Marc Nyssen
Erik Blockeel
Rene Bourgain
Marc Nyssen
Erik Blockeel
Rene Bourgain
For several years, the formation and evolution of thrombi in small arteries of rats has been quantitatively studied at the laboratory of PHYSIOLOGY and PHYSIOPATHOLOGY at the V.U.B. Global size parameters can be determined by projecting the image of a small arterial segment onto photosensitive cells. The transmitted light intensity is a measure for the thrombotic phenomenon. This unique method permitted extensive in vivo study of the platelet-vessel wall interaction and local thrombosis.
Now, a further development has emerged with the aim to improve the resolution of these measurements in order to get information on texture and form of the thrombotic mass at any stage of its evolution. Therefore a thorough understanding of how light propagates through non hemolized blood was essential. For this purpose, the MEDICAL INFORMATICS department developed a system to record and process digital images of the thrombotic phenomenon.
For the processing and attempt to reconstruct the thrombi, a model describing the light transmission in a dispersive medium such as flowing blood had to be worked out. Application of results from Twersky's multiple scattering theory, combined with appropriate border conditions and parameter values was attempted.
In the particular situation we studied, the dispersive properties of the flowing blood were found to be highly anisotropic. An explanation for this phenomenon could be given by considering the alignment of red blood cells in the blood flow. In order to explain the measured intensity profiles, we had to postulate alignment in the plane perpendicular to the flow as well. The theoretical predictions are in good agreement with the experimental values if we assume almost perfect alignment of the erythrocytes such that their short axes are pointing in the direction of the center of the artery. Conclusive evidence of the interaction between local flow properties and light transmission could be found by observing arteries with perturbated flow.
Thrombus formation and evolution are of primary interest in vascular research. Thrombi can occlude smaller vessels, disturbing the blood flow or even cutting it off completely. The result can be brain damage, paralysis or death due to lack of oxygen in the area of the brain, cut off from its normal blood supply by embolized thrombi.
For the study of several aspects of arterial thrombosis phenomena both on microscopic and macroscopic scales, an experimental environment was developed for "in vivo" thrombosis related investigations in small laboratory animals [1]. The delicate "in vivo" experiments require many precautions and parameter control was a major problem. Yet, a set up could be realized that gives reproducible results and enables us to study phenomena such as the complex interactions with the vessel wall, which are known to be of fundamental importance and cannot be simulated "in vitro".
In vitro experiments were successfully conducted by Didisheim and Grabowski [2]. For both "in vitro" and "in vivo" systems, thrombus detection can be performed optically, because the optical density for visible light ( 400 - 800 nm. wavelength) of thrombi is smaller than that of the surrounding whole blood.
Bourgain, Six and Andries [1] developed a sensor array with thirty ( two rows of fifteen or three rows of ten ) light sensitive resistors (LDR's), upon which the enlarged image of a mesenteric artery (white Wistar rat) is projected. In this segment a thrombus is induced following a standardized procedure. When the thrombus starts to grow, the increasing light intensity falling upon one or several LDR's generates electronic signals that can be monitored and processed into parameters that measure the evolution of the thrombotic mass.
The microprojection method gives excellent results but the resolution is limited by the number of sensors. Therefore, we attempted to increase the resolution of the recording system by using a television camera in combination with a digital image processing system to obtain a resolution of sixty image points or pixels per arterial diameter. The dimension of the resulting pixels is four by three square micrometer, hereby reaching the size of a typical blood cell projection.
With this resolution, small changes in thrombus size can be measured. The thrombus projected area is immediately obtained from the pixel array. Local thickness information can be deduced from the pixel intensity measurements in combination with the theoretical model and working hypothesis that are essential because we have only a single projection of the object at our disposal.
The experimental set up is similar to the arrangement described in [3], except for the fact that the LDR array is replaced by a high quality T.V. camera equipped with a Newvicon tube . The camera is kept in a fixed position behind the microscope (see figure 1). The illumination is provided by a stabilized light source of 100W, with fibre optics lightguide giving a very even field of illumination with small angular distribution in the axis of the microscope. An interference filter with passband at 700nm. placed right behind the halogene lamp delivers a quasi monochromatic beam near the isobestic wavelength of hemoglobin. The enlarged artery image is projected upon the camera tube, in the image plane of the optical system. The video signal is digitized into a 128 by 128 pixels image format with 256 gray levels resolution ( 8 bits ) by the VINCENT (*) image processor. Optical magnification is tuned so that the arterial diameter covers sixty pixels in the center of the image field leaving a strip of about thirty image elements at either side to cope with the unavoidable movements due to heartbeat and respiration. The lateral movements of the artery are compensated by software in the alignment program, in contrast to the LDR system, where these movements are followed by an optoelectronically controlled moving stage carrying the LDR's.
VINCENT digitizes incoming frames at video rate but sends one image per second to the VAX 11/785 computer through a parallel direct memory access (D.M.A.) channel. There, the images are stored in the hierarchic file system of the UNIX (**) operating system. The temporal sampling at 1 per second was judged to yield sufficient information.
A colour video monitor shows the captured images during the experiment.
Pseudo colour representation helps the operator to evaluate the illumination
conditions at all times. Recorded or processed sequences can be returned
to the VINCENT system from the VAX computer through the fast D.M.A. link.
A joystick pointer allows operator interaction or the determination of
coordinates in the picturefield. For both the VAX computer
and VINCENT system, all necessary utilities were written to allow easy
operation. The main philosophy was to consider the VINCENT system a UNIX
workstation and making all interactions between the two machines transparent
to the user.
Figure 1.
Let us consider a detailed cross sectional view of the artery on figure
2
Figure 2.
If we follow a pencil ray, entering the artery at P1, we see that it will undergo partial reflection at all interfaces it encounters and absorption and multiple scattering in the blood and absorption in the thrombus before it will finally hit the camera tube. As blood is the optically densest medium, most of the attenuation will occur in the blood mass. In general, we have:
The value of the definite integral of K(y) is called the optical path. If K were a constant ( which is not the case here ), the Lambert-Beer law would be found. In the case of flowing blood, we are confronted with a more complicated situation: the high concentration of anisotropic erythrocytes leads to orientation depending multiple scattering.
Indeed, when we examine the image formed by a typical artery in vivo
as shown by figure 3, we see that although the physical distance the light
travels is longest at the centre of the artery, the optical path is not
maximal there. This results in the "white band" visible on the
picture.
Figure 3.
An explanation for this phenomenon can be found if we combine the multiple scattering theory of Twersky [4] with the assumption that the erythrocytes in flowing blood are aligned, not only in the direction of the flow but also in a plane perpendicular to the vessel axis.
From symmetry considerations, there exist three possible configurations:
random positioning, long axes pointing to the centre of the artery or short
axes pointing to the centre. Figure 4 shows the three possibilities.
Figure 4.
For these three configurations, the optical pathway was calculated taking into account Twersky's results and appropriate parameters. One of the fundamental results, obtained by Twersky [4], is that the function K(y) is inversely proportionnal to the geometrical "shadow" of the projection obtained from the individual particles, perpendicularly to the propagation direction of the main bundle.
therefore becomes:
whereK1is independant of the direction of the particles. S(y) represents the projection of an erythrocyte, on a plane perpendicular to the axis of propagation.
We shall now evaluate this expression, for the arterial geometry we are interested in.
Figure 5 is situated in a plane, perpendicular to the blood flow. R
corresponds to the inner radius of the artery.
Figure 5.
In the surrounding of location P (fig. 5), we postulate that the cels flow by in perfect alignation. For the purpose of this qualitative evaluation, we approximate the geometry of an erythrocyte by a rectangle, with surface AxB. This approximation is a very good one for the biconcave form that undisturbed erythrocytes have in arteries with a diameter of about 300 micrometer.
The projection S(y) in P is:
The optical pathway L, becomes for a given position x:
or explicitely:
with:
and
and with V = B / A,
if we now substitute z = y + Vx, then we obtain dz = dy and the limits of integration become Vx and
The indefinite integral becomes:
with
the indefinite integral becomes:
For the definite integral, we obtain:
The results are presented in figure 6. The abscissa of the graph is
scaled in relative distance from the centre of the artery so that x=1 is
situated at the edge of the bloodstream. The optical paths are all scaled
to 1 for x=0. Results for configuration 1, 2, 3 are marked O, I and X respectively.
Figure 6.
It is clear that only the third configuration gives rise to an optical pathway leading to the images we actually record. Therefore this configuration is assumed to be the correct one and was adopted as a basis for the model.
With this working hypothesis about the erythrocyte orientation and taking into account the optical absorption and scattering properties of whole blood, a numerical model was constructed.
The linear transport equation for photons:
was integrated numerically over a discrete raster, representing the vessel wall, blood mass and a great variety of thrombus configurations. In this equation I(s) represents the intensity in position s, L the optical pathway, depending on absorption and scattering. The factor B is the source term that takes into account the light, scattered back into the direction of the sensor, after a first scattering event. Higher order scattering events are neglected.
Typical results are summarized in figure 7.
Figure 7.
This graph shows the relative light intensity ( relative to the intensity
prior to thrombus formation) versus the thrombus thicknesses (abscissa).
The curves are labeled in relative distance from the arterial centre, 1
being the radius of the blood mass. It can be seen that a given thrombus
thickness gives rise to very different relative intensity changes, depending
on the position in the artery.
All preparations and the operative technique as described in [3] remain unchanged. When the illumination conditions and the image is optimally focused, the registration sequence can start. Just before and after every experiment, reference dark images (captured with the light source cut off) are registrated (D1,D2). During the period previous to ADP superfusion, 10 images are captured (R1 ...R10). Starting with the ADP superfusion, a sequence of artery images is digitized and send to the host computer at a rate of 1 image per second. This process continues during the whole experiment, until well after embolisis (I (i), i= 1....i max). Following procedure is then performed to extract the thrombus evolution from these images.
On figure 8, the graphical representation of six processed images is
shown. The arcs drawn as the first lines of the pseudo-3d plots represent
the full arterial aperture. The estimated platelet mass can clearly be
seen downstream. Blood flow is directed from upper right to lower left.
The thrombus builds up gradually from (a) to (d), then embolysis takes
place.
Figure 8.
In sequence 1 we can observe the formation of a large thrombus in a .1 mm thich artery, capture frame rate is 1 image per second, the sequence holds 100 images:
tape35-3.mpg
In the second sequence, the processed images are presented in a sequence, the blue background differentiates between very low thrombus thickness and zero.:
A second example is shown in following sequence pair: tape34.mpg the recorded data and trom34.mpg the corresponding processed thrombus sequence.
Figure 9.
It was shown that a videodensitometric procedure could be developed to capture and interprete image sequences, recorded during thrombus induction into mesenteric arteries of the rat. Multiple scattering theory in combination with the alignment hypothesis of erythrocytes in the arteries, led to light transmission profiles that are in good agreement with the measurements. Based upon these elements, a numerical model was developed. The results of this model are used in a procedure to process and interprete experimental induction, formation and evolution of arterial thrombi in vivo. The theoretical resolution of this method reaches the level of 1 cell. Further investigation is necessary to confirm this model, to improve the alignment procedures and to take into account flow disturbance by the thrombotic mass itself. On line processing is a more remote possibility.
The authors are much endebted to
Roger Andries for setting up the experiments.
trom35-3.mpg