 grey levels, is stored in the memory. The intensity quantization levels can be changed by the operator or by the computer program. The system also comprises two TV monitors and a joystick marker for changing the contents of the picture in the memory, or for selecting objects for special processing. The software developed for the CPO-2/K-202 system consists of the picture processing subroutine library PICASSO (for references see [12,14]) developed at the Institute of Biocybernetics and Biomedical Engineering, Warsaw. The cells to be analyzed were chosen from 16 mm black and white Kodak Plus X reversal film. They had been filmed with a Wild Fluotar 100/1.30 oil phase contrast objective at intervals of 2 sec. For each cell, several positions were analyzed. The original image was first converted into a digitized picture in 16 levels of grey. It was then transformed into a binary picture by means of the dynamic thresholding method [ 143 and subjected to the final “cleaning” and closing of the contour, if necessary. The original film photograph, its digitized image displayed on the TV monitor, the final binary picture and the cell contour are presented in Fig. 1.

SELECTION

OF

PARAMETERS

In order to analyze locomotive cells with regard to : dislocation, speed and changes of shape the following quantitative parameters 1. The center of mass for the cell body and for the whole cell. 2. Direction of the main axis of the whole cell. 3. Cell area and perimeter. 4. Directional characteristics of extensions. 5. Quantitative cell shape representation. 1. Determination

direction of movement, were selected :

of the center of mass

The center ofmass determined (a) for the whole cell including extensions and (b) for the cell body minus extensions as schematically presented in Fig. 2. The center of mass is determined as the average of the coordinates of all points within the cell contour. In a first approximation, a homogenous “mass distribution” within the whole cell is assumed. Changes in the position of the center of mass indicate dislocation, while differences between the two centers (a) and (b) express possible changes in shape that occur during dislocation.

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333

Fig. 2. Determination of the center of mass of a locomotive cell. x (full line): Axis of the reference coordinate system, parallel to the frame margin. a: Center of mass of the whole cell. b: Center of mass of the cell body. Dotted line: main axis of the cell. 4 : Angle of the main axis.

2. Direction of the main axis

The main axis indicates the orientation of the cell with regard to the margin of the film frame. In polarized cells, the main axis seems to be connected with the direction of movement. The main axis is defined as the line corresponding to the minimal moment of inertia and for symmetric shapes it represents the longest symmetry axis. For asymmetric forms, the main axis divides the cell in such a way that the sum of all perpendicular connections between points of the contour and of the axis is identical on both sides. In the coordinate system connected with the center of mass, the direction of the main axis is given by the angle 4 according to the equation : O<$Glr

tan(2fj) = *, Y n

x

n

where I, = 1 y; and I, = 1 x3 are moments i=l

of inertia about

the x and y axis,

i=l

respectively, and I,, = ii1 xjy, is the moment of deviation. 3. Area and perimeter Determination of the area of the whole cell together with the length of the cell contour gives information on cell size and shape.

Fig. 3. Determination of the cell body axis. b : Center of mass of the cell body. connecting the center of the body with main axis of the extension (angle 6).

and characteristics of extensions. x : Reference coordinate Full line: direction of the extension determined by the line the center of the extension tangle 4’) (see text). Dotted line : Cell body, 0 Cell extension, m Cell part not considered as an extension.

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K. LEWANDOWSKA, J. DOROSZEWSKI, G. HAEMMERLI and P. STR~ULI

4. Determination

and characteristics

ofextension(s)

The presence of extension(s) is established by determining those parts of a cell that lie outside the area computed as representing the cell body (Fig. 3). As a first step, the cell body is defined by fitting a circle to the largest part of the cell. This is achieved by means of the circular propagation procedure [14] that estimates the center and the radius of a circle rendering the best approximation of the main part of the cell. The part of a cell lying inside the circle is called the cell body, while those parts which lie outside of the circle are treated as potential extensions. In the next step. the perimeter of these potential extensions is determined. When the fraction of the perimeter which is in immediate contact with the cell body is small in comparison with the whole perimeter (cf. [14]), this part of the cell is considered an extension. If a cell is elongated and closer to an ellipse than to a circle, some of the cell parts left outside the body will not be treated as extensions. This means that the discrimination between a significant extension and minor variations of the cell periphery are objectively carried out by the computer. A cell can have one or more extensions of varying size. The areas of the extensions are computed and, for the largest one, further characteristics, i.e. direction and shape, are determined. This is done on the basis oftwo angles. The first angle (4’) is given by the segment connecting the center of the cell body with the center of the extension represented by the center of mass of the extension which is determined separately. The second angle (4”) is given by the main axis of the extension (i.e. the axis of minimal moment of inertia determined for the extension separately). The first angle provides information on the position of the extension with regard to the cell body, the second is a parameter for determining the shape of the extension. The difference between the two angles is small when the extension is long and thin, for a broad extension the two axes are almost perpendicular to each other. 5. Determination

of the cell shape

Two quantitative approximations and three global shape factors are utilized. The rectangular approximation of shape is determined by fitting the smallest possible rectangle around the cell contour along its main axis. The shape of the rectangle indicates the degree of elongation. Changes in the rectangle reflect changes in shape. For a more detailed description of the cell configuration, six sections are measured (see Fig. 4): 1. Distance between the contour points on the main axis. 2 Distance between the contour points along the line that passes through the center of mass and that is perpendicular to the main axis. 3. and 4. Distances perpendicular to the main axis and passing through points of the main axis half way from the center to the contour.

Fig. 4. Determination of the cell shape by application of the rectangular approximation and the sections. x : Reference coordinate axis. a: Center of mass of the whole cell. 4 : The main axis angle (see Fig. 2). The longer side of the rectangle lies parallel to the main axis of the cell. Open circles represent points at the cell contour determined by the six sections (defined in the text).

Fig . 1. Ima ge processing steps in the CPO-2 system. (a) Microphotograph ofa leukemic ( fro] ma pha: se contrast time lapse film. (b) Digitized image of the cell displayed on the TV the CF ‘O-2 system. (c) Binary picture resulting from the processing. (d) Contour of the image.

L5 222, tnitc3r of lary cell

Fig. 6. Sequence of a locomotive L 5222 leukemia cell. The arrow beside the cell in position I indicates the direction of movement. An erythrocyte on the left serves as marker. Phase contrast: optical : x 900. magnification

336

Computer analysis of cell locomotion

331

5. and 6. Distances parallel to the main axis and located half way between the center and the contour. In this way, twelve points of the contour can be determined which, if connected, give a more detailed image of the cell. Global shape factors are used to characterize the cellular shape by means of a single numeral. Global shape factor values are not dependent on the position, size and direction of the cell. As they describe different aspects of the cell’s shape, it was decided to use the Malinowska factor [15], the Haralick factor [16] and the Blair and Biss factor [17] simultaneously. The Malinowska factor is based on the ratto of the perimeter to the area and allows the computation of changes in shape with regard to the complexity of the cell contour. The Malinowska factor is determined as follows:

L and S denote the perimeter and the area of the cell, respectively. The value of the Malinowska factor increases when the cell contour becomes more complex. For a circle it is equal to zero. The Haralick factor also serves for determining the complexity ofcontours. It is defined as :

where p is the mean radial coordinate of points on the cell contour with respect to the center of mass and IScorresponds to the r.m.s. deviation of the coordinates. As was the case for the Malinowska factor, larger values of this parameter correspond to complex contours, while zero values are obtained for round cells. The Blair and Biss factor expresses the extent of a cell’s elongation. It is calculated as S

fBL = (2a S[ rz ds)“’ ’ S

where S denotes the cell area, r is the distance between the area element ds and the-center of mass. The integration is performed over the whole cell surface. To illustrate the properties of the global shape factors, we have chosen a few examples of different shapes that a cell can exhibit during the movement. They are presented in Fig. 5. Shapes A, B, C, D and E represent gradual changes from a smooth circular cell to one with a complex contour. The values of the Blair and Biss factor are almost identical for forms A, B and C; those for forms D and E are very close to the former three. This demonstrates that the Blair and Biss coefficient cannot distinguish between a smooth circle and a circle with a complex contour. The values of the Haralick factor increase with the complexity of the contour, but they fall within the small range of values from 0.02 to 0.09. The Malinowska factor values are small for shapes A and B but increase with the complexity of the contour. The value we obtained for form E was 15 times greater than that for B. The contours of the forms F-K represent various extents of elongation and changes of shape. The values of the Blair and Biss factor increase with the overall elongation of the shapes. However, this coefficient does not permit to distinguish G from H, and neither does the Haralick factor. For both figures, the mean unit distance from the center to the contour is identical. On the other hand, G and H can be told apart by the application ofthe Malinowska factor, because G is smooth if compared to H. The ratio of the perimeter to the area appears to be almost identical for C and F, and D and G. This demonstrates that higher values of the Malinowska coefficient correspond both to an elongated smooth form and to a circular form with a complex contour. The highest values for both the Blair and Biss and the Haralick factor are found for forms I and K. Form I corresponds to the image of a polarized cell. Form K represents the aspect of a cell changing its polarization. In general, it can be said that, while

338

K. LEWANDOWSKA,J.

DOROSZEWSKI,G.HAEMMERLI

and P. STR~LJLI

F

.K 0.30.

.E H K:,

'G D.80

0.20.

.K .I

-F .H 0.10.

D. -G F:c

I

0 ’

8. .A fMA

.E -D *C 0. 'A

'F t:D rrn

fHA

0.90

HsG

1.0

fB1

Fig. 5. Properties ofglobal shape factors. Top: examples ofdifferent patterns selected for the analysis of shape factors. Bottom : global shape factors.f,, : Malinowska factor&,: Haralick factor,&, : Blair and Biss factor. Ordinates : values obtained for the different forms shown on top (abstract numerals). Left scale refers tofu, and fnA. right scale (reversed) tofa,.

the Blair and Biss factor describes the overall elongation of a shape without taking into account contour complexities, an increase in value of the Haralick factor reveals an uneven distribution of the cell contour. The highest values are reached for elongated shapes. The Malinowska factor cannot distinguish between different shapes but can be useful to distinguish between forms with a similar elongation, as was the case for forms G and H.

APPLICATION

TO THE

CELL

MODEL

To illustrate the applicability of the presented parameters to our cell model, we have chosen a locomotive L5222 cell in its characteristic polarized shape (Fig. 6). The cell stopped locomoting at the end of the sequence, became spherical, and then again produced extensions. Ten frames from a time-lapse sequence were selected that represent the changes of shape occurring during the locomotive activity. The time intervals between the positions are not identical. The different parameters were computed for each frame after its transformation into a binary picture. The subsequent positions of both the center of mass of the whole cell and of the cell body minus extension(s) are presented in Fig. 7. The difference in the location of the two centers results from the presence of one large extension. When the cell rounds up (position 9), the two centers coincide. Determination of the velocities for each of two consecutive positions revealed that, at the beginning, the cell moved at a relatively high speed (ca. 6 pm min- ‘) then slowed down, until it came to rest (positions 8 and 9) and then moved again. The configurational changes of the cell, as determined by the rectangular approximation of

Computer

analysis

of cell locomotion

339

26.

lo-

2'5

2'9

.

35

Fig. 7. Position of the centers of mass during locomotion. Abscissa and ordinate: distances (in pm) to the border of the film frame. Open circles and full line: coordinates of the center of mass for the whole cell. Full circles and dotted line: coordinates of the center of mass for the cell body without extensions. Numbers l-10 correspond to the subsequent positions of the cell from the time lapse sequence (Fig. 6). Small numbers along the pathway of the cell indicate the velocities computed for the center of mass for the whole cell and expressed in pm min- ‘.

the shape, are shown in Fig. 8. The longer sides of the rectangle he parallel to the direction of the main axis. For most of the positions, the rectangle corresponds to the actual elongation of the cell. For some positions (positions 1, 2, 9) however, we obtained squares. The phase contrast photographs show that such forms are produced by the disappearance of the extension and by broadening of the cell body perpendicular to the main axis (see Fig. 6). With the exception of position 2, the elongation of the cell, expressed by the longer sides of the rectangle, is in good accordance with the direction ofthe extension (full lines). For the cell in position 2, the direction of the main axis of the cell body differs from the direction of the extension. This is due to the broadening of the cell body perpendicular to the extension and to the existence of a second small extension. The reversal in polarization of the cell in positions 6 and 7, clearly recognisable in the phase contrast photographs (Fig. 6), appears as a change of almost 180” in the direction of the extension. The main axis of the extension (dotted lines) is almost perpendicular to the direction of the extension in positions 3,4,5 and 10. This effect results from the appearance of rather short and wide extensions. The smallest difference in the angles 4’ and 4” for the extension in position 8 corresponds to a very thin extension. The six sections (see Fig. 4) were also calculated for the ten positions of the locomotive cell and are presented in Fig. 9. The shapes obtained by the application of these sections closely resemble those of the phase contrast photographs. Careful analysis, however, reveals that for some positions, the “quantitative computer scheme” is not a strict copy of the cell. When the extension is not strictly parallel to the main axis of the cell, or when it is rather small, it is not always recorded in the computer image. This is the case for the cell in position 8, and partly for the cells in positions 1, 2, 6 and 7. This is mostly due to the fact that, even for large extensions, there are not enough points for their description.

340

K.

LEWANDOWSKA,

J. DOROSZEWSKI, Ci. HAEMMERLI and P. STRKULI

26.

6 14.

lo-

6

25

29

+

Fig. 8. Shape changes during locomotion determined by the rectangular approximation. Abscissa and ordinate as in Fig. 7. The same sequence as in Fig. 7. The longer side of the rectangle corresponds to the main axis of the cell. The direction of the largest extension (full line) and the main extension axis (dotted line) are indicated for each position. Open circles: center of mass of the whole cell. Full circles: center of mass of the cell body. To avoid overlapping the dimensions of the rectangles are reduced by 6.6.

The two lines that characterize the major extension of the cells are also shown in Fig. 9. The full line connecting the center of the body with the center of the extension describes the localization of the extension with respect to the cell body. The dotted line represents the main axis of the extension. When the dotted line is perpendicular to the full line, the extension is broad. The cell body area and the area of the whole cell, also computed for the ten positions, are given in Fig. 10(a). The area of the whole cell decreases slightly from position 1 to 2, increases from position 2 to 4, decreases from position 7 to the minimal value corresponding to the almost spherical cell in position 9, and increases again toward position 10. The highest area values belong to cells with a relatively large extension (positions 4,s and 7) with the ratio of the extension area to the cell body area reaching values of 0.3-0.35. For positions 1 and 2 where the ratio is 0.1, the cell is closer to a spherical shape, and only a small part of cellular material belongs to the extension. This observation is confirmed if the values obtained for the whole cell area are compared to those of the cell body area. An increase in the whole cell area (positions 3-4) is accompanied by an enlargement of the extension. In position 9 the two centers coincide but the area of the body is slightly lower than the whole cell area. This is due to the existence of small parts of the cell that are neither included in the body nor recognized as extensions. The increase of the two areas in position 10 reveal the reappearance of the extension. The perimeter values for cells in the different positions are given in Fig. 10(b). Changes in the perimeter together with those of the area suggest : (a) an increase in the complexity of the cell contour for positions l-2 and 5-6 (increase in perimeter values, decrease in area values), and confirm (b) a rounding up of the cell in positions 7-9 (decrease in both values).

Computer analysis of cell locomotion

25

29

341

33

Fig. 9. Shape changes during locomotion determined by sections. Abscissa and ordinate as in Fig. 7. Same sequence as in Figs. 7 and 8. The shape of the cell in the different positions is given by the connections of the contour points determined by the six sections. The two axes computed for the extension are the same as in Fig. 8. The cellular dimensions are reduced by 5.0.

When we compare the changes in global shapefactors [Figs. 10(c)-(e)] with the changes of shape illustrated in Fig. 9, we can gain a better understanding of the changes taking place in cellular shape. We observe an increase of the Blair and Biss factor [10(e)] from position 1 to 4 together with an increase of the Haralick factor [10(d)]. This increase represents the elongating of the cell from position 1 to 4 connected with the loss of symmetry around its center. Subsequent increases and decreases in values of the Malinowska factor [Fig. 10(c)] observed from position 1 to 4 indicate changes in the complexity of the cell contour. From position 1 to 2 and from 3 to 4, the contours become more complex ; the contour in position 3 seems to be relatively smooth. This is indicated by a Malinowska factor value which is lower in spite of the elongation. A slight rounding-up of the cell (position 4-5) is indicated by the decrease in all three coefficient values. From position 5 to 6, the cell elongates slightly and its contour becomes more complicated.‘Concurrently, all factors increase, especially that of Malinowska. The transition from position 6 to 7, regardless of the change in polarization, is characterized by a smoother cell conto.ur (note that in position 6, two extensions are seen). Rounding-up of the cell from position 7 to 8 is expressed by the drastic decrease of the shape factors. The Blair and Biss factor together with the Malinowska factor decrease further in position 9, whereas the Haralick factor slightly increases. This represents a retraction of the extension, but full symmetry (a circle) is not achieved. The decrease in the Blair and Biss factor and in the Malinowska factor cannot be entirely due to the cell’s moving out of the plane of the focus. Although, the process of rounding up is always connected with a slight change in focus, the cells do not “float” but retain their adhesions to the substrate [ 181. When the cell moves from position 9 to 10, the three coefficients increase again. It means elongation, reappearance of the extension (lack of symmetry), and a more complex contour : the cell is moving again. The above example shows that the simultaneous application of the three global shape factors can provide detailed information on changes in cellular shape. However, when

342

K. LEWANDOWSKA, J. DOROSZEWSKI, G. HAEMMERU and P. STRKULI

b

1

.

1

2

3

4

5

A

T_

6

7

8

9

10

Fig. 10. Area, perimeter and global shape factors computed for the locomotive cell. Abscissa: Positions of the locomotive cell according to Figs. 6-9. (a) Ordinate : Area in pm’. Full line : wholecell area. Dotted line: area of the cell body without extensions. (b) Ordinate: length of perimeter in pm. (c) Values of Malinowska factor: abstract numerals. (d) Values of Haralick factor: abstract numerals. (e) Values of Blair and Biss factor: abstract numerals.

applied separately, they could be misinterpreted. We believe, that the three global shape factors might prove to be of still more value when they are applied together but separately to the cell body and to the extension(s).

DISCUSSION Computer analysis of the film sequence of a locomoting leukemia cell provides more detailed and precise information than graphic evaluation alone. This is particularly true of the shape changes occurring during locomotion. Conventional graphic exploitation of film sequences allows a description of these changes in general terms, e.g. transition from a spherical to a polarized configuration and vice versa. By computer analysis, we can subdivide such transitions into distinct parameters which, by dynamic interaction, merge into the overall aspect of the locomoting cell. The parameters selected so far : center of mass, main axis, approximation of shape, area, perimeter and directional characteristics of the largest extension have proven to be useful, but additional features may be required in future studies. Computer analysis of cell locomotion entirely depends on the morphologic exploitability of time lapse films. Due to the optical limitations of phase contrast microscopy, many delicate changes in the architecture ofa locomoting cell are insufficiently or not at all recorded. It is by these changes, however, that the interplay of propulsion and adhesion that constitutes locomotion is ultimately expressed. The pertinent changes can only be visualized by scanning electron microscopy. The combination of this technique with microcinematography has initiated a new approach to studies on cell motility [19] and will provide a firm basis for investigating the mechanophysiology of cell locomotion. Such studies reauire a three-

Computer

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343

dimensional consideration of the cell, for which an adequate computer technology is not yet available. For pattern recognition of cellular locomotion, on the other hand, computer image processing may prove helpful. These patterns depend on distinct cellular configurations tenaciously maintained by various kinds of motile cells, e.g. the different classes of normal and neoplastic blood cells [4]. Within the cell type-dependent patterns, adaptations can be induced by external influences. L5222 cells are not only capable of locomoting in the spherical shape, as considered in the present communication, but also in a flattened shape if this is required by their microenvironment [20]. Considering such diversities, computer image processing might become an important tool wherever locomotion patterns are constituents of complex cellular systems. SUMMARY The ability of cells to move plays an important r61e in many biological and pathological phenomena as e.g. in penetration and spread of cancer. In the present work, the locomotory activity of leukemia L5222 cells in culture chambers has been studied by the aid of a computer system and the methodology of this approach is described. The analysis was performed on a Polish computer image processing system CPO-2 connected to the minicomputer K-202; the digitized picture consisted of 512 x 512 points in 16 grey levels. The cells to be analyzed were filmed with a phase contrast objective at intervals of 2 set on a 16 mm black and white film. In order to analyze locomotive cells with regard to dislocation, direction of movement, speed and changes of shape, the following quantitative parameters were selected: the center of mass, direction of the main axis, cell area and perimeter, directional characteristics of the largest extension. The cell shape was described by two quantitative approximations and three global shape factors. As an illustration of the applicability of the method and chosen parameters a film sequence representing typical changes of cell shape and positions during the locomotive activity has been analyzed in detail. It is concluded that the computer analysis ofa locomotive leukemia cell provides more detailed and precise information than graphic evaluation alone. The possibilities and limitations of this approach are discussed. Acknowledgements-The authors gratefully acknowledge the fruitful collaboration and stimulating discussions Mr. Z. Kulpa, Mr. A. Bielik, Mrs. M. Rychwalska and Mrs. M. Piotrowicz from the Institute of Biocybernetics Biomedical Engineering. It is a pleasure to thank Dr. L. Przpdka for his photographic work.

with and

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14. Z. Kulpa, A. Bielik, M. Piotrowicz and M. Rychwalska, Measurements of shape characteristics of moving cells using computer image processing system CPO-2. Prof. International Conf. on signals and images in medicine and biology BIOSIGMA Paris, pp. 286-292 (1978). 15. K. Malinowska, Evaluation of shape coarseness of fibre cross sections, Przeglad Wlokienniczy 4 (1975). 16. R. M. Haralick, A measure of circularity of digital figures, IEEE trans. syst. man cybernet. SMCd, 394-396 (1974). 17. D. J. Blair and T. H. Biss, The measurement of shape in geography: an appraisal of methods and techniques. Geography Department of Nottingham Univ. Bull. vol. 11 (1967). 18. G. Haemmerli (unpublished observations). 19. H. Felix, G. Haemmerli and P. Strluli, Dynamic morphology of leukemia cells. A comparative study by scanning electron microscopy and microcinematography. Springer, Berlin (1978). 20. G. Haemmerli, H. Felix and P. Strluli, Motility of L.5222 rat leukemia cells in the flattened state. Evidence against emperipolesis, Virchows Arch. B. Celf Path. 24,165-178 (1977). About the Author - JAN DOR~~ZEWSKI was horn in Warsaw, Poland on 8 November 1931. He attended the Medical Academy in Warsaw from 1949 to 1954. From 1954 to 1967 he worked in the Department of Medical Radiology of the Warsaw Medical Academy and since 1960 was Head of the Department of Radioisotopes. He worked on the methods of cell labeling and the kinetics of transplanted lymphocytes. In 1967 Mr Doroszewski began the work in the Medical Center of Postgraduate Education in Warsaw where, at present, he is an Associate Professor and Head of the Department of Biophysics and Biomathematics. His research activities center around the problems of cell adhesion, especially under flow conditions, and other fields of cellular biophysics. He is active also in the domain ofcomputer methods in medicine and is engaged in the research on methodological and formal aspects of diagnosis. He is Vice-President of the Committee of Medical Physics of Polish Academy of Sciences. About tbe Author - KRYSTYNA LEWANDOWSKA received her M.Sc. degree in biophysics

from Warsaw University in 1973. Since then she has been working in the Department of Biophysics and Biomathematics at the Medical Center of Postgraduate Education in Warsaw. The principal field of her interest are adhesive properties of blood and neoplastic cells. Her recent works have concerned leukemic cells engaged in active locomotion on solid substrata and its relation to cell adhesivity. About the Author - GISELA HAEMMERLIwas born on 12 July 1923. She received

from the Mainz Medical Pathology Department Research Fellow at the Resident in the Cancer include cell biology and

her Medical Degree School, Germany. Between 1955 and 1956 Dr Haemmerli worked in the of Georgetown University, Washington D.C. From 1956 to 1958 she was Sloan Kettering Institute, Xew York. Since then she has become Chief Research Division, IJniversity Hospital, Ziirich. Her principal interests the motility of normal and neoplastic cells.

About the Author - PETER STR~ULI was born

on 31 March 1918. He attended Medical School in Ziirich and Geneva and passed the State Board Examination and Medical Degree in Ziirich. He received training in gynaecology and obstetrics in Winterthur, Switzerland and Montreal, Canada. From 1956 to 1960 he was Resident at the Institute of Pathology, University of Ziirich. He became Chief Resident in 1960 and Head of the Department of Cancer Research in 1964. In 1965 he was awarded a Ph.D. for his work in experimental cancer research. Between 1967 and 1970 he was Research Associate in Washington, D.C. with the Armed Forces Institute of Pathology, Biophysics Branch and at Georgetown University. His special interest is invasive growth under the special conditions during local spread from a primary tumour.