1.8 lm) of the rat cremaster muscle. We found that when wall shear stress response was not considered, the layer variability could lead to a slight decrease ...
Annals of Biomedical Engineering ( 2010) DOI: 10.1007/s10439-010-0216-y
Modulation of NO Bioavailability by Temporal Variation of the Cell-Free Layer Width in Small Arterioles PENG KAI ONG, SWATI JAIN, and SANGHO KIM Division of Bioengineering and Department of Surgery, Faculty of Engineering, National University of Singapore, 9 Engineering Drive 1, Block EA #03-12, Singapore 117576, Singapore (Received 3 September 2010; accepted 19 November 2010) Associate Editor Kerry Hourigan oversaw the review of this article.
Abstract—The cell-free layer exhibits dynamic characteristics in the time domain that may be capable of altering nitric oxide (NO) bioavailability in small arterioles. However, this effect has not been fully elucidated. This study utilized a computational model on NO transport to predict how temporal variations in the layer width could modulate NO bioavailability in the arterioles. Data on the layer width was acquired from high-speed video recordings in arterioles (ID = 48.4 ± 1.8 lm) of the rat cremaster muscle. We found that when wall shear stress response was not considered, the layer variability could lead to a slight decrease (1.6–6.6%) in NO bioavailability that was independent of transient changes in NO scavenging rate. Conversely, the transient response in wall shear stress and NO production rate played a dominant role in reversing this decline such that a significant augmentation (5.3–21.0%) in NO bioavailability was found with increasing layer variability from 24.6 to 63.8%. This study highlighted the importance of the temporal changes in wall shear stress and NO production rate caused by the layer width variations in prediction of NO bioavailability in arterioles. Keywords—Nitric oxide, Microcirculation, Wall shear stress, Vasodilation.
INTRODUCTION The functional role of nitric oxide (NO) in the regulation of vascular tone is especially important in the arteriolar network of the microcirculation11 and is mainly attributed to the specialized structure of the arterioles that enables active diameter changes in response to blood flow-induced signals. These small blood vessels are distinctively characterized by the Address correspondence to Sangho Kim, Division of Bioengineering and Department of Surgery, Faculty of Engineering, National University of Singapore, 9 Engineering Drive 1, Block EA #03-12, Singapore 117576, Singapore. Electronic mail: bieks@nus. edu.sg
presence of a NO-responsive smooth muscle layer that surrounds the endothelial cells (ECs) which forms part of the vascular wall. The ECs serve as essential sites for NO production in the arterioles9,34 by responding to hemodynamic signals acting on the luminal surface of these cells exposed to blood flow. Due to its high diffusivity in interstitial fluids, the newly synthesized NO can readily diffuse from the endothelium in opposite radial directions into either the blood lumen (LU) or the smooth muscle layer. The bioavailability of NO in the smooth muscle layer is a critical determinant of vascular tone since NO can activate soluble guanylate cyclase (sGC), an enzyme that stimulates the release of cyclic GMP (cGMP). This signaling molecule is responsible for relaxing the smooth muscle cells, causing vasodilation.2,33 Thus, physiological concentrations of NO required for eliciting smooth muscle relaxation often refer to the NO level required for eliciting half-maximum activity of sGC which ranges from 237,49 to 250 nM.40 Due to the close proximity of the NO production source to red blood cells and the high reactivity of NO with hemoglobin (Hb),9,26 it is unclear how sufficient NO can be maintained in the smooth muscle layer to elicit physiological response on vascular tone in the presence of the red blood cells26 flowing in the LU. NO preservation is known to be a consequence of the attenuation of NO interaction with the Hb by some forms of NO diffusion barrier. While an initial study based on the ‘‘competitive experiment’’43,44 as well as subsequent experimental and theoretical work10 are in favor of intracellular diffusion limitations such as red blood cell membrane and associated cytoskeleton NO-inert proteins, other studies28,42 are supportive of extracellular diffusion factors such as the unstirred boundary layer 2010 Biomedical Engineering Society
ONG et al.
surrounding each red blood cell and the presence of a red blood cell-free layer (CFL) near the vessel wall. The CFL formation results from the tendency of red blood cells to migrate away from the vessel wall and the layer may reduce the flow resistance by decreasing the effective viscosity near the vessel wall. This effect in general becomes more pronounced as the vessel diameter is decreased.21 NO transport in small arterioles is complicated by formation of the CFL since there could be opposing influences imposed by the layer.13 The CFL creates a physical diffusion barrier to NO transport by widening the separating distance from the NO source in the endothelium to red blood cells in the flow stream. This phenomenon is likely to lower the exposure of NO to scavenging by red blood cells in the LU which in turn helps to improve the preservation of NO bioavailability in the arteriolar vessel.26,42 On the contrary, NO preservation could be attenuated by an increase in NO scavenging rate caused by a more compact red blood cell core in the LU due to the CFL.24 Furthermore, it is also possible that NO production in the endothelium could be mitigated by a diminished wall shear stress due to the reduction in effective viscosity near the vessel wall.4,47 Most computational studies6,24,42 that examined the effect of the CFL formation on NO transport in the arterioles utilized a steady state layer model where the layer width is non-varying in the time domain, resulting in constant rates of NO scavenging by the red blood cells and NO production in the endothelium. However, during arteriolar flow, red blood cells are exposed to various hemodynamic interactions in the flow stream and their frequent protrusions into the CFL can lead to dynamic changes in the layer width.1,20 Previous studies31,38 have demonstrated that such transient behavior of the layer width could lead to an augmentation of wall shear stress. This increase in mechanical stimulus acting on the arteriolar endothelium would then be expected to enhance NO synthesis. In addition, it might also be possible that NO bioavailability in the arteriole can be further modulated by an alteration in NO scavenging of the blood core due to transient changes in core hematocrit which varies simultaneously with the layer width. Despite the possible influences that temporal variations in the layer width can impose on NO bioavailability in the arteriole, this effect has not been examined. We hypothesized that temporal variations in the layer width would improve overall NO bioavailability in the arteriole predominantly through the transient modulation of wall shear stress and NO production. In this study, a time-dependent computational model on NO transport was implemented to test this hypothesis and in vivo temporal data on the layer width in arterioles of the rat cremaster muscle were used for the
model. We examined how transient changes in physiological responses accompanying the temporal variations in the layer width can affect theoretical predictions of NO bioavailability that are based on a steady state model. The latter is defined by a uniform CFL width with constant rates of NO scavenging and NO production. Accordingly, we investigated three different cases of the time-dependent model with transient and/or sustained (constant) forms of physiological responses as shown in Table 1.
MATERIALS AND METHODS Animal Preparation A total of 10 Wistar–Furth rats weighing between 190 and 250 g were utilized in this study. All animal handling and care procedures were in accordance with that outlined in the Guide for the Care and Use of Laboratory animals (Institute for Laboratory Animal Research, National Research Council, Washington, DC: National Academy Press, 1996) and approved by the local Animal Subjects Committee. A detailed description of the animal preparation procedures can be referred to our prior study.20 In brief, the rat cremaster muscle was exteriorized and utilized for the observation of arteriolar blood flow. Measurement of Rheological and Physiological Parameters A blood sample (~0.1 mL) was withdrawn from the femoral artery for hematocrit and aggregation measurements. Hematocrit was determined with a microhematocrit centrifuge (Readacrit, Clay Adams) while the degree of red blood cell aggregation was measured periodically during the experiment using an aggregometer (Myrenne aggregometer; Myrenne, Roetgen, Germany). Arterial pressure was continuously recorded with a physiological data-acquisition system (MP 100 System; BIOPAC Systems, Goleta, CA). Adjustment of Red Blood Cell Aggregation Red blood cell aggregation was simulated to levels observed in healthy humans by the infusion of Dextran TABLE 1. Different cases of the time-dependent model. Type of physiological responses
CASE I CASE II CASE III
NO scavenging rate
NO production rate
Constant Transient Transient
Constant Constant Transient
NO Diffusion in Arterioles
Centerline Velocity and Edge Velocity The centerline velocity was obtained from the highspeed video recordings by the dual-window method via a video sampler (Model 204A, Vista Electronics) and velocity correlator system (Model 102BC, Vista Electronics).3,16,46 The edge velocity (Vedge) of the red blood cell core was determined by tracking movements of outermost cells manually across 10 digital frames using image analysis software (SigmaScan Pro 5).30 Experimental Protocol Dextran 500 was administered through the jugular vein to elevate the aggregation level and an arterial blood sample was withdrawn from the femoral artery to measure values of hematocrit and aggregation level. The rat was then mounted on the microscopic stage and an unbranched region of an arteriole was chosen for the study based on the criteria of stable flow, clear focus, and good contrast of the image. An intravital microscope (Ortholux II, Leitz) was used in conjunction with a water immersion objective (409, Olympus) and a long working distance condenser (Instec, Boulder, CO) with numerical apertures of 0.7 and 0.35, respectively. In addition, a blue filter (transmission peak 400 nm, model no. 59820) was used to enhance light absorption by the red blood cells so as to improve the contrast between the cells and background. A highspeed video camera (FASTCCAM ultima SE, Photron USA) was utilized to record blood flow in the arteriole at a frame rate of 4500 s21. A total of 4500 frames were obtained for one side of a vessel which corresponded to a video recording time of 1 s. A typical example of temporal variation in the CFL width in an arteriole (ID = 50 lm) is shown in Fig. 1. To demonstrate the temporal variations of the layer clearer, data for 0.025 s is only shown here. Statistical Analysis A statistical parameter, coefficient of variation (Cv), was used to describe the temporal variability in the CFL width where Cv ð%Þ ¼ CFLsd =CFLmean 100% where CFLsd is the standard deviation of the layer width and CFLmean is the mean layer width. Most of the statistical analyses including regression fits and
8
Blood Lume n
6
Location (µm)
500 (average molecular mass 460 kDa; Sigma) dissolved in saline (6%). A total of 200 mg/kg body weight was infused over the course of 1–2 min to achieve a plasma–dextran concentration of ~0.6%. A blood sample was withdrawn for hematocrit and aggregation level determination ~10 min after the dextran infusion.
CFL-Blood Lume n inte rface
4
2 Ve sse l wall
0 0.000
0.005
Me an CFL width
0.010
0.015
0.020
0.025
Time (s) FIGURE 1. Temporal variations of the cell-free layer width in an arteriole (ID 5 50 lm).
95% confidence intervals of the experimental data were performed using a statistical software package (Prism 4.0, Graphpad). Two-tailed unpaired t tests were used to determine differences in responses with and without association of temporal variations in the layer width. All physiological and rheological data were reported as means ± SD. For all statistical tests and regression fits, p < 0.05 was regarded statistically significant.
Mathematical Model A one-dimensional (1-D) transient model was developed to account for NO concentration changes in the arteriole due to temporal changes in the layer width. The Cartesian coordinate system was used for this purpose since our layer width measurements were obtained from a 2-D imaging plane where there is good image contrast between the red blood cell core and the background (tissue and plasma). A four-compartmental model of the arteriole (Fig. 2) was considered which comprises of the LU, CFL, EC layer, and tissue layer (T). For simplicity, the following assumptions have been made: (1) the mode of NO transport by convection in the axial direction of the vessel can be neglected,18 (2) same diffusion coefficients of NO in all compartments can be approximated by the diffusivity (D) of NO in water,42 (3) a first order reaction rate constant can be used in all compartments except CFL to represent loss of NO by various sinks,24,42 and (4) NO is produced at the luminal (y2) and abluminal (y3) surfaces of the EC layer where its cell membrane is infinitesimally thin and is associated with the NO-producing enzymes (eNOS).42
Governing Equations By applying the above assumptions, the timedependent NO concentration profile in the various
ONG et al.
BCs: Tissue Endothelium CFL
y3 y2 y1
At y ¼ y1 ;
At y ¼ y2 ; y (µm)
Vessel center 0
Time (s) FIGURE 2. Schematic diagram of the arteriole model in Cartesian coordinates. Four compartments are defined in this model, namely the blood lumen (0 < y < y1), cell-free layer (y1 < y < y2), endothelium (y2 < y < y3), and tissue (y3 < y < ¥) regions. The interface (y1) between the cell-free layer and blood lumen exhibits dynamic variations in the time domain.
compartments can be simplified to a general form as described by Eq. (1)
(1) LU (0 < y < y1)
BCs: At y ¼ 0; At y ¼ y1 ;
ð2Þ
dClu;NO ¼0 dy
ð3Þ
CCFL;NO ¼ Clu;NO
ð4Þ
where klu,NO is the first order reaction rate constant of NO scavenging by red blood cells in the LU and y1 represents the temporal variation of the LU width. (2) CFL (y1 < y < y2) @CCFL;NO @ 2 CCFL;NO ¼ DCFL @t @y2
CEC;NO ¼ CCFL;NO
ð7Þ
(3) EC Layer (y2 < y < y3) @CEC;NO @ 2 CEC;NO kEC;NO CEC;NO ¼ DEC 2 @t @y
ð5Þ
ð8Þ
BCs: At y ¼ y2 ;
dCCFL;NO dy dCEC;NO DEC dy
qCFLjEC;NO ¼ DCFL
ð1Þ
CC,NO is the concentration of NO and DC is the diffusion coefficient where the subscript C represents the compartment under consideration. kC,NO is the NO reaction rate constant in the compartment where applicable. Continuity of NO concentration and conservation of NO mass apply at the boundaries of all compartments. In addition, a zero concentration gradient boundary condition was imposed at the vessel centerline and far away from the vessel. The specific NO concentration profile and applied BCs for each compartment is as follows:
@C1u;NO @ 2 Clu;NO ¼ Dlu klu;NO Clu;NO 2 @t @y
ð6Þ
where y2 is the vessel radius and (y2 2 y1) depicts the temporal variation of the CFL width. Since red blood cells are absent in this layer, there is no NO sink due to scavenging by the cells. In addition, other reactions (i.e., auto oxidation) were assumed to be negligibly slow.
Blood Lumen
@CC;NO @ 2 CC;NO ¼ DC kC;NO CC;NO 2 @t @y
dCCFL;NO dClu;NO ¼ Dlu dy dy
DCFL
At y ¼ y3 ;
qECjT;NO ¼ DEC
ð9Þ
dCEC;NO dCT;NO DT dy dy ð10Þ
where kEC;NO (first order reaction rate constant) describes NO consumption within the EC layer, y3 is the distance of the abluminal surface of the endothelium from the vessel centerline and (y3 2 y2) is the EC thickness. qCFLjEC;NO and qECjT;NO represent NO production rates at the luminal and abluminal boundary of the EC layer, respectively. Equal production rate was assumed at each surface. (4) Tissue Region (y3 < y < ¥) @CT;NO @ 2 CT;NO ¼ DT kT;NO CT;NO 2 @t @y
ð11Þ
BCs: At y ! 1; At y ¼ y3 ;
dCT;NO ¼0 dy
ð12Þ
CEC;NO ¼ CT;NO
ð13Þ
where kT;NO is a first order reaction rate constant for NO consumption in the tissue layer. y(¥) is assigned to be a thickness of 2500 lm. It should be noted that the vascular wall adjacent to the EC layer is considered as
NO Diffusion in Arterioles
part of the tissue region, with properties homogeneous to that of the tissue.
wall shear rate ðc_ w Þ and plasma viscosity (lp) as shown in Eq. (19). sw ¼ c_ w lp
Model Parameters (1) Core Hematocrit and NO Scavenging NO scavenging rate in the LU k1u;NO was considered to vary with temporal changes in the CFL width based on simultaneous changes in core hematocrit (HC). By applying the mass balance for HC and systemic hematocrit (HSYS), respectively, at each discrete time point in a cylindrical tube flow using Eq. (14), a transient profile in HC can be obtained. To describe the hematocrit and flow velocity functions in Eq. (14), the in vivo experimental data of the HSYS, CFL width, vessel radius, and centerline flow velocity (Vc) were utilized. As Chen et al.6 have suggested, parabolic hematocrit and velocity profiles were used for aggregating blood flow at high flow rates. Detailed equations on the hematocrit and velocity profiles are presented in Eqs. (15) and (16). Mass balance equation: Z y2 Z y2 2p HðyÞVðyÞydy ¼ HSYS 2p VðyÞydy ð14Þ 0
0
Parabolic hematocrit function: HðyÞ ¼ HC H ð yÞ ¼ H C
y2 y y2 y1
for 0
