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Koutsiaris 2013_a

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Koutsiaris 2013_a

  1. 1. Regular Article Wall shear stress quantification in the human conjunctival pre-capillary arterioles in vivo Aristotle G. Koutsiaris a, ⁎, Sophia V. Tachmitzi b , Nick Batis c a Bioinformatics Laboratory, Department of Medical Laboratories, School of Health Sciences, Technological Educational Institute of Larissa, Larissa, Greece b Ophthalmology Department, General Hospital of Larissa, Larissa, Greece c Technology of Informatics and Telecommunications Department, School of Technology, Technological Educational Institute of Larissa, Larissa, Greece a b s t r a c ta r t i c l e i n f o Article history: Accepted 4 November 2012 Available online 12 November 2012 Blood volume flow (Q), wall shear rate (WSR) and wall shear stress (WSS) were quantified, for the first time, in the conjunctival pre-capillary arterioles of normal human volunteers with diameters (D) between 6 and 12 μm. The variation of the blood velocity throughout the cardiac cycle was taken into account using high speed video microcinematography. The dual effect of arteriolar diameter, firstly on the WSR and secondly on the dynamic viscosity of blood, was taken into account in the estimation of WSS. The average Q, WSR and WSS, throughout the cardiac cycle ranged from 13 to 202 pl/s, 587 to 3515 s−1 and 1.7 to 21.1 N/m2 re- spectively. The best fit power law equations, giving the increase of Q and the decrease of WSR and WSS with diameter, are presented for the systolic and diastolic phase as well as for the averages throughout the cardiac cycle. According to the WSS best fit equation, the average WSS decreases from 10.5 N/m2 at D=6 μm down to 2.1 N/m2 at D=12 μm. © 2012 Elsevier Inc. All rights reserved. Introduction The amount of blood transferred by any vessel to any tissue is given by the blood volume per second or volume flow (Q) going through the vessel cross-section. The quantification of the volume flow of blood in the microvasculature is useful for estimating the amount of chemicals exchanged between blood and tissue. In addi- tion, it is useful for the construction of theoretical models of vascular function and design. The pressure exerted by the moving fluid on the inner surface of a tube, along the direction of the flow, is called wall shear stress (WSS) and depends on the dynamic viscosity of blood and on the wall shear rate (WSR). WSS has been implicated in many physiological as well as pathological phenomena occurring in the cardiovascular system. Regarding physiological phenomena, Rodbard (1975) proposed for the endothelial cells the existence of a critical WSS set point; values above this set point induce endothelium to generate vasodilation signals and values lower than this set point trigger constriction of the vascular smooth muscle. Twenty years later, Pries et al. (1995b) further proposed that this set point is a function of the local transmural pres- sure calling this proposal the “pressure-shear” hypothesis. Today, known vasoactive factors, produced by the endothelium, are the nitric oxide (NO), prostacyclin (PGI2) and bradykinin (BK). Some of them (NO and PGI2) are not only involved in signaling but their production also prevents the activation of platelets and the for- mation of thrombi (Busse and Fleming, 1995). In addition, it is usually considered that WSS is a major modulator of genes involved in endothelial cell division, differentiation, migra- tion and apoptosis (Macdonald et al., 2010; Naik and Cucullo, 2012). Regarding pathological phenomena, Caro et al. (1969) postulated that endovascular areas of low shear favored the development of atheromatic lesions. Since then some progress was made and even though the whole process is not yet fully clear, the accepted general mechanism is that hemodynamic related factors and mainly WSS influence the normal behavior of endothelial and smooth muscle cells of the vascular wall, as well as the behavior of blood monocytes which adhere to the endothelium, invade the intimal layer and become macrophages triggering the formation of atheromatic plaque (Nerem, 1995). Monocyte adhesion is promoted by the vascular cell adhesion molecule-1 which is expressed after the phosphorylation of apoptosis-signal-kinase-1 (ASK1) caused in a low shear stress en- vironment (Gaynes et al., 2012). Finally, physiological WSS values are necessary for the design of in vitro apparatus to study various phenomena or biological mecha- nisms such as angiogenesis (Kang et al., 2011), the blood brain barrier (Cucullo et al., 2011; Naik and Cucullo, 2012) and cancer metastasis (Köhler et al., 2010; Richter et al., 2011). In addition, WSS values are necessary for the design of vascular targeted drug carriers (Charoenphol et al., 2010). Despite the critical importance of WSS in unraveling important mysteries of the cardiovascular physiology and pathology, today Microvascular Research 85 (2013) 34–39 ⁎ Corresponding author at: 9 Miauli St, Larissa, 41223, Greece. E-mail addresses: ariskout@otenet.gr, ariskout@teilar.gr (A.G. Koutsiaris). 0026-2862/$ – see front matter © 2012 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.mvr.2012.11.003 Contents lists available at SciVerse ScienceDirect Microvascular Research journal homepage: www.elsevier.com/locate/ymvre
  2. 2. there is no sufficient amount of accurate in vivo WSS measurements in human subjects. The objective of this work was the quantification of blood volume flow (Q), wall shear rate (WSR) and wall shear stress (WSS) in the human smallest diameter arterioles of the eye using axial velocity measurements from a previous work (Koutsiaris et al., 2010). The quantification method described in the following section takes into account the microvessel diameter in the estimation of the cross-sectional velocity Vs by using a profile factor function (PFF) which requires as input axial velocity measurements (Koutsiaris, 2005). Then Q and WSR can be estimated in relation to microvessel diameter using Vs. In addition, the dependence of dynamic viscosity on diameter is taken into account using the in vivo viscosity law (Pries et al., 1994). Therefore, the unique characteristic of this WSS quantification method is that it takes into account the combined effect of diameter, firstly on WSR and secondly on dynamic viscosity, leading to the final estimation of WSS. The aforementioned method was applied here, for the first time, to the precapillary arterioles of the human eye where significant pulsa- tion exists (Koutsiaris et al., 2010). So, averages of Q, WSR and WSS, during the cardiac cycle, are presented separately from systolic and diastolic values. The equations of the power law best fit trend lines describing the relationship of Q, WSR and WSS with diameter could be valuable to basic science researchers who need reference to in vivo values for their experiments in the laboratory or their theoretical models. In ad- dition these equations could be helpful to clinical researchers in order to study how physiological WSS values change in disease states or after the administration of drugs. Materials and methods Experimental arrangement The experimental set up shown in Fig. 1 consisted of a slit lamp (Nikon FS-3 V) connected with a high-speed CCD camera (12 bit, PCO Computer Optics GmbH, Germany) and a PC (Pentium 4, 3 GHz). The system produced digital images of 320×240 pixels at a frame rate of 96 frames per second (fps) with an enhanced maximum magnification of 242× and a digital resolution of 1.257±0.004 μm/pixel. More details on the experimental set up can be found elsewhere (Koutsiaris et al., 2010). Subjects Fifteen (15) normal human volunteers were included in the study with an age between 24 and 38 years, an average body mass index (BMI, defined as the number of body kilograms over the square of the height) of 23±3 kg/m2 , no smoking or alcohol habit, no ocular or systemic disease and they were not under any medication. Nine (9) volunteers were men and six (6) were women. Data from female subjects were acquired after their menstruation and before the premenstrual period of 8 days. Images were recorded from the right eyes (temporal side of the bulbar conjunctiva) and no volunteer contributed by more than two microvessels to the total sample. Recordings were not taken into account when a 20% (or more) change occurred in either of the initial systolic or diastolic arterial blood pressure. In addition, subjects with a diastolic blood pressure greater than 90 mmHg were excluded from the study as hypertensive. All subjects waited at least 40 min for adaptation in a room temperature between 22 and 24 °C. The project was approved by the research ethics committee of the university hospital of Larissa and informed consent was obtained from all participants in the study. Image registration Images were registered employing a manual approach and using a graphical user interface programme developed in MATLAB soft- ware platform. One image from each image sequence was tagged as ‘reference’ and the remaining ‘mobile’ images were all registered to the reference using 2 white cross-hair tools forming a simple grid of 9 rectangular quadrilaterals. Mobile images were translated along the x and y axes (two-dimensional registration) so that its characteristic regions were aligned with the ‘reference’ image. The manual registration procedure is described in more detail in a previ- ous work (Koutsiaris et al., 2010). Internal diameter (D) and axial velocity (Vax) pulse quantification The internal diameter (D) was estimated using the Pythagoras's the- orem from the coordinates of the intersection points between a vertical line to the vessel axis and the outer limits of the erythrocyte column. The diametric value assigned to each arteriole was the average of 3 or 4 different measurements. Objective lens CCD CameraHuman Conjunctiva Optical Axis LCD MONITOR Slit lamp PC Fig. 1. Schematic diagram of the experimental set-up. 35A.G. Koutsiaris et al. / Microvascular Research 85 (2013) 34–39
  3. 3. Axial erythrocyte velocity (Vax) was measured using the axial dis- tance DC travelled by a RBC or a plasma gap, over a fixed time interval Δt: Vax ¼ DC=Δt ð1Þ Δt is known from the frame rate of the camera as equal to 10.04 ms. Estimation of cross-sectional velocity Vs and volume flow Q In microvessel diameters less than approximately 20 μm, blood cannot be considered as a “continuum” and a velocity profile cannot be used in the ordinary sense in order to estimate cross-sectional velocity (Koutsiaris, 2012). So, for the conversion of the axial velocity Vax to the cross-sectional velocity Vs a profile factor function (PFF, Koutsiaris, 2005) was used, assuming that the average human erythrocyte diameter is equal to 7.65 μm (Koutsiaris et al., 2007). Blood volume flow (Q) was estimated by the product of the cross-sectional velocity VS and the cross-sectional area S (assuming a circular cross-section): Q ¼ VS π D 2 4 ð2Þ Estimation of wall shear rate WSR Wall shear rate (WSR) was determined using VS values: WSR ¼ 8 VS D ð3Þ Estimation of wall shear stress WSS The wall shear stress (WSS) was estimated from the formula: WSS ¼ η WSR ð4Þ where η is the dynamic viscosity (apparent) of blood which was estimated as a function of diameter using the in vivo viscosity law (Pries et al., 1994) and a technique described by Koutsiaris et al. (2007). The in vivo viscosity law requires the instantaneous values of the systemic hematocrit (Hs) and the discharge hematocrit (Hd) for each microvessel separately. Since instantaneous hematocrit measure- ments for each microvessel could not be performed here, average values were used for all the microvessels: Hs=45% and Hd =18%. Changes during the cardiac cycle In contrast to the venular part of the human microcirculation, the arteriolar part exhibits a pulsating behavior with an average resistive index equal to 53% (Koutsiaris et al., 2010). Consequently the quanti- ties of velocity, volume flow, wall shear rate and wall shear stress change significantly throughout the cardiac cycle. Every pulsating waveform related to the cardiac cycle is character- ized by a peak systolic (PS) and an end diastolic (ED) value. The time interval between 2 successive PS values defines the pulse period and during this period the average (AV) value can be estimated. There- fore, each hemodynamic quantity was presented in 3 parts: a) peak systolic (PS), b) average (AV) and c) end diastolic (ED). In each of the aforementioned parts, the equation of the power law best fit trend line describing the relationship of the hemodynamic quantity with the diameter was presented, together with the corre- sponding correlation coefficient (r). Statistical analysis Microsoft Office EXCEL 2003 (professional edition) was used for statistical analysis. Correlations were estimated with Pearson's corre- lation coefficient. Results Measurements were taken from 30 different precapillary arteri- oles of the bulbar conjunctiva with diameters ranging from 6 to 12 μm. At least 150 images were recorded from each microvessel, cor- responding to a recording time of approximately 1.5–2 s and a total of more than 5000 images were registered manually for subsequent measurement of axial velocity Vax (Koutsiaris et al., 2010). Axial velocities (Vax), cross-sectional velocities (Vs), volume flows (Q), wall shear rates (WSR) and wall shear stresses (WSS) for all the 0 1 2 3 4 5 6 7 5 6 7 8 9 10 11 12 13 Diameter D (µm) PSVax(mm/s) (a) 0 1 2 3 4 5 6 7 5 6 7 8 9 10 11 12 13 Diameter D (µm) AVVax(mm/s) (b) 0 1 2 3 4 5 6 7 5 6 7 8 9 10 11 12 13 Diameter D (µm) EDVax(mm/s) (c) Fig. 2. Axial erythrocyte velocity (Vax) in relation to the diameter of the pre capillary arterioles of the eye (from Koutsiaris et al., 2010). (a) peak systolic axial velocity (PSVax), (b) average axial velocity (AVVax) and (c) end diastolic axial velocity (EDVax) are shown in triangles, circles and crosses respectively. 36 A.G. Koutsiaris et al. / Microvascular Research 85 (2013) 34–39
  4. 4. microvessels are shown in Figs. 2–6 respectively. Peak systolic, averages and end diastolic values are presented in parts (a), (b) and (c) of each of the aforementioned figures respectively. So, peak systolic Vax (PSVax), peak systolic Vs (PSVs), peak systolic Q (PSQ), peak systolic WSR (PSWSR) and peak systolic WSS (PSWSS) are presented in Figs. 2(a), 3(a), 4(a), 5(a) and 6(a) respectively. Average Vax (AVVax), average Vs (AVVs), average Q (AVQ), average WSR (AVWSR) and average (AVWSS) are presented in Figs. 2(b), 3(b), 4(b), 5(b) and 6(b) respec- tively. End diastolic Vax (EDVax), end diastolic Vs (EDVs), end diastolic Q (EDQ), end diastolic WSR (EDWSR) and end diastolic WSS (EDWSS) are presented in Figs. 2(c), 3(c), 4(c), 5(c) and 6(c) respectively. PSVax ranged from 0.62 to 5.84 mm/s (Fig. 2a), PSVs from 0.55 to 4.95 mm/s (Fig. 3a), PSQ from 16 to 362 pl/s (Fig. 4a), PSWSR from 733 to 6562 s−1 (Fig. 5a) and PSWSS from 2.1 to 39.4 N/m2 (Fig. 6a). The upper limit values of 6562 s−1 and 39.4 N/m2 are not shown in the corresponding graphs for a better presentation of the results but they were taken into account in the estimation of the trend lines described in the following paragraphs. The ranges of the aforementioned quantities are smaller for the av- erage values throughout the cardiac cycle: 0.52–3.26 mm/s for AVVax (Fig. 2b), 0.46–2.65 mm/s for AVVs (Fig. 3b), 13–202 pl/s for AVQ (Fig. 4b), 587–3515 s−1 for AVWSR (Fig. 5b) and 1.7–21.1 N/m2 for AVWSS (Fig. 6b). EDVax ranged from 0.40 to 1.80 mm/s (Fig. 2c), EDVs from 0.35 to 1.51 mm/s (Fig. 3c), EDQ from 10 to 115 pl/s (Fig. 4c), EDWSR from 330 to 2004 s−1 (Fig. 5c) and EDWSS from 0.9 to 12.0 N/m2 (Fig. 6c). In all parts of Figs. 4–6 the best fit power law trend line equation and the corresponding correlation coefficient (r) are shown. Using these equations, the trends of volume flow, wall shear rate and wall shear stress can be quantified for every diametric value between 6 and 12 μm. For example, the average Q throughout the cardiac cycle (Fig. 4b) increases from 37 pl/s at D=6 μm up to 139 pl/s at D=12 μm, the average WSR (Fig. 5b) decreases from 1752 s−1 at D=6 μm down to 823 s−1 at D=12 μm and the average WSS (Fig. 6b) decreases from 10.5 N/m2 at D=6 μm down to 2.1 N/m2 at D=12 μm. 0 1 2 3 4 5 6 5 6 7 8 9 10 11 12 13 Diameter D (µm) PSVs(mm/s) (a) 0 1 2 3 4 5 6 5 6 7 8 9 10 11 12 13 Diameter D (µm) AVVs(mm/s) (b) 0 1 2 3 4 5 6 5 6 7 8 9 10 11 12 13 Diameter D (µm) EDVs(mm/s) (c) Fig. 3. Cross-sectional velocity (VS) in relation to the diameter of the pre-capillary ar- terioles of the eye. (a) Peak systolic cross-sectional velocity (PSVs), (b) average cross-sectional velocity (AVVs) and (c) end diastolic cross-sectional velocity (EDVs) are shown in triangles, circles and crosses respectively. PSQ = 1.85 D 1.88 r = 0.66 0 100 200 300 400 5 6 7 8 9 10 11 12 13 Diameter D (µm) PSQ(pl/s) (a) AVQ = 1.21 D 1.91 r = 0.75 0 100 200 300 400 5 6 7 8 9 10 11 12 13 Diameter D (µm) AVQ(pl/s) (b) (c) EDQ = 0.89 D 1.84 r = 0.76 0 100 200 300 400 5 6 7 8 9 10 11 12 13 Diameter D (µm) EDQ(pl/s) Fig. 4. Volume flow (Q) in relation to the diameter of the pre capillary arterioles of the eye. (a) Peak systolic volume flow (PSQ), (b) average volume flow (AVQ) and (c) end diastolic volume flow (EDQ) are shown in triangles, circles and crosses respectively. The best fit power law equation is shown in black line together with the correlation co- efficient (r). 37A.G. Koutsiaris et al. / Microvascular Research 85 (2013) 34–39
  5. 5. In Figs. 2 and 3 there are no standard trend line best fits (linear, logarithmic, power law or exponential) because the correlation coef- ficient r was less than 0.16. It seems, in practice, there is no correla- tion between velocity and diameter at least in the limited range of the diameters examined here. A histogram is shown in Fig. 7, where the frequencies of 7 different groups of the AVVax are presented. The skewness and the kurtosis of the frequency distribution were positive (+0.77 and +0.91, respec- tively) but sufficiently low to consider the distribution as normal and use the mean value and the standard deviation (SD). The mean axial velocity of the average values of all the microvessels shown in circles in Fig. 2b was: bAVVax>=1.66 mm/s±0.61 (SD) and the mean cross-sectional velocity of the average values of all the microvessels shown in circles in Fig. 3b was: bAVVs>=1.36 mm/s±0.51 (SD). Discussion The mean value of all average axial velocities shown in Fig. 2b was 1.66 mm/s±0.6 (SD) which is almost identical to the mean of 1.6±0.5 mm/s from 14 rabbit mesentery precapillary arterioles with diameters equal or less than 12 μm (Koutsiaris and Pogiatzi, 2004). It is a little lower than the mean of 2±1.7 mm/s from mea- surements at rat mesenteric arterioles (Pries et al., 1995a) with an average diameter of 13.2 μm which is higher in comparison to the average of 8.5 μm in the present work. Blood volume flow, wall shear rate and wall shear stress were quantified for the first time in the pre-capillary microvasculature of the bulbar conjunctiva of the human eye for diameters ranging between 6 and 12 μm. Volume flow and hematocrit are the primary physical quantities for the correct estimation of the oxygen supply and WSS is necessary PSWSR = 18820 D -1.12 r = 0.47 0 1000 2000 3000 4000 5000 5 6 7 8 9 10 11 12 13 Diameter D (µm) PSWSR(s-1) (a) AVWSR = 12352 D -1.09 r = 0.54 0 1000 2000 3000 4000 5000 5 6 7 8 9 10 11 12 13 Diameter D (µm) AVWSR(s-1) (b) EDWSR = 9083 D -1.16 r = 0.59 0 1000 2000 3000 4000 5000 5 6 7 8 9 10 11 12 13 Diameter D (µm) EDWSR(s-1) (c) Fig. 5. Wall shear rate (WSR) in relation to the diameter of the pre capillary arterioles of the eye. (a) Peak systolic wall shear rate (PSWSR), (b) average wall shear rate (AVWSR) and (c) end diastolic wall shear rate (EDWSR) are shown in triangles, circles and crosses respectively. The best fit power law equation is shown in black line togeth- er with the correlation coefficient (r). The triangle (6 μm, 6562 s−1 ) is not shown in graph (a) for a better presentation of the results but it was taken into account in the estimation of the best fit equation. PSWSS = 1082 D -2.38 r = 0.75 0 5 10 15 20 25 5 6 7 8 9 10 11 12 13 Diameter D (µm) PSWSS(N/m2) (a) AVWSS = 710 D -2,35 r = 0.81 0 5 10 15 20 25 Diameter D (µm) AVWSS(N/m2) (b) EDWSS = 522 D -2,41 r = 0.84 0 5 10 15 20 25 5 6 7 8 9 10 11 12 13 5 6 7 8 9 10 11 12 13 Diameter D (µm) EDWSS(N/m2) (c) Fig. 6. Wall shear stress (WSS) in relation to the diameter of the pre capillary arterioles of the eye. (a) Peak systolic wall shear stress (PSWSS), (b) average wall shear stress (AVWSS) and (c) end diastolic wall shear stress (EDWSS) are shown in triangles, cir- cles and crosses respectively. The best fit power law equation is shown in black line to- gether with the correlation coefficient (r). The triangle (6 μm, 39.4 N/m2 ) is not shown in graph (a) for a better presentation of the results but it was taken into account in the estimation of the best fit equation. 38 A.G. Koutsiaris et al. / Microvascular Research 85 (2013) 34–39
  6. 6. for the study of the morphological alterations of endothelial cells (Κataoka et al., 1998) and of the corresponding genetic mechanisms. As a consequence of its definition volume flow increases with in- creasing diameter and as it is shown in Fig. 4b the relationship of the average volume flow with the diameter can be approximated by a 2nd power law relationship. This concurs with the results reported for the human post capillary venules (Koutsiaris et al., 2007) and departs from the 3rd power law proposed by Murray (1926). In Figs. 5 and 6, it is shown that WSR and WSS decrease with in- creasing diameter but WSS decreases at a much steeper gradient than WSR and this is a consequence of the strong non linear nature of the in vivo viscosity law. As a result, the AVWSS value given by the trend line shown in Fig. 6b, is five times higher at D=6 μm (10.5 N/m2 ) compared to the value of 2.1 N/m2 at D=12 μm. The AVWSR value given by the trend line shown in Fig. 5b on the other hand is only 2.1 times higher at D=6 μm (1752 s−1 ) in comparison to the value of 823 N/m2 at D=12 μm. The aforementioned range of AVWSS values coincides with the range of values (3–10 N/m2 ) reported from other animal tissues (Lipowsky, 1995; Pries et al., 1995b). However, the AVWSS value at D=6 μm is almost double than that expected by some authors (Lipowsky, 1995) and more than 5 times higher than that expected by other authors (Naik and Cucullo, 2012). It seems also that the arteriolar trend line AVWSS values in the human eye are approximately 3 times higher than the venular trend line AVWSS values (Koutsiaris et al., 2007), in the corresponding di- ameters. This concurs with results reported from other mammal tis- sues (Lipowsky, 1995) and perhaps it correlates with differences in the restrictive properties of the blood brain barrier among arterioles, capillaries and venules (Macdonald et al., 2010). In this work, volume flow, wall shear rate and wall shear stress were quantified in the human pre-capillary arterioles of the conjunc- tiva in relation to microvessel diameter taking into account the pulsa- tion of arteriolar blood flow. The presented fitting results support a 2nd power law relation between average volume flow and diameter values. In addition there is an approximately 5 fold increase of the wall shear stress values as blood moves from the higher diameter pre-capillary arterioles down to the smaller diameter capillaries in the human bulbar conjunctiva. Finally, average wall shear stress values in the pre-capillary arterioles are approximately 3 times higher than those in the corresponding diameter post-capillary venules. References Busse, R., Fleming, I., 1995. Regulation of platelet function by flow-induced release of en- dothelial autacoids. In: Bevan, J.A., Kaley, G., Rubanyi, G.M. (Eds.), Flow-dependent regulation of vascular function. 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Richter, U., Schröder, C., Wicklein, D., Lange, T., Geleff, S., Dippel, V., Schumacher, U., Klutmann, S., 2011. Adhesion of small cell lung cancer cells to E- and P- Selectin under physiological flow conditions: implications for metastasis formation. Histochem. Cell Biol. 135, 499–512. Rodbard, S., 1975. Vascular Caliber. Cardiology 60, 4–49. Κataoka, N., Ujita, S., Kimura, K., Sato, M., 1998. Effect of flow direction on the morpholog- ical responses of cultured bovine aortic endothelial cells. Med. Biol. Eng. Comput. 36, 122–128. 0 2 4 6 8 10 12 0.52 1.04 1.56 2.08 2.60 3.12 3.64 AVVax (mm/s) Frequency Fig. 7. A histogram of the average axial velocities (AVVax) shown in Fig. 2b. AVVax data were categorized in 7 groups. 39A.G. Koutsiaris et al. / Microvascular Research 85 (2013) 34–39

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