Imaged-Based Detection of Heterogeneity of Microsphere Distribution in the Canine Heart

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(1)MSc Physics Physics of Life and Health Master Thesis. Imaged-Based Detection of Heterogeneity of Microsphere Distribution in the Canine Heart by. Duy Ha Ly 10393676 August, 2014 60 ECTS September 2013 – August 2014. Supervisor/Examiner: Dr. ir. Maria Siebes. Second Examiner: Dr. Henk A. Marquering. Academic Medical Center, University of Amsterdam.

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(3) Abstract Although the distribution of flow in heart muscle is not homogenous, normally all cells in the heart receive sufficient oxygen at baseline and exercise. However, in the presence of coronary disease ischemia and eventually infarction at a regional level may be the result. The structure of the vascular bed by itself forms a predisposition factor for regional ischemia. It is therefore important to understand the relation between regional perfusion and the structure of the vascular bed. In this study data obtained by an innovative imaging cryomicrotome, developed at the Dept. of Biomedical Engineering and Physics at the AMC, were used to investigate some relationships between morphometric properties of the vascular tree and the distribution of microspheres as flow tracers. The fluorescently labeled microspheres were injected during physiological experiments. The vascular tree was reconstructed after filling the vascular bed with a fluorescent replica material. The hearts were frozen, mounted in the cryomicrotome and sliced sequentially at a slice thickness of 50 µm. After each cut, images were taken at appropriate filter settings for excitation and emission wavelengths. From all these images the vascular bed could be reconstructed from segments defined by branch points, diameter and length. Also the Cartesian coordinates of the microspheres could be determined. We focused especially on the properties of the terminal segments of the reconstructed tree that were studied by a newly developed random ball classification method. A main finding is that correlation between microsphere and terminal segment density is much better at the endocardium (inner layer of the heart muscle) than at the epicardium (outer layer of the heart muscle). We also found that the nearest distance between microspheres and terminal segments is shorter at the endocardium. These findings together suggest that there is better organization of the microcirculation at the endocardium than at the epicardium. The terminal segments in the reconstructed tree varied in diameter between 30 and 150 µm with a peak at 55 µm. However, the real terminal segments have a diameter of 10 µm which is not detected by our method. As a result we found that the number of microspheres assigned to a terminal segment by nearest distance increased with the diameter and length of terminal segments. Simulated microsphere distributions demonstrated that nearest distance distribution between microsphere populations and terminal segments are determined by the reference population (the population to which the nearest distance is calculated) and are practically independent of the amount of microspheres injected. In conclusion, we have found that microspheres and therefore blood flow, is heterogeneously distributed in the heart muscle as determined by properties of the vascular tree. More research is warranted to understand the relevance of this finding in relation to vascular disease.. 3.

(4) Table of Contents Chapter 1. General introduction ............................................................................................5. Chapter 2. Imaging Cryomicrotome ....................................................................................10. Chapter 3. Difference between simulated random and real microsphere distributions .......15. Chapter 4. Quantitative analysis of microspheres in relation to the vascular bed ...............22. Chapter 5. Regional distribution of microspheres and terminal segments ..........................31. Chapter 6. Discussion and Future outlook...........................................................................38. References. ............................................................................................................................42. Appendix A ............................................................................................................................44. 4.

(5) Chapter 1 General introduction Cardiovascular diseases form the top cause of mortality in Western and Eastern countries. It is essential to gain better insight the physiology of heart and blood flow in order to improve diagnosis and treatment of especially coronary artery disease (CAD). Anatomy The coronary arterial system comprises arteries that surround the surface of the heart, epicardium, and branch to penetrate the myocardial wall. These vessels form a unique source of oxygen-rich blood supply to the heart tissue or myocardium. Figure 1.1 depicts the course of the epicardial coronary arteries and the global anatomy of the heart seen from the front.. Figure 1.1: The coronary artery anatomy. The right coronary artery (RCA) mainly supplies blood to right atrium and right ventricle. The left anterior descending (LAD) and left circumflex artery (LCX) mainly supply blood to the left atrium and left ventricle.. Physiology Normally coronary blood flow is under control of local blood flow regulation. Two different manifestations of flow regulation can be distinguished: metabolic regulation and autoregulation. Metabolic regulation determines the relationship between blood flow and tissue metabolic activity in the organ. Increases or decreases in the tissue metabolism lead to the increases or decreases in blood flow to ensure that the tissue is adequately supplied by oxygen and products of metabolism are removed. Waste products of metabolism are for example CO2 and lactate. In coronary physiology, one speaks about the match between oxygen supply and demand. The notion autoregulation is used to indicate that blood flow is rather independent from changes in arterial pressure when oxygen consumption is constant. If the pressure is decreased in the coronary arteries, blood flow initially falls. Concurrently, the arterial resistance decreases restoring blood flow despite the reduction of pressure in the 5.

(6) Chapter 1. General introduction. coronary artery. Autoregulation and metabolic vasodilation are demonstrated in Fig 1.2. Flow is rather independent on pressure when pressure is higher than 40-50 mmHg in what is called the autoregulation plateau. This plateau shifts more or less parallel with a change in oxygen consumption.. Figure 1.2: Control of coronary blood flow by an autoregulatory mechanism. The solid line shows the relationship between arterial pressure and flow without autoregulation, the dashed line represents the autoregulation plateau due to normal oxygen demand (top) and low oxygen demand (bottom).. Note the heavy line through the triangles with describes the relationship between blood flow and pressure when the small arteries responsible for flow control are fully relaxed by a vasodilator drug, e.g. adenosine, administered to the coronary circulation. The distinction between the autoregulation plateaus and this relationship at full vasodilatation indicates that blood flow has to be actively controlled by changing resistance of small arteries by smooth muscle in their walls. Please note that full vasodilation can also be obtained when coronary pressure is decreased by a narrowing in the larger arteries. Hence, the events occurring at full vasodilatation, indicated as hyperemia, are very relevant for understanding the distribution of flow in coronary disease. The regulation of coronary blood flow is affected locally and may equalize blood flow in different regions despite different biophysical conditions. For example, in the endocardium (inner layer of the myocardium) coronary vessels are much more compressed by heart contraction than at the epicardium (outer layer of the myocardium). These differences are especially clear when the coronary vessels are fully dilated as is demonstrated in Figure 1.3. In this figure, the hemodynamic conductance of these layers (flow per g of tissue divided by the arterial-venous pressure difference) is presented as function of the diastolic time fraction (DFT) with coronary arterial pressure as parameter. 6.

(7) Figure 1.3: The hemodynamic conductance of endocardium and epicardium corresponding to DFT.. The regulation of coronary blood flow is also dependent on the vascular site. In left and right ventricles, the intramural pressure is greatest near the endocardium and least near the epicardium. However, this pressure does not reduce the endocardial blood flow because the greater blood flow to the endocardium during diastole compensates for the greater blood flow to the epicardium during systole. The blood flows to the epicardial and endocardial are approximately equal under normal conditions. Hence, the tone of endocardial resistance vessel is less than that of the epicardial resistance vessels due to the fact that extravascular compression is greatest at the endocardial surface of the ventricle. Coronary blood flow distribution and its measurement Coronary blood flow can be limited by disease of the large coronary arteries resulting in local or distributed vessel narrowing, stenosis, as well as disease of the microcirculation. These limitations can result in areas of the heart muscle with shortage of oxygen, ischemia, or even in muscle death, infarction. Blood flow in the heart is distributed by the coronary arterial tree. Therefore, an important goal in cardiovascular research is to understand the structural development of coronary arteries in relation to the heterogeneity of regional blood flow. It is important to understand this heterogeneous distribution in order to recognize areas at risk when vascular stenosis occurs. Visualization with subsequent virtual reconstruction of the coronary arterial tree is important for increasing our understanding of blood flow heterogeneity. There are several available techniques for imaging. The X-ray angiogram is used standard to visualize the major coronary arteries during catheterization procedures and to identify coronary stenosis. X-rays can also be used to visualize smaller arteries within the myocardial wall postmortem (1). The limitation of this angiography technique is the difficulty to obtain quantitative information of the branching characteristics and vessel segment dimensions. These problems were overcome by the vascular casting method. Coronary arteries are filled by cast material then tissue surrounding the cast is removed or made translucent (2-4). The result of this 7.

(8) Chapter 1. General introduction. procedure is a plastic replica or observable intramural structure of the coronary bed respectively. From the plastic replica the length and diameter of vessel segments are measured and used to describe the coronary branching pattern and its prediction for flow heterogeneity. However, accurate measurements require breaking of branches of the tree's cast and therefore, similar to angiography technique, this method does not provide spatial information of coronary vessels related to heart tissue and 3D information of the branching tree. More recently micro-CT has been introduced which allows 3D analysis but it allows only a single contrast medium to be visualized. However, the advantage of this technique is the ability to study the coronary development in longitudinal studies of diseases (5). MicroCT can provide high resolution images of small animal vascular structure with voxels < 10 µm. Nevertheless, the small field of view of micro-CT (FOV < 5 cm) forms the limitation of this method for studying blood flow (perfusion) of hearts in larger mammals and humans. An imaging cryomicrotome provides high resolution images up to 30 µm and large field of view (up to 20cm) to collect the spatial information of the coronary arterial tree. This technique is based on the successive sectioning of a frozen heart while imaging the cutting surface of the remaining bulk. From the complete image stack of images the three dimensional structure of the coronary tree can be reconstructed by image processing (6, 7). The measurement of blood flow is essential in the study of coronary research. Quantitative techniques for blood flow measurement in coronary arteries and tissue perfusion are available. For the flow in large arteries the most common techniques are electromagnetic flowmetry (EM), laser Doppler and ultrasonic transit-time (8). Electromagnetic flowmetry employs the electromagnetic force or potential different resulted from the movement of blood flow to calculate the volume of flow. These flow probes can be mounted surgically around an epicardial artery. The EM method is not current anymore and replaced by the transonic probe. Ultrasonic transit-time uses an ultrasound signal emitted from a transducer mounted on a vessel, and deflected by a fixed acoustic reflector. The reflected signal is and then captured by the transducer which measures the time of travel of the sound pulse from which blood flow is derived. Laser Doppler technique uses the scattering of reflected laser light from the tissue of interest to measure the relative change in regional blood flow. Perfusion is defined as the amount of flow that passes through a unit of tissue volume. In human coronary perfusion can be measured by ultrasound bubbles injected in the blood stream, then locally destroyed in an organ by a high power ultrasound pulse after which bubbles reappear in the region of interest. Measurement of rate of bubble contrast increase in this reappearance phase is then a measure of perfusion. In addition, blood perfusion can be measured by the microsphere techniques (9, 10). In these techniques, an amount of microspheres are injected into an artery which then distributes these spheres proportional to blood flow in the circulation. The amount of microspheres lodged in a tissue region represents its blood perfusion. The quantification of microspheres may be performed by gamma counting, dye extraction or spectrometry (11, 12). The tissue may receive multiple different labeled microspheres indicative of perfusion under different physiological conditions. The microsphere techniques have been discussed in my literature study. The limitation of all those techniques is the deficiency of the spatial information of flow distribution in relation to the coronary tree and since in acquiring the data the tissue has to be 8.

(9) cut for analysis there is only one possibility for determining the tissue partitioning. This deficiency is overcome by the Imaging Cryomicrotome. Individual positions of labeled microspheres can be determined with respect to anatomical location. Distribution of microspheres can then be analyzed repeatedly according to arbitrary virtual cutting schemes. A major advantage is that the vascular structure can be reconstructed virtually as well when the coronary vessels' are filled with a fluorescent labeled replica material (13). Hence, microsphere distribution can be determined in relation to vascular structures. The principle of cryomicrotome is discussed in the next chapter and is applied to obtain the experimental data generated for chapters 3, 4 and 5. The AMC developed imaging cryomicrotome is the only instrument presently used to study microsphere distribution in relation to the anatomy of coronary vasculature (14). The goal of this master thesis research is to study how the coronary tree associates with regional flow within heart tissue. This research project comprises three scientific questions. The first question relates to the randomness of microsphere distribution in tissue. Microspheres are delivered to the heart tissue through blood vessels and at every branch point in the tree there is in element of chance into what daughter vessel it will travel. This element of randomness should be understood in order to distinguish this effect from heterogeneity in flow induced by anatomical and physiological reasons. The second question relates to the distribution of microspheres in relation to the distribution of terminal segments in the coronary arterial tree. True terminal segments are in the order of 10 µm but are not detected by the cryomicrotome. Hence we studied the relation between microspheres and the detectable terminal segments in our reconstructed trees. Finally, the third question relates to regional distribution of microspheres and terminal segments with special attention to depth in the myocardial wall and the axial position of the tissue in the heart. This thesis focusses on the development of concepts and methods to analyze and interpret data on flow and tree heterogeneity rather than on completed studies on larger data sets. That work still has to be done later. Hence, on limited datasets I have developed and tested methods that are described in three major sections: 1) The quantitative analysis of microsphere distribution by simulation (Chapter 3); 2) Microsphere distribution in relation to the terminal segments of the arterial vascular tree (Chapter 4); 3) The regional distribution of microsphere in relation to terminal segments and their properties as density and diameter (Chapter 5). These three sections are preceded by a chapter describing the technique of microsphere and terminal segment detection by the imaging cryomicrotome technique (Chapter 2) and followed by a general discussion (Chapter 6).. 9.

(10) Chapter 2. Imaging Cryomicrotome. Chapter 2 Imaging Cryomicrotome The original purpose of the imaging cryomicrotome was to determine the distribution of fluorescent microspheres within organs as perfusion distribution indication (6, 15). The technique has been improved by the AMC group to collect structural details of the coronary arterial tree (13, 16). The principle of the imaging cryomicrotome is based on slicing a heart serially while imaging the cutting plane of the bulk with a set of excitation and emission filters. The heart sample is situated in freezer at –20 Celsius. In the original design of Barlow Scientific, the reciprocal linear motion of cutting blade was controlled by the rotating rod attached to a rotating crank and wheel, which created sinusoidal variation in the cutting force and speed across the frozen surface with each stroke and prevented high quality reconstruction from the individual fluorescent images. The Biomedical Engineering and Physics research group in the AMC designed a more robust imaging cryomicrotome in which the vertical speed of the cutting blade is constant across the frozen surface. After cutting, the sample is moved horizontally to bring the remaining bulk surface back to the focal plane of the camera. A CCD camera equipped zoom lens is placed perpendicular to the surface of the sample to minimize the angular distortion and focusing difficulties. The fluorescent signals are measured by the application of excitation filters in the light path to and emission filters in the light path from the cutting plane to the CCD camera. The process of cutting and imaging is controlled by a computer via LabView software. A series of two-dimensional images builds a three-dimensional picture of the sample. Figure 2.1 shows a schematic overview of the imaging cryomicrotome. The frozen sample is sliced typically at 30 – 50 µm thickness. The sample is illuminated with a 300 W Xenon lamp or a set of powerful light emitting diodes. The filters wheels contain five optical filters in order to select excitation and emission wavelength. The filters are defined by the central wavelength and bandwidth in nm (see Table 2.1). The surface of the remaining bulk is imaged at 4096 x 4096 pixels by a 16-bit camera equipped with a variable focus lens (Nikon 70 – 180 mm, f/4.5-5.6, The Netherlands). Depending on the number of fluorescent color channels, complete datasets may reach over 100 GB and are acquired in 3 - 5 days of continuous cutting and imaging.. 10.

(11) Figure 2.1: Schematic overview of the imaging cryomicrotome. Table 2.1: The filter combination used to quantify imaged fluorescent colors. Note that some colors are detected by more than one that filter combination allowing spectral unmixing.. Filter wavelength (exitation/emission) 440/480 440/505 440/635 510/555 560/635 640/712. Fluorescent imaged Cast material only Green microspheres and cast material Red and yellow microspheres Yellow and green microspheres Carmine and red microspheres Scarlet and red microspheres. Before freezing the hearts their vessels are filled at constant pressure of 80 mm Hg with Batson no. 17 fluorescent replica material consisting out of a monomer base solution, a catalyst and a promoter. The blue or yellow replica material is allowed to harden for 24h. The entire heart is embedded in Indian ink 1% and sodium solvent then frozen at -20 Celsius for at least 24h. Subsequently, the frozen heart is placed on the cryomicrotome and sectioned serially from base to apex. A particular volume rendering of fluorescent vessels in a canine heart from imaging cryomicrotome is displayed in Figure 2.2. This 3D coronary tree was constructed from 1960 2D images at 50 um in slice thickness after imaging processing (maximum intensity projection, deblurring). Figure 2.3 depicts the concomitant visualization of the microsphere distribution and vascular structure from the fluorescent replica material. The Red microspheres were injected into the LAD region. With the application of spectral unmixing, up to 6 different fluorescent labels can be used in the cryomicrotome (14). 11.

(12) Chapter 2. Imaging Cryomicrotome. Figure 2.2: 3D reconstruction of coronary arterial tree in a canine heart.. Figure 2.3: Microsphere distribution corresponding to the left anterior descending coronary artery.. The unmixing of spectral overlap When using multiple labeled microspheres simultaneously, the fluorescent spectral overlap forms an important concern since there is no unique filter combination that can be used to provide a single contrast of one color in the mixture of multiple colors. In order to obtain corrected intensities of each color, two steps are required: 12.

(13) 1. The excitation filters are selected to maximize the intensity per color while keeping the overlap at a minimum. 2. Images captured with different filters are combined to measure the intensity response to each color more accurately. In an experiment, each combination of excitation and emission filters provides image of two colors to be separated. The intensity of one image is described by: σ , , l , l = l , l , + l , l , . (2.1). , , l′ , l′ = l′ , l′ , + l′ , l′ , . (2.2). Where σ , , l , l is the intensity at location (i, j) on 2D image taken at layer n with a specific excitation l and emission l filter combination. The intensity of the microsphere distribution , will be seen along with distribution , of the other color due to spectral overlap. In this equation, l , l and l , l are the scale factors that depend on the excitation and emission wavelengths, ranging between 0 and 1. The filter factors l , l . and l , l are chosen such that l , l is approximately 1. An additional image at the same layer n is selected with different filter combination l′ , l′ in condition that , is visible and , is invisible. The intensity of additional image is obtained: Where , is the intensity of microsphere distribution caused by the spectral overlap with respect to , . The intensity of unique color , can result from the subtraction below: , = σ , , l , l − , , l , l . (2.3). = l ,l ∗ Φ . l. . ,l. . The factor Φ is used to compensate for the difference in exposure time between σ , , l , l and , , l′ , l′ . The negative of this subtraction is considered to be zero intensity in the final image of unique color. The transparency effects Due to the scattering of light from the deeper layers of a sample the surface image contains information on these deeper layers as well. Hence there may be more microspheres visible in the cutting plane than actually present in that plane. In fact, the same microsphere will be visible in subsequent images at increasing intensity and then disappear. The cutting layer at which the light disappears is considered to be the location of microsphere. However, this approach provides a false detection when nearby microspheres is counted as one. Therefore, a correction of the transparent effect is an important step in the detection algorithm. The light intensity distribution of a point source can be expressed as: 13.

(14) Chapter 2. Imaging Cryomicrotome *+, -., /. . !", #, $ º % &'() % ,σ01-σ, , . . !", # º % &'( % ,σ0-σ, ,. (2.4). With !", #, $ is the point spread function, µ is the attenuation coefficient and z is the distance from the light source. When the intensity changes over a single slice or z = 1, the !", #, $ can be simplified to: *+, -., /. (2.5). Hence, the expression for the intensity contribution of the in-plane microspheres is given by: ¶ ¶ 2 , = , − % &'( ∑2=& ¶ ∑<= &¶ 45 6, 7 %. *8*9 , *:*; , ,σ0 -σ, ,. (2.6). With 2 , , the intensity contribution from microspheres currently and , is the total intensity in location (i, j) at slice n. Hence, the transparent effect throughout the stack of images can be corrected by using Equation 2.6. The auto-fluorescent effect Auto-fluorescent effect is the result of natural emission of fluorescent light by biological structures when excited at certain wavelengths. Auto-fluorescence is especially noticeable at an excitation of 440nm. To correct this effect for microsphere detection, a 2D white Top Hat filter is used to separate small scale structures in the image from large intensity gradients. However, a Top-Hat filter decreases the absolute peak of microsphere intensity, thereby increasing the signal to noise ratio. To compensate the intensity reduction, an intensity scaling filter is introduced: 0 @AB , < , = > , × EF2G @AB < , < 255 @AB , > . K7ℎ EF2G = . − MNO > 255. (2.7). Where , is the rescaled intensity, α is the lower threshold above the background noise and β is the upper threshold of maximal microsphere intensity observation.. 14.

(15) Chapter 3 Difference between simulated random and real microsphere distributions I. Introduction Due to the nature of the coronary vascular structure but also to regional functional differences, blood flow in the heart tissue is heterogeneous. Microsphere injections can reveal such flow heterogeneity since microspheres distribute with flow (10). However, even in case of homogenous flow distribution microspheres will be spatially heterogeneously distributed due to a random element of chance in entering a vessel segment at bifurcations. Hence, one has to understand how random distribution properties are interfering with flow heterogeneity. There are different ways to study the heterogeneity of microsphere distribution. In this chapter we concentrate on the nearest distance of neighboring microspheres. In the ideal condition, microspheres would be distributed evenly for example on the vertices of a cube filled space. In that case, the nearest distance to the neighbor would be constant for all microspheres. However, randomness in the distribution will introduce variability in the nearest neighbor distance which can be expressed by a histogram. The shape of this histogram bears information on the randomness of microsphere distribution independent of flow heterogeneity. The added heterogeneity of blood flow should widen the histogram compared to the condition of a pure random distribution of microspheres alone. Often it is important to know how an intervention does influence the regional blood flow and therefore microsphere distribution. Such an effect can follow from the distribution of nearest distances between the two distributions. We denote this as an inter-group distribution. When studying nearest distance within a single population we denote this as an intra-group distribution. One of the major parameters of heterogeneity is the amount of microspheres involved. Hence special attention will be given to this impact. A second factor determining flow heterogeneity is the boundaries of the space over which the microspheres are distributed. A long stretched out volume will have more effect on the quantification of microsphere heterogeneity than a spherical shape. In our virtual experiment we used a space corresponding to the perfusion area of a major coronary branch, the LAD. The purpose of this chapter is to gain insight into the randomness of microsphere distribution independent of flow by simulating microsphere distribution with different parameters. Then, these characteristic random distributions are compared with real microsphere distributions in the heart. Hence, this chapter follows the following outline: 1) Virtual distribution of intra-group nearest neighbor distance with focus on the effect of number of microspheres; 2) Virtual distribution of inter-group nearest neighbor distances and the effect of number of microspheres; 3) Comparison of the virtual results with experimental results.. 15.

(16) Chapter 3 Difference between simulated random and real microsphere distributions II. Methods 1. The space in which microspheres were virtually distributed followed from the delineation of a typical LAD perfusion area of a canine heart. This area was determined from the stack of images obtained by the cryomicrotome. The inner and outer boundaries of the heart formed well-defined borders and were automatically detected by a self-developed program. The boundaries crossing over the heart muscle followed from the end-points of terminal segments of the vascular tree defined by the origin of the LAD. 2. In this chapter the distance between nearest neighbor microspheres are calculated where the microspheres form a single population or distinguishable populations. The nearest neighbor distance is always calculated from one group to the other and hence, the number of distance’s calculated equals the number of microspheres that is used as the source population. A program has been developed that calculates the distance between nearest neighbors of populations of which the x, y, z values are put in separate lists. The frequency of all distances of nearest neighbor microspheres was normalized by the total number of distances calculated and displayed as a histogram with specific bin size (bin width = 50 µm). 3. Intra-group simulation: Three different virtual microsphere distributions were created with 50k, 100k and 200k microspheres respectively where the 3D coordinates of each sphere (x, y and z positions) were simulated by a pseudo random generator in a space enclosing the tissue space. In case the resulting coordinates were outside the tissue space the position was rejected. The intragroup nearest distance of microspheres in the different populations were determined as described under b. 4. Inter-group simulation: Similar to the intra-group simulation, five populations of microspheres were simulated including: 1k, 10k, 20k, 50k and 100k. The inter-group distances of microspheres of two different populations were determined. Three populations were used as reference populations (20k, 50k and 100k), all populations were used as target population for determining intergroup distances between nearest microspheres with the three reference populations. 5. Experimental procedure: Three different colors of fluorescent microspheres (15 µm in diameter) were injected into the LAD of the canine heart. In the experiment encoded as CFI-02, carmine fluorescent microspheres were injected during maximum vasodilation of coronary arteries (adenosine condition) while green and scarlet ones were injected at resting stage. Then the heart was frozen and sliced serially by the imaging cryomicrotome. The complete volume rendering of this heart had a voxel resolution 50 µm3. In order to evaluate whether experimental data sets behave differently from random distributions, three virtual random distributions were generated simulating the injections at basal and adenosine conditions, respectively, using the corresponding amount of virtual microspheres.. 16.

(17) 6. Quantitative analysis of microsphere deposition: For the estimation of inter-group nearest neighbor distance distributions it is important to define the target group, which is the population from which the distances are calculated and the reference group which is the group to which the distances are taken. In order to quantify the minimal distance pattern of nearest neighbor microspheres, a program was developed in Lazarus (Lazarus 1.0.14). This program determined the minimal distance between nearest neighboring microspheres according to their spatial information. 7. Statistical analysis: All statistical analyses were performed using Prism 5 (GraphPad Software, CA) and Grapher 8 (Golden Software, CO). D’Agostino and Pearsons test was used to test normality of the data. The t-test checked the significant difference of two normal distributions expressed by peak and Full Width Half Maximum (FWHM) while the Mann-Whitney test was used for two non-normal distributions. The skewness value is used to determine if the data distribution is non-symmetrical. The formula for skewness is: P%KN%66 = T<SUS VWF<FX QR&RSF. (3.1). The data that is perfectly symmetrical has a skew value of zero. The distribution of data is skewed left when skewness value is negative and skewed right when skew value is positive. Although not all data are normally distributed, we used the coefficient of variation, CV, to evaluate the dispersion of data points around the mean. YZ = . T<SUS SWF<FX R. (3.2). III. Results 1. The intra-group distance distribution pattern: a. Virtual microspheres: Figure 3.1 depicts the histograms of intra-group distance with different amounts of microspheres: 50k, 100k and 200k. The curves follow a non-normal distribution with a rather small skewness factor of 0.1. For simplicity the histograms are described by peak value and the width at half peak. When the total amount of microspheres in the population increases the peak shifts to a smaller distance and the width at half peak becomes smaller as well. Ignoring the non-normal distributions, the, CV, of neighboring distances in three histogram was similar, approximately 37%.. 17.

(18) Chapter 3 Difference between simulated random and real microsphere distributions. Figure 3.1: Histograms of intra-group minimal distances of randomly distributed microspheres in different populations normalized by the total number of microspheres: 50k, 100k and 200k. b. Experimental microspheres: Only one heart was available were microspheres were injected at baseline and at adenosine. In this heart, 32721 microspheres injected at baseline were detected and 62583 injected at full vasodilation with adenosine. The histograms of the intra-group nearest neighbor distributions are depicted in Figure 3.2. These histograms are skewed and hence not Gaussian distributed. The nearest intra-group distance at the peak of the histograms is practically the same: 500 µm. The normalized peak of adenosine is higher than at baseline corresponding to smaller skewness of the histogram which were 0.41 and 0.54 for the adenosine and basal histograms respectively. There are apparent differences in comparison with the histograms in figure 3.1. In Figure 3.2, the peak and the skewness of the two histograms are rather similar while on the basis of Figure 3.1 one would expect a dependency on the total amount of microspheres injected which was not the case for experimental intragroup distance. Moreover, the CV’s of the experimental curves were higher at rest and hyperemia, 0.76 and 0.70 respectively.. Figure 3.2: The distribution of intra-group minimal distances of experimental microspheres in basal and adenosine conditions.. 18.

(19) Normalize Frequency. 2. The inter-group distance distribution pattern of virtual and experimental microspheres: a. Virtual microspheres: Figure 3.3 displays the results of all distance distributions between different virtual microsphere populations. The populations with 20k, 50k and 100k microsphere were used as reference groups. The target groups had amounts between 1k and 100k microspheres. The figure demonstrates the separation of histograms into 3 groups which were defined by the amount of spheres in the reference group. Similar to intra-group histogram, the inter-group distributions of random microspheres is non-normal distribution. The distance at peak value is only shorter with higher amounts of reference spheres. Hence, the histograms are hardly affected by the amount of microspheres in the target groups.. Figure 3.3: The frequency distribution of inter-group minimal distances of randomly generated populations normalized by the total number of microspheres.. b. Virtual and experimental microspheres: For each of the two different experimental populations obtained at baseline and at vasodilation, three different random distributions were generated with the respective amount of microspheres. The virtual inter-groups 2 (RDBase2) or 3 (RDbase3) relative to virtual group 1 (RDBase1) as reference group were compared with the experimental inter-group (Baseline) normalized to RDBase1. As demonstrated in Figure 3.4a, for the baseline condition, the two histograms of virtual data alone are rather similar, but the histogram of the experimental data deviates remarkably from the virtual data. At the peak of all three curves the minimal distance is 700 µm. The differences between experimental and simulation curves were also related to relative skewness value which were 0.6 vs 0.11. The distance distribution of baseline microspheres was significantly different from random microspheres (P <0.0001). This underlines again that the distribution of microspheres in the coronary circulation was not random. 19.

(20) Chapter 3 Difference between simulated random and real microsphere distributions Similar to basal condition, the minimal distance of corresponding adenosine groups were determined (see Figure 3.4b). The observation of adenosine microspheres reveals that the peak of adenosine group is lower when the skewness is higher than with the random groups, 0.56 vs 0.13 respectively. The distance peak is unchanged in these three cases, at around 600 µm. The distance distribution of microspheres in adenosine and random simulation was significantly different (P <0.0001).. A 0.1 0.08. B Number of Baseline Msph : 32721 Ref RDbase2 - Target RDbase1 RDbase3 RDbase1 Baseline RDbase1. 0.1 0.08. Number of Adenosine Msph: 62583 Ref RDade2 - Target RDade1 RDade3 RDade1 Adenosine RDade1. 0.06. 0.06. 0.04. 0.04. 0.02. 0.02. 0. 0. 0 2 4 6 8 10 12 14 16 18202224 Minimal nearest neighbor distance x 102 (µm). 0 2 4 6 8 10121416182022 Minimal nearest neighbor distance x 102 (µm). Figure 3.4: The frequency of intergroup distance pattern of random microspheres and experimental microspheres while using one random population as the target group.. c. Baseline and adenosine microspheres: The inter-group relationship of baseline and adenosine microspheres is demonstrated in Figure 3.5 with either population as reference. Both histograms depict a bimodal distribution. The 1st peak of both histograms is close to 100 µm in nearest distance but the 2nd peak of the two curves is at different nearest distances, 500 µm for baseline and 700 µm for adenosine. The frequency of first peak is higher for adenosine than for baseline as reference group, 0.52 and 0.027 respectively. Similarly, the frequency of 2nd peak of adenosine is higher than at baseline. The skewness of the curve around the second peak in adenosine is smaller than in baseline, 0.46 and 0.54. We have tried to see whether the microspheres represented in the 1st peak had some preference location in the heart. This was not the case. The density of these microspheres was somewhat higher in the midmyocardium but similar for the epicardial and endocardial layer.. Figure 3.5: The inter-group distances between baseline and adenosine microspheres.. 20.

(21) IV. Discussion. In this chapter the characteristic distribution of intra-group and inter-group populations of nearest distances for randomly distributed microspheres were compared with experimental microspheres distributed by the coronary vascular network. The purely stochastic distributed microspheres resulted in distributions which were not normally of nature but with low skewness values. The coefficient of variation was independent of the number of simulated random microspheres and was about 0.37. This value indicates a limit for distinguishing real flow distribution from the stochastic component involved in microsphere distribution. For comparing different populations it is important to define the reference population. The number of microspheres in this population determines to a high degree the parameters of the histograms of inter-group nearest neighbors. This can be understood in the following way. When the target group is doubled in number there is twice as much nearest neighbors to be found. Part of this added target points will be closer to the points of the reference group but another part further away. Hence, the relative shape of the histograms is maintained. The histograms of experimental microspheres distribution deviated significantly from those randomly distributed. The skewness is significantly higher than for the pure random distributions. This indicates that some areas have received more microspheres than to be expected when these were distributed only randomly at a homogenous flow. Hence, it is possible to study heterogeneity of blood flow distribution in the heart with microsphere that exceeds heterogeneity induced by pure random processes. Apart from this general conclusion the inter-group distance between baseline and adenosine population demonstrated a bimodal form (see Figure 3.5). This bimodal form has been demonstrated before by Decking et al (17). This 1st peak of distance distribution demonstrates microsphere clustering in space. Most likely this suggests that microspheres have a preference in pathway which preference is the same for baseline and for adenosine. We could not really find areas of preference in location in the heart. It may be that there is a better relation with structural factors of the coronary tree but this was not analyzed in this study. It is important to identify these vascular pathways since clustering indicates that microspheres not only distribute proportional to flow and hence form a limitation in the application of microspheres to determine flow distribution. In the earlier papers on microsphere distribution the effect of vascular structure on microsphere distribution has been ignored. Tissue was considered to be homogeneous and interpretation was based on perfusion distribution modulated by a random process described by Poisson noise. Based on the typical shape of the nearest distance distribution, which demonstrates a peak value independent of the number of microsphere, it is clear that vascular structure has a determining role in the distribution of microspheres and should be further studied to incorporate that factor.. 21.

(22) Chapter 4. Quantitative analysis of microspheres in relation to the vascular bed. Chapter 4 Quantitative analysis of microspheres in relation to the vascular bed I. Introduction Blood flows through the branching vascular tree carrying microspheres with it to the sites in the microcirculation where they lodge. One may therefore expect a relation between density and nearest distance of these small arteries and these same quantities of microspheres. It has been suggested that microspheres do lodge in arteries of 50 µm and smaller. This is below the resolution of the cryomicrotome. The aim of this study is to compare the distribution of microspheres in relation of the distribution of end-segments in the reconstructed coronary tree. Before studying the relationship between microspheres distribution and terminal segments we have to understand some properties of the terminal segments in the virtual tree as a class of vessels. For example, terminal segments have nonuniform diameter since this depends on the filling of the vascular tree by the replica material. Also, length of terminal segments may differ not only depending on vessel diameter but also as a result of natural variation. Not all terminal segments have carried microspheres since the number of injected microspheres is too small for that. Hence we can distinguish terminal segment with likelihood to have carried one or more microspheres by a criterion based on nearest distance of a microsphere to a terminal segment. In that way, we can select a group of microspheres carrying segments and compare certain properties with the total group of terminal segments. In Chapter 3 we concluded that microsphere distribution is not a random process and flow heterogeneity could be demonstrated. In this chapter we will try to understand the heterogeneity in microsphere distribution on the basis of variability in the properties of the terminal segments.. II. Methods 1.. Average diameter of terminal arterioles: A terminal segment in the reconstructed tree is a segment determined by two endpoints one of which has no neighboring segment. Each segment comprises of multiple center points having a known location in space. A unique diameter of a segment is determined from the images as a mean of diameters at all center points determined from the intensity distribution in the plane perpendicular to the segment at the center point. For diameter measurement, the Full Width Half Maximum (FWHM) criterion is applied. The criterion is based on the position of a step edge after it is convolved with a Gaussian. The original position of the step edge is located at position of half of the maximum intensity. The width is measured with a two dimensional Gaussian: * *.. ", # = -\ % ,],,]^, 22. (4.1).

(23) With I0 as the maximum intensity, σ is the width of the Gaussian in the horizontal direction of the slice, the direction in which the largest Gaussian is expected, and σ’ is the width of the Gaussian in the vertical direction of the slice. The position of half maximum intensity r follows easily from the width of the Gaussian for one dimension case: %. &. _, ,],. = ' 5. B ' = −2` ' ln ' 5. B = c2 ln2 ` d"%e. (4.2) (4.3) (4.4). The complete FWHM d of a Gaussian: O = 2c2 ln2 ` d"%e. (4.5). The diameter of one terminal segment is the averaged diameter of all center points belong to that terminal segment. O =. ∑ fg0 Sf. (4.6). With m is the total number of center points in a terminal segment, dn is the diameter of center point n (1 < n < m). 2. Minimum distance between microsphere and terminal segment: The relationship between a microsphere and its terminal segment is determined on the assumption that a microsphere is considered to be delivered by the nearest terminal segment that has shortest distance to microsphere. A dedicated program was developed in Lazarus (Lazarus 1.0.14) which collects the x, y, z information of the microspheres and the morphometric information of all coronary segments making up the 3D vascular tree. The distance between a microsphere and a terminal segment is calculated as follows: O, = c"h − "T ' + #h − #T ' + $h − $T ' − EMOi6 A@ j%BkNMe %lk%N7. (4.7). With d(P,S) is the distance between the microsphere P(xp,yp,zp) to a point S(xS,yS,zs) on terminal segment. There are three possible scenarios of the relative position of the microsphere towards a nearest terminal segment as depicted in Figure 4.1. {{{{{{{{{{| - Case 1: dP1,S = dP1,S1 when Dot1 1,{{{{{{{{{{| 2 1 <= 0 {{{{{{{{{{| {{{{{{{{{{| - Case 2: dP2,S = dP2,S’ when Dot2 1,{{{{{{{{{{| 2 1 > 0 and Dot2 1,{{{{{{{{{{| 2 1 < Dot{{{{{{{{{{| 2 1,{{{{{{{{{{| 2 1. {{{{{{{{{{| {{{{{{{{{{| - Case 3: dP3,S = dP3,S2 when Dot3 2,{{{{{{{{{{| 2 1 > 0 and Dot3 1,{{{{{{{{{{| 2 1 => Dot{{{{{{{{{{| 2 1,{{{{{{{{{{| 2 1. 23.

(24) Chapter 4. Quantitative analysis of microspheres in relation to the vascular bed. Figure 4.1: The illustration of shortest distance d corresponding to segment S1S2.. The frequency of distance between microspheres to their nearest terminal segments is normalized by total number of detected microspheres and thereafter displayed by histogram with 50 µm as bin size. An impression of the determination of shortest distances between microspheres and terminal segments is provided in Figure 4.2.. Figure 4.2: The illustration of shortest distance (blue dash line) between microsphere (red dot) and terminal segment of vascular tree (black solid line). By counting blue dash line in one terminal segment, spatial information of microspheres that are delivered from that segment can be determined.. 3. Experimental procedure: After anesthesia and surgery (not described in detail here), the necessary catheters were positioned at the ostium of the left anterior descending artery, LAD. Fluorescent microspheres (15 µm in diameter) were gradually infused over a period of 1 min. The experiments were performed in the context of other physiological experiments (18, 19). After the experiment, the animal was killed by fibrillating the heart by means of a battery voltage applied to the surface of the heart. The heart was then excised and the major coronary arteries cannulated. These major arteries were then perfused with a buffer solution containing adenosine for vasodilation of the microcirculation. When all blood was removed from the coronary circulation the major arteries were infused by a fluorescent replica material (excitation/emission: 440/480). The fully prepared heart was frozen at -20oC and placed in 24.

(25) the cryomicrotome for subsequently cutting. The spatial information about microspheres and coronary segments was collected by an automatic computational program developed at the Biomedical Engineering and Physics Department, AMC, The Netherlands (16). In this chapter we will discuss the results of two experiments labelled CFI-04 and CFI-10. 4. Classification of layers:. The LAD territory of heart is further divided into three regions with equal thickness indicated by endocardium, mid layer and epicardium. The tissue volume for each sub-region is determined from the outline images.. Figure 4.3: The separation of heart tissue in endocardium (red), mid (green) and epicardium (blue) in the LAD region of CFI-04.. 5. Simulation: A set of random microspheres was created by pseudo random generator. In order to achieve consistent comparison, number of random microspheres was equal to the number of experimental microspheres and also located in the LAD region. 6. Statistical analysis: All data was collected, analyzed and plotted using Prism 5 (GraphPad Software, CA) and Grapher 8 (Golden Software, US). ANOVA analysis was used for multiple data sets, with the post-hoc Tukey test for parametric data. The Kruskal–Wallis test was used for nonparametric data with the Dunn’s multiple comparisons analysis. A p-value < 0.05 was considered statistically significant. III. Results In CFI-04, the number of detected microspheres was 55158 and the number of terminal segments was rather similar at 55812. Figure 4.4a shows the histogram of minimal distance distribution between terminal segments and microspheres including random (dash curve) and experimental microspheres (solid curve). Most of the microspheres were located close to 800 µm from nearest terminal segments. The patterns of two curves were demonstrated to be 25.

(26) Chapter 4. Quantitative analysis of microspheres in relation to the vascular bed. statistically different (P <0.001) but practically rather similar. The peak and width of random microspheres is smaller and slightly shifted to left of experimental microspheres.. Figure 4.4: Histogram of nearest distance of experiment and simulation.. Although there seems to be reasonable agreement between the theoretical and experimental curves for the whole LAD region, microsphere distributions are significantly different between endocardium and epicardium (see Figure 4.5). Interestingly, these differences are also found when the distribution of nearest distances of randomly distributed microspheres to the terminal segments are calculated as depicted in panel C and D.. A. CFI04 - experiment. 0.1. B. CFI10 - experiment. 0.1. Endocardium Midmyocardium Epicardium. 0.08. 0.08. 0.06. 0.06. 0.04. 0.04. 0.02. 0.02. 0. Endocardium Midmyocardium Epicardium. 0 0. 2. 4. 6. 0. 8 10 12 14 16 18 20 22 24. 2. 4. 6. 8 10 12 14 16 18 20 22 24. 2 Nearest distance between microsphere and terminal Segment x102 (µm) Nearest distance between microsphere and terminal Segment x10 (µm). C. CFI04 - random. CFI10 - random. D 0.1. 0.1. Endocardium Midmyocardium Epicardium. 0.08. Endocardium Midmyocardium Epicardium. 0.08. 0.06. 0.06. 0.04. 0.04. 0.02. 0.02. 0. 0 0. 2. 4. 6. 8 10 12 14 16 18 20 22 24. Nearest distance between microsphere and terminal Segment x102 (µm). 0. 2. 4. 6. 8 10 12 14 16 18 20 22 24. Nearest distance between microsphere and terminal Segment x102 (µm). Figure 4.5: The nearest distance between experimental microspheres and terminal segments in endocardium, midmyocardium and epicardium.. 26.

(27) The histograms of diameters of the terminal segments for the two dog hearts are depicted in Figure 4.6. In CFI-04, 36722 terminal segments had a diameter between 50 µm to 100 µm and 16743 a diameter smaller than 50 µm. The number of terminal segments with diameter larger than 100 µm is small and about 5% (see Figure 4.6a). Similar to CFI-04, diameters between 50 and 100 µm amount to approximately 80% of total terminal segment diameters in CFI-10 (see Figure 4.6b).. Figure 4.6: Diameter histogram of terminal segments of coronary arteries in CFI-04 and CFI-10.. As demonstrated in Figure 4.7 there is a relationship between the diameter of a terminal segment class and the number of microspheres assigned to that class. The larger the diameter of the class is, the higher the number of microspheres is obtained . The difference in slope between the two experiments relates to the number of microspheres injected which was much lower in CFI-10 than in CFI-04. CFI10. CFI04 10. 10. 8. 8. 6. 6. 4. y = 0.04x + 1.66 R² = 0.90. 4 Y = 0.02 * X + 2.08 R2 = 0.70. 2. 2. 0. 0 < 30 31- 41- 51- 61- 70- 81- 91- 101-111-121-131-14040 50 60 70 80 90 100 110 120 130 140 150 Diameter of Terminal Segment (µm). < 30 31- 41- 51- 61- 70- 81- 91- 101-111-121-131-14040 50 60 70 80 90 100 110 120 130 140 150 Diameter of Terminal Segment (µm). Figure 4.7: The microsphere distribution vs terminal segment diameter in CFI-04 (left panel) and CFI-10 (right panel). (Mean ± SEM). 27.

(28) Chapter 4. Quantitative analysis of microspheres in relation to the vascular bed. The histogram of length of the terminal segments is depicted in Figure 4.8. In both hearts, the class with length between 250 and 500 µm contained the most segments and the number of segments per class decreased with increasing length. Terminal segments shorter than 250 µm amount to about 7% of the total.. Figure 4.8: The length histogram of terminal segments of coronary arteries in canine heart CFI-04 and CFI-10.. As is demonstrated in Figure 4.9, more microspheres were assigned to longer terminal segments. The number of microspheres in each class related very well the average length of each class. Again the slope in CFI-10 is smaller than in CFI-04 because of the lower number of microspheres injected.. Figure 4.9: The microsphere distribution corresponding to terminal segment length in CFI-04 (left panel) and CFI-10 (right panel. (Mean ± SEM). 28.

(29) Figure 4.10 illustrates that the distance between microsphere and terminal segment increases in CFI-04when the terminal segment diameter is larger. However, it was not the case for CFI-10 in which nearest distance is constant during the variation of terminal segment diameter.. Figure 4.10: The microsphere distribution corresponding to terminal segment length in CFI-04 and CFI-10. (Mean ± SEM). IV. Discussion In this chapter we successfully established the connection between microspheres and terminal segments of the vascular tree by estimating shortest distances between them.. Although the theoretical simulated and experimental distributions are statistically significant different, the shapes are rather similar. This can be understood from the simulations on microsphere distributions done in Chapter 3. We demonstrated there that the reference population determines the shape of the inter-group nearest distances. In the present chapter we used the terminal segments as reference population. This makes sense from an engineering point of view since the question to answer is how far a microsphere is located from its nearest terminal segment. Hence, it is to be expected that the number of microspheres, injected or simulated, have a minimal influence on the distribution curves. There are clearly regional differences between the different layers of the heart both for the experimental microspheres as for the randomly distributed population. It seems that the distributions of experimental microspheres are somewhat smaller than from the random simulated microspheres but there are clearly similarities. This again implies that the structure of the vascular tree has a dominant role in the distribution of nearest distances between microspheres and terminal segments. This vascular structure must therefore be significantly different over the layers of the heart. This however, is the topic of the next chapter.. 29.

(30) Chapter 4. Quantitative analysis of microspheres in relation to the vascular bed. The quality of the filling of the coronary circulation can be derived from the histograms of diameter and length of the terminal segments. Ideally one would expect that terminal segments would all have the same diameter which is not the case. It is not clear yet what exactly the parameters are for filling of the vessels by the replica material. It is clear that the process is not homogeneous. This conclusion is also supported by the distribution of length of terminal segments. However, there is a poor correlation between length and diameters of vascular segments in general, which was also confirmed in this study (data not shown). It is obviously the combination of length and diameter that determines the filling process of the vessels. To understand this better a model analysis of the filling process of the intact vascular network is needed. However, this was outside the scope of this study. The positive correlation between numbers of microsphere connected to segments of a certain diameter can be understood. It is reasonable to assume that in reality the real terminal segments will have a diameter close to the capillaries and will be in the order of 10 µm. Hence, a reconstructed terminal segment will consist out of thicker vessels from which the smaller once are pruned. The thicker the terminal segment in the cast a larger number of smaller vessels will have been pruned. Microspheres that were transported to those smaller vessels are now allocated to the thicker terminal segment of the cast. Moreover, in one of the experiments it has been demonstrated that a larger terminal segment diameter could deliver microspheres further. In the other heart, the distance between microsphere and terminal segment remained the same for larger diameter. The explanation of this observation can be the missing of branching vessels on thicker segments due the cast filling. Similarly, one can understand the relation between length and number of related microspheres. The longer the terminal segment the more small side branches will have been pruned. The use of distance between microsphere and nearest terminal segment is not only useful for interpretation of microsphere distribution but also for the assessment of quality of cast filling. In practice, it is difficult to archive the perfect anatomical structure due to the variation of the resistance and compliance of vascular bed as well as external artifacts during cast filling. The most regular distance between microsphere and terminal segment or the peak of histogram can help to determine how well the vessels are filled by replica material. Moreover, in reproducing the pathway of a microsphere to tissue the chance of predicting this path correctly is higher when the distance between microsphere and its nearest terminal segment is shorter.. 30.

(31) Chapter 5 Regional distribution of microspheres and terminal segments I. Introduction In Chapter 4, we found that amount of suspended microspheres near a terminal branch is proportional to its diameter and length and hence there is a relationship between microsphere deposition and vascular anatomy. In the earlier chapter, we have neglected the differences in anatomy of the vasculature between the different regions of the heart while significant differences have been demonstrated between the inside and outside layers of the myocardium. Hence, it is possible that the heterogeneity of microspheres in blood flow can be dominated by the heterogeneity of terminal segment density over different layers. In order to study the relationship between the microsphere distribution and density of terminal segment we used the random ball method. In this method a sphere of specified volume in space is generated containing heart tissue. The number of microspheres and terminal segments in relation to the volume of heart tissue contained in the sphere are determined. The ball is then randomly moved through the heart muscle space. Depending on the size of heart and diameter of ball, the number of random balls generated should be sufficient to cover most of the regions of heart tissue.. Figure 5.1: Left panel: The random ball location in the LAD region of CFI-04 with vasculature and microspheres (shown in green). Right panel: Random balls in endocardium (yellow) and epicardium (blue) with microsphere distribution (red) within LAD region (light grey).. 31.

(32) Chapter 5. Regional distribution of microspheres and terminal segments. The purpose of this chapter is to study the heterogeneity of microspheres and terminal segments in different regions of myocardium. In this way it is attempted to demonstrate the differences between the endocardial and epicardial layer from base to apex. Important factors to be considered in the distribution of microspheres are related to the physiological processes affecting coronary blood flow in general and its transmural distribution in particular. These processes are discussed in chapter 1 but repeated here. 1) coronary blood flow is strongly regulated by autoregulation and metabolic regulation implying that local blood flow is matched and 2) when autoregulation is exhausted by e.g. the pressure drop of a stenosis or prevented by a drug such as adenosine, local blood flow is strongly determined by secondary factors like wall stress and tissue pressure. Because of the many factors involved, all deserving special attention, this chapter will not report on the distribution of microspheres as flow indicator but on the nearest neighbor analysis between microspheres and between microspheres and terminal segments as well as on the distribution of terminal segments which is an anatomical rather than a physiological parameter. II. Method 1. Random ball method: Multiple balls are created by selecting x, y and z coordinates of center points generated by a pseudorandom number generator. The center point is located within the borders of heart region in space. If >75% volume of the random ball (defined by its center point and selected radius) lies within heart tissue, the ball region is considered adequate to sample the parameters aimed at. If not, another center point is randomly chosen and the volume around this point is examined. The overlap of two neighboring balls should not exceed 50% of the volume. The construction of random balls will continue until there is no random ball that can be created within the borders of the heart. Therefore, the number of random balls is dependent on the size of random ball and the volume of heart tissue. A terminal segment which is partly or completely within a random ball is assigned to that ball. The microspheres that are assigned to a terminal segment of the ball on the nearest neighbor criterion are assigned to the ball as well.. Figure 5.2: The illustration of random ball creation in relation to terminal segments and microspheres. (Yellow circle = random ball; Red dot = microsphere location; Dashed line = distance from microsphere to nearest terminal segment).. 32.

(33) 2. Classification of layers: The LAD-perfused tissue region of heart was further divided into three circumferential regions with equal thickness indicated by endocardium, mid layer and epicardium. The region was divided from top to bottom into 4 sections with 16.5 mm in thickness (top section was the base layer, 2nd and 3rd were the mid layers and 4th was the apex layer). The tissue volume for each sub-region was determined from the outline images. 3. Experiment procedure: The procedure of experiment was described in the Method of Chapter 4. We reused the distribution of red microspheres in this study. Random balls with 6 mm in diameter were created in the endocardial layer and epicardial layer. Subsequently, the number of terminal segments and microspheres per terminal segment within each random ball were counted. 4. Statistical analysis: All statistics were performed in using Prism 5 (GraphPad Software, CA) and Grapher 8 (Golden Software, CO). D’Agostino and Pearsons test was used to test normality of the data. ANOVA was used for multiple data sets, with the post-hoc Tukey analysis for normally distributed data. The Kruskal–Wallis followed by Dunn’s multiple comparisons was used for non-normally distributed data. A p-value <0.05 was considered statistically significant. III. Results: 1. Quantitative analysis of terminal segments and microspheres in endocardial, midmyocardial and epicardial layers: Table 5.1 shows the total number of microspheres in endocardium, mid-myocardium and epicardium. The total number of microspheres in epicardial layer was larger than in endocardial layer when the heart volume of epicardium was smaller than endocardium. In addition, the density of microspheres of epicardium was twice as high as endocardium. The variation of terminal segment and microsphere in both endocardium and epicardium was unchanged in 4 times of random ball creation. Epicardium had higher variation of terminal segments than endocardium, 0.70 ± 0.01 and 0.28 ± 0.01 (Mean ± SEM) respectively. Similar to terminal segment, the coefficient of variation of microspheres per random ball was larger within epicardium than endocardium, 102 ± 2% vs. 86 ± 1%. Moreover, the endocardium had a higher number of terminal segments but the least microspheres compared to the epicardium. Table 5.1: The information of microspheres in CFI-04 myocardium:. 33.

(34) Chapter 5. Regional distribution of microspheres and terminal segments. Table 5.2: Density of terminal segments and microspheres per random ball in CFI-04 (RB = random ball; CV= coefficient of variation; Msph = microsphere). Repetition. # of RB. ENDO. 1 2 3 4. 59 90 58 72. EPI. 1 2 3 4. 248 234 289 308. Mean of CV of Terminal Mean of Msph TerSeg/ball Segment per ball 81 0.27 66 84 0.27 68 83 0.30 77 85 0.26 77 22 22 22 22. 0.73 0.69 0.70 0.69. 120 120 112 125. CV of Msph 0.88 0.86 0.85 0.85 1.04 0.97 1.03 1.04. 2. The relationship between microsphere and terminal distribution in epicardial, mid and. endocardial layers: As depicted in Figure 5.3a, the relationships between number of microspheres and total terminal segments ended in random ball of different layers are expressed by the linear regression through the origin. The difference in the slope of three regression shows that the number of microsphere related to terminal segment per random ball was not similar from epicardium to endocardium. In the epicardium, the density of terminal segments per each random ball was small, from 1 to 80 terminal segments/ball. In mid-myocardium, this number was larger, from 5 to 100 terminal segments/ball. Endocardium had the highest number of terminal segments per random ball, from 60 to 140 terminal segments/ball. Moreover, the correlation between the number of microspheres and total terminal segments ending in each ball was low in epicardium and mid-myocardium due to many scattered data points, which are not well described by the linear regression model. This scattering could be resulting from the fact that not all terminal segments carried microspheres. In contrast, the average number of microspheres delivered from terminal segments was higher in the epicaridum than endocardium, 200 vs. 70 microspheres, respectively. By eliminating terminal segments which have no close neighbor microsphere, we found that the slope of regression model of the relationship between number of microspheres and terminal segments per random ball increased to a higher value and that the correlation improved (Figure 5.4a). In both cases, the number of microspheres tended to increase from base to apex for a given number of terminal segments per random ball (see Panels b-d in Figs. 5.3 and 5.4). In the endocardium, the number of microspheres was associated with the number of terminal segments per random ball from base to apex direction (Figures 5.3b and 5.4b). In contrast, this correspondence is decayed in mid-myocardium and epicardium (Figures 5.4c and 5.4d). Scattering of microspheres for the same number of terminal segments per random ball within the epicardium was even higher than in the mid-myocardium, especially in the mid-level sections.. 34.

(35) A. LAD. B. ENDO of LAD. 800. 800. 600. 600. 400. 400. 200. 200. 0. 0. 0 40 80 120 160 Terminal segments per random ball. C. MID of LAD. 0 40 80 120 160 Terminal segments per random ball. D. EPI of LAD. 800. 800. 600. 600. 400. 400. 200. 200. 0. 0. 0 40 80 120 160 Terminal segments per random ball. 0 40 80 120 160 Terminal segments per random ball. Figure 5.3: The relationship between the population of microspheres and total terminal segments per random ball of canine heart CFI-04, separated by longitudinal section from base (red) to apex (blue).. Figure 5.4: The relationship between microspheres and terminal segments that have close neighbor microspheres per random ball in canine heart CFI-04, separated from base (red) to apex (blue).. 35.

(36) Chapter 5. Regional distribution of microspheres and terminal segments. IV. Discussion This chapter aimed to establish regional differences of microsphere and terminal segment distribution. We employed the random ball technique developed by Glenny group for microsphere distribution and extended this to include terminal segments (20). It is important to realize that first the terminal segments were determined with the end-position in the random ball. In deviation from the method of Glenny as described by Krueger et al. (20), who counted microspheres within the random ball, now all microspheres connected to the selected terminal segments were selected. As a result some microspheres allocated to a random ball were outside the ball. In this way a relation between the distribution of terminal segments and microspheres could be obtained. There was a clear difference in density of microspheres between endocardium and epicardium. One has to be aware of the fact that such difference may be due to physiological circumstances and hence interpretation of absolute values should be done with care. However, both hearts analyzed demonstrated a much better correlation between number of microspheres and density of terminal segment at the endocardium than at the epicardium. These differences become especially clear when only the terminal segments with allocated microspheres are used. The largest scatter of data is in the epicardial layer, which indicates that the branching pattern of vessels in that region is not so well organized for the distribution of microspheres and hence flow, compared to the endocardium. The heterogeneity in the relation between microsphere and terminal segments is not only the result of differences between endocardium and epicardium but is also caused by differences in the axial direction of the heart. Because microspheres pass through terminal segments, the microsphere heterogeneity is likely governed by the density of terminal segments in different sections. Unfortunately, the number of microspheres was overall not well related to the density of terminal segment. In Chapter 4, we found that number of microspheres is proportional to the diameter and the length of terminal segment, but the quantification of microspheres and terminal segments in this chapter did not take those properties into account. Thus, it can be the reason for the scattering of microspheres corresponding to a specific number of terminal segments. Another drawback of the experimental data is the number of microsphere close by a terminal segment. There are several regions that have terminal segments but no nearby microsphere. A preferential distribution of microspheres in blood flow through terminal segments could be the cause. Regional differences in the relation between vascular structure and microsphere distribution are also apparent from the differences in distribution of nearest distances between endocardium and epicardium. On average, the nearest distance at the endocardium is smaller than at the epicardium. The nearest distances within the random balls have not been analyzed yet, but it would certainly be interesting to investigate.. 36.

(37) Microsphere distribution as well as terminal segment location was observed to be diverse in endocardial and epicardial layers. The volume of endocardium and epicardium can cause this variety. In the LAD region, the volume of epicardium is larger than the volume of endocardium (see Fig. 4.3 and Table 5.1). The higher compression of endocardium during heart contraction, requiring more blood vessels in order to receive sufficient blood and oxygen, can be another explanation for this phenomenon. This assumption has been verified in our study where the average number of terminal segments in the endocardium is higher than epicardium in random ball.. 37.

No results found