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Am J Physiol Heart Circ Physiol 288: H2047-H2054, 2005. First published December 16, 2004; doi:10.1152/ajpheart.00496.2004
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Structural remodeling of mouse gracilis artery after chronic alteration in blood supply

Gabriel Gruionu,1,2 James B. Hoying,1,2,4 Axel R. Pries,3 and Timothy W. Secomb1,4

1Biomedical Engineering Program, 2Vascular Research Group, University of Arizona, Tucson, Arizona; 3Department of Physiology, Charité-Universitätsmedizin Berlin, Campus Benjamin Franklin, Berlin, Germany; and 4Department of Physiology, University of Arizona, Tucson, Arizona

Submitted 7 June 2004 ; accepted in final form 9 December 2004


   ABSTRACT
TOP
 ABSTRACT
MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 GRANTS
 REFERENCES
 
The goals of this study were to determine the time course and spatial dependence of structural diameter changes in the mouse gracilis artery after a redistribution of blood flow and to compare the observations with predictions of computational models for structural adaptation. Diameters were measured 1, 2, 7, 14, 21, 28, and 56 days after resection of one of the two blood supplies to the artery. Overall average diameter, normalized with respect to diameters in untreated vessels, increased slightly during the first 7 days, then increased more rapidly, reaching a peak around day 21, and then decreased. This transient increase in diameter was spatially nonuniform, being largest toward the point of resection. A previously developed theoretical model, in which diameter varies in response to stimuli derived from local metabolic and hemodynamic conditions, was extended to include effects of time-delayed remodeling stimuli in regions of reduced perfusion. Predictions of this model were consistent with observed diameter changes, including the transient increase in diameters near the point of resection, when a remodeling stimulus with a time delay of ~7 days was included. The results suggest that delayed stimuli significantly influence the dynamic characteristics of vascular remodeling resulting from reduced blood supply.

metabolic response; shear stress; vessel wall conduction; adaptation; computational model

THE PRIMARY FUNCTION of the vasculature is to perfuse blood through tissues. As demands for oxygen and nutrients fluctuate, vessels must respond appropriately to match blood supply to demand. Acute changes in metabolic state are matched by adjustments in the tone of vascular smooth muscle, resulting in rapid, short-term vasodilation or vasoconstriction. When tissue demands are chronically altered, such as in exercise or tissue growth and repair, vessels undergo structural remodeling, resulting in changes in diameters over time scales of days or longer (15, 17, 18, 30, 40). In particular, during ischemic revascularization following partial or total blood flow interruption to a mouse hindlimb, structural remodeling of persistent vessel elements in the ischemic tissue (collateralization) is an important aspect of establishing reperfusion pathways (5, 32, 37). During this tissue repair process, the cells of the vessel wall proliferate, regress, and/or rearrange themselves and the surrounding extracellular matrix to alter vessel structure (32, 38). Structural remodeling (angioadaptation) allows for long-term adjustment of flow resistance while maintaining an ability to adjust tone in response to acute stimuli (43).

Several chronic stimuli have been shown to cause long-term changes in vessel diameter. These stimuli include changes in blood flow and the resulting wall shear stress (16, 40, 42), alterations in intravascular pressure and circumferential wall stress (2, 9, 20, 35), and changes in the tissue metabolic state (18, 31). In addition, vasoactive responses can be conducted upstream along the vessel wall, between vessel segments (7, 34). Theoretical studies imply that chronic effects of conducted responses are important in structural remodeling (26). Observed steady-state distributions of vessel diameters in stable vascular networks are adequately predicted by model simulations including all these stimuli (24, 26).

When interruption of blood flow leads to tissue ischemia, a biphasic vascular response can be observed, as, for example, in wound healing (3, 8). During the initial phase, microvascular proliferation and outward remodeling of existing vessels result in above-normal levels of vascular density. Vascular regression and "pruning" (27) occur during the second phase, and the vasculature approaches its normal state. Such behavior, in which variables "overshoot" their equilibrium values, is characteristic of dynamic systems with time delays (21). In the case of ischemia, the release of cytokines by tissue cells and infiltrating leukocytes in response to hypoxia and inflammation is a possible source of time-delayed effects. These cytokines may include growth factors, inflammatory cytokines, and matrix modulators (12, 19, 31). The production of cytokines and the resulting vascular responses involve several molecular and cellular processes, including gene transcription, protein synthesis, and cell division and growth, and occur over a period of days to weeks after the ischemic event (13, 32, 38). Such time-delayed responses to alterations in metabolic conditions resulting from hypoxia and inflammation have not been considered in previous theoretical simulations of structural remodeling of the vasculature.

In the present study, the temporal and spatial changes of the inner diameter of the mouse gracilis artery were observed after resection of one of its two blood supplies. The observed diameter changes were compared with the results of theoretical simulations of structural adaptation in response to altered hemodynamic and metabolic conditions by using a previously developed theoretical model (24–26), which was extended to include the effects of time-delayed responses to hypoxia and inflammation.


   MATERIALS AND METHODS
TOP
 ABSTRACT
 MATERIALS AND METHODS
RESULTS
 DISCUSSION
 GRANTS
 REFERENCES
 
Experimental animals and surgical procedure. Male FVB/n mice were used for all experiments according to procedures approved by the University of Arizona Institutional Animal Care and Use Committee. Surgical procedures were timed so that all mice were 7–11 wk old and had a body weight of 27.4 ± 3 g at the time of data collection. The gracilis artery, the main blood supply to the gracilis muscle on the medial side of the thigh, is fed by two arteries, the muscular branch of the femoral artery and the saphenous artery (Fig. 1). The gracilis artery runs parallel to the muscle fibers over almost the entire length of the muscle (Fig. 2). The transverse arterioles (TAs) branch off at intervals along the length of the vessel and supply the capillary network. In some specimens, two adjacent TAs connect to form a loop arcade structure (Fig. 2).



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  		Fig. 1. Photograph of medial side of mouse thigh, with skin removed to show muscles. FA, femoral artery; GA, gracilis artery; MB, muscular branch of FA; SA, saphenous artery. In the model, the blood supply from the SA was interrupted by removing the portion of the vessel between the ligatures (dotted line).

 


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  		Fig. 2. A and B: digitized images of control (A) and 14-day remodeled (B) mouse gracilis muscle, visualized using India ink. TA, transverse arteriole. In some specimens, 2 TAs come together to form a loop arcade (asterisk). C and D: schematics of the simplified vascular network used in the theoretical models. Node i is the point of bifurcation of a TA. Arrows show direction of blood flow.

 
The blood supply to the gracilis artery was disrupted by removing a portion of the saphenous artery spanning 5 mm above and below the point where the saphenous artery connects with the gracilis artery (Fig. 1). Both saphenous artery and vein were removed, but the accompanying nerve was kept intact. Removal of the vein was necessary to ensure interruption of blood supply to the gracilis artery and also because, technically, it is difficult to separate the femoral vein from the artery without damaging the vein. To interrupt the blood supply from the saphenous artery, we anesthetized the mouse with 2.5% Avertin (Aldrich) at a dose of 0.15 ml/10 g body wt injected intraperitoneally and removed the hair from the medial side of the left hindlimb with a depilatory lotion. A skin incision was made on the medial side of the thigh 5 mm away from the saphenous artery to minimize the effect of skin injury on gracilis artery remodeling. Incisions were closed with 7.5-mm Michel suture clips. The mice were euthanized 1, 2, 7, 14, 21, 28, or 56 days after surgery (n = 6, 5, 6, 7, 6, 6, and 5 mice, respectively). The untreated control group mice (n = 6) received no surgery. The saphenous artery of the sham control mice (n = 6) was exposed but maintained intact. Mice were euthanized 7 days after the sham surgery.

India ink visualization. To visualize the gracilis artery network, nontoxic India ink (no. 3232; Hunt Manufacturing) was dialyzed against PBS, filtered through filter paper (no. 1; Whatman), and stored at 4°C. Before use, the ink solution was warmed to 37°C. Heparin (100 U/ml final concentration) and sodium nitroprusside (10–5 M final concentration) were added to the ink solution. The left ventricle was cannulated with a polyethylene (PE60) catheter, and the blood was flushed with PBS containing heparin and sodium nitroprusside. A volume of 2–4 ml of ink solution was immediately perfused into the vasculature at a constant pressure of 90–100 mmHg, measured with a manometer attached to the injection syringe. All major vessels were ligated at their origins from the heart to avoid backflow of ink. Animals were either placed at 4°C overnight to allow the India ink to stabilize in the vessels (day 2, 7, and 28 groups) or the medial side of the thigh was covered with a cotton gauze soaked in 25% ethanol immediately after ink perfusion (day 1, 14, 21, and 56 groups). The gracilis muscle on both sides was carefully dissected, placed flat on a microscopic slide to maintain its original length, and dehydrated in a graded series of alcohol solutions (25, 50, 75, 95, and 100% ethanol) for ~12 h in each alcohol dilution. The muscles were subsequently cleared in 100% methyl salicylate. The vasculature was analyzed with a stereomicroscope after the muscle was gently sandwiched between two microscope slides and transilluminated.

Morphometric analysis. Morphometric data (length and inner diameter of gracilis artery and number of TAs) were obtained from digitized microscopic images by using Sigma Scan software (SPSS Science, Chicago, IL). The inner diameter was measured at points spaced 300 µm apart along the artery. To show the spatial dependence of diameter, the length of each artery was divided into eight equal regions (Fig. 2, C and D). For each region, data from all arteries observed for a given time point and treatment were combined to calculate the mean and standard error of the region diameter. Statistical significance between control (untreated) and remodeled (treated) diameters in each region at each time point was determined using a paired t-test. A P value <0.05 was considered significant. A normalization procedure was used to correct for variations in observed diameters of untreated gracilis arteries. For each region, a reference diameter was defined as the overall average of the untreated diameters at all time points. The ratio of the average treated diameter to the average untreated diameter was computed at each time point for each region. The normalized treated region diameter at each time point was obtained by multiplying this ratio by the corresponding reference diameter. With this procedure, variations in normalized diameter with time reflect differential changes between diameters of remodeled and control contralateral vessels. To facilitate analysis of the time course of diameter changes, these normalized diameter data were combined for three main sections of the gracilis artery: the MB section (regions 1–3 close to the connection with the muscle branch of the femoral artery), the middle section (regions 4–6), and the SA section (regions 7 and 8 close to the connection to the saphenous artery) (Fig. 2, C and D). The resulting section diameters were used for comparison with the theoretical model predictions.

Estimation of hemodynamic parameters. The simulation of structural adaptation required estimation of pressure, flow, and wall shear stress as functions of position along the gracilis artery for a given spatial variation of diameter. Nodes were defined at the end points of the artery and at the points where TAs branch off, such that segment i of the artery links node i with node i + 1 (Fig. 2, C and D). The number of TAs was assumed to be 16, giving 16 segments and 17 nodes along the artery. The observed number of TAs was generally in the range from 12 to 18. A total length of 6.6 mm was assumed, representing the average of measured values, and the TAs were assumed to be spaced at equal intervals along the length. The end of the artery supplied by the muscular branch of the femoral artery was assumed to be at arterial pressure, PA = 100 mmHg (39), giving a boundary condition P1 = PA. For simulations of the untreated artery, the TA at node 17 was omitted and the connection to the saphenous artery was represented by setting P17 = PA.

The flow rate entering the TA connected to node i was assumed to depend on the pressure Pi at that node according to i = (Pi – PV)/RTA, where PV is venous pressure, assumed to be 2 mmHg (39), and RTA is the flow resistance of the pathway connecting the TA to the venous pressure. This resistance is given by RTA = (PA – PV)/ ref, where ref is a reference value of the TA flow. In the absence of suitable data for the mouse, the reference TA flow was estimated from data obtained from rats. Under conditions of normal tone, the volume blood flow for the rat gracilis muscle is 4.6 ml/min per 100 g of muscle (36). Total blood flow per gracilis muscle of the adult rat (13 wk) was computed as 2.4 µl/min for an average muscle volume of 53.2 mm3 (36). This resulted in a reference blood flow rate ref = 29 nl/min, based on an average of 83.7 TAs per gracilis muscle (23).

The flow rate in arterial segment i is given by i = (Pi – Pi+1)/Ri, where the flow resistance of the segment is Ri = 128Li{eta}/[{pi}(Di)4], Li and Di are its length and diameter, and {eta} = 3 cP is the approximate apparent viscosity of blood for vessels in the diameter range of 10–30 µm (26). The equation for conservation of blood flow at node i is then

(1)
The resulting system of linear equations was solved to obtain the pressures Pi at each node. The wall shear stress and the mean pressure in segment i are given by {tau}w,i = Di(Pi – Pi+1)/(4Li) and Pm,i = (Pi + Pi+1)/2.

Simulation of structural adaptation. The theoretical simulations of structural adaptation use a modified version of a previously published model, which is based on the assumption that the changes in diameter at each point along the vessel, occurring with each increment in time, depend on the net effect of hemodynamic and metabolic stimuli (26). In mathematical terms, with each time step {Delta}t, the diameter Di of segment i changes according to

(2)
where T (in days) is a characteristic time scale for structural changes and Stot,i is a dimensionless quantity representing the combined effects of stimuli causing structural changes in the diameter of segment i. Stot,i is defined as the sum of six terms representing the individual stimuli:

(3)
The first term in this equation represents the effect of wall shear stress, resulting from blood flow. Increased wall shear stress stimulates increases in structural diameter. The second term represents the effect of intravascular pressure, which generates circumferential stress. Increasing pressure leads to reduction in diameter. The functional form of this term is based on a correlation between wall shear stress and pressure observed in microvascular networks of the rat mesentery (26):

(4)
The third term in Eq. 3 represents the effect of local metabolic conditions and has the role of maintaining parallel flow pathways, by causing diameters to increase in segments with very low flow, which would otherwise be unable to meet local tissue oxygen demand. The constants in this term are km, the metabolic stimulus constant, ref, the reference blood flow, and HD, the discharge hematocrit. The fourth term in Eq. 3 represents effects of conducted responses that propagate upstream along the vessel wall. These responses are assumed to decay exponentially with distance along the vessel and to be summed at diverging bifurcations. For instance, the conducted signal Sc in the parent vessel propagated from two downstream daughter segments a and b, of lengths La and Lb, is given by

(5)
where Ma and Mb are the metabolic stimuli of segments a and b, and L is a length constant. The resulting stimulus is assumed to be saturable, with a maximum value of kc, the conducted stimulus constant, and a half-maximal value when Sc,i, the conducted response in segment i, is equal to S0. In the present model, the daughter branches are the TAs and the downstream segments of the artery. TAs are assumed to generate a conducted response according to their blood flow, STA= km·log[ref/(TAHD) + 1], where ref is a reference value for flow and TA is the calculated TA flow. Values of parameters describing the metabolic and conducted responses were obtained or estimated from previous studies (26) as follows: metabolic response parameters are km = 0.81, HD = 0.4, and ref = 40 nl/min; conducted response parameters are kc = 2.93, L = 1,000 µm, and S0 = 20.

The fifth term in Eq. 3, Sd, represents the effects of time-delayed remodeling stimuli resulting from hypoxia and inflammation in regions in which the level of TA flow falls below the level needed to prevent ischemia. This term was not included in previous models (26). The resulting stimulus is assumed to depend on TA flow levels at all earlier times, after the removal of one blood supply at time t = 0. The delayed stimulus acting on segment i at time t is assumed to be given by a convolution integral:

(6)

The function f(TA,i) represents the rate of cytokine release as a function of TA flow. It is assumed that the release of cytokines is stimulated only when the TA flow falls below a critical level crit necessary to maintain adequate tissue perfusion and increases linearly with further decreases in TA flow. This is represented by assuming that f(TA,i) = max(crit – TA,i, 0). The kernel function K(s) represents the dependence of the effect on the time delay s. The kernel function is assumed to have a lognormal dependence on s:

(7)
where kg, c, and Tmax are unknown parameters. This function is chosen to increase smoothly from an initial value of zero to a maximum value and then to decay exponentially with time. The time-delayed effects of hypoxia and inflammation over the time interval after the removal of one blood supply are included by integrating from 0 to t. The unknown parameters T, crit, kg, c, and Tmax were estimated to minimize the mean square deviation between predicted diameters and normalized measured diameters, including data from all three sections (MB, middle, and SA) and all available time points. A simplex procedure was used for the minimization (22). The resulting estimates were T = 4.5 days, Tmax = 7.3 days, c = 0.82, kg = 0.0019, and crit = 23.55 nl/min.

Figure 3 shows an example of the time-dependent functions involved in the delayed response for a vessel segment close to the point of resection. The kernel function K(s) has a maximum at Tmax = 7.3 days (Fig. 3A). Interruption in the blood supply results in an immediate reduction in TA flow below the critical level (crit) (Fig. 3B). This period of ischemia results in a delayed remodeling stimulus, computed as the convolution product of the deficit in TA flow and the kernel function K(s), that reaches a peak approximately at approximately day 12 (Fig. 3C). Vessel diameter continues to increase until approximately day 20 (Fig. 3D). By this time, TA flow has been restored close to the critical level, crit, and so the delayed remodeling stimulus is greatly reduced. With this reduction in delayed stimulus, diameter decreases toward a new equilibrium value (Fig. 3D).



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  		Fig. 3. Time courses of variables associated with the delayed response. A: kernel function K(s). B: flow in TA branching off the artery near the point of resection. crit, critical level of TA flow necessary to maintain adequate tissue perfusion. C: delayed remodeling stimulus Sd in the corresponding region of the artery. D: variation of diameter in corresponding region of artery.

 
The sixth and final term in Eq. 3 is a constant, kb, that sets a baseline level for vessel diameter changes and acts equally on all segments. It is determined by simulating structural adaptation in the case where both blood supplies are intact and applying the condition that the total volume of the gracilis artery after adaptation must equal the volume estimated from the measured diameters in that case.

Computer codes were written in MATLAB software language (MathWorks, Natick, MA). For a given distribution of segment diameters, the pressure, blood flow rate, and shear stress for each node and segment were estimated by solving the system of equations given by Eq. 1. The resulting total stimulus (Stot) was then computed according to Eq. 3. Updated diameters at the next time step were obtained using Eq. 2. Time steps {Delta}t = 0.1 days were used. This process was repeated multiple times to generate the predicted time course of diameters in each region. To simulate the control (untreated) case, we continued the simulation until the diameters reached an equilibrium state ({Delta}Di {approx} 0). To simulate remodeling after the removal of one blood supply, we used the normalized diameters for each region as the initial conditions. The program was run for a number of time steps corresponding to the number of days following surgery. In initial simulations, the delayed response (Sd,i in Eq. 3) was not included.


   RESULTS
TOP
 ABSTRACT
 MATERIALS AND METHODS
 RESULTS
DISCUSSION
 GRANTS
 REFERENCES
 
Vascular morphology and structural responses. To show the dependence of diameter changes on position along the artery, we plotted the measured mean control and remodeled diameters as a function of vessel region number (Fig. 4). With no surgery or sham surgery, diameters did not differ significantly between the left and the right hindlimbs. After interruption of the saphenous blood supply, the diameter changes varied according to position along the vessel. Compared with control values, diameters in regions 1–3 exhibited no change or slight outward remodeling at all time points. Diameters in regions 4–6 showed significant increases at day 1 and days 7 to 56 with peak values at day 21. In regions 7 and 8, vessel diameters were unchanged or slightly decreased up to day 7 but increased above control values at days 14, 21, and 28. At day 56, they returned close to control values.



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  		Fig. 4. Measured diameters in each of 8 equal regions along the gracilis artery for sham and no surgery groups and for indicated times post surgery. *P < 0.005, significant difference between control and remodeled diameter.

 
The time course of observed diameter changes, normalized to correct for diameter changes in untreated limbs, is shown in Fig. 5 (filled circles). Averages are shown for the entire artery and for the three sections as defined previously, i.e., MB (regions 1–3), middle (regions 4–6), and SA (regions 7 and 8). The overall mean measured diameter increased slightly up to day 7 and then increased more rapidly, reaching a peak during the period from day 14 to day 28, before decreasing at day 56 close to day 7 control values (Fig. 5A). This behavior was spatially nonuniform. The transient increase in diameter was most prominent in the SA section, adjacent to the point of resection, and least prominent in the MB section, where the blood supply was intact (Fig. 5, B–D).



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  		Fig. 5. Time course of measured ({bullet}) and predicted ({triangleup}, model predictions not including delayed response; {circ}, model predictions including delayed response) normalized diameters of gracilis artery after interruption of 1 blood supply. A: overall means for entire artery. B: means for MB section (regions 1–3). C: means for middle section (regions 4–6). D: means for SA section (regions 7 and 8).

 
Simulations of structural adaptation. The theoretical model was first applied to simulate the distribution of diameters under control conditions (Fig. 6). The parameter kb was estimated by applying the condition that the overall predicted volume of the artery matched that estimated from the measured diameters, giving kb = 0.234. The same value was used to simulate the adapted diameters in the treated vessels. In the simulations, equal feed pressures (PA= 100 mmHg) were assumed at both ends of the gracilis artery, and the distribution of predicted diameters was therefore symmetrical with respect to the midpoint of the vessel. The asymmetry seen in the experimental data may reflect a lower pressure at the SA than at the MB connection node.



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  		Fig. 6. Spatial distributions of measured and predicted diameters in the untreated gracilis artery with 2 intact blood supplies ({bullet}, experimental results; {circ}, model predictions).

 
The theoretical model was then used to simulate the process of remodeling after the removal of the SA blood supply. Predicted overall and section diameters as a function of time are shown in Fig. 5 together with the corresponding experimental data. The initial simulations, in which the delayed response was not included, gave predicted diameters that were generally consistent with the measured values up to day 7, but at later times, the predicted values monotonically approached equilibrium values (Fig. 5, open triangles). The observed strong increase in measured diameters in the middle and SA sections at days 7 to 21 and the subsequent decrease at day 56 could not be adequately represented using this version of the theoretical model (Fig. 5, C and D). When the delayed response was included (Fig. 5, open circles), predicted diameter variations with time approximated the observed changes up to day 56, including the transient increase in diameters observed in the middle and SA sections.

The variation of artery diameter with position and time is represented in Fig. 7 in the form of a contour plot. The observed changes (Fig. 7C) show a complex spatial and temporal variation. Comparison of the theoretical predictions without and with the delayed response (Fig. 7, B and C) again shows that the model with delayed response provides a closer overall match to the observed behavior.



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  		Fig. 7. Contour plots showing spatial and temporal dependence of measured and predicted normalized diameters of gracilis artery after interruption of 1 blood supply. A: measured results. B: model predictions not including delayed response. C: model predictions including delayed response. Diameters (in µm) are coded according to color bar at top right. In B and C, bar at bottom shows the eventual equilibrium distribution of diameter.

 

   DISCUSSION
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 ABSTRACT
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
GRANTS
 REFERENCES
 
The present study provides detailed information about the spatial variation (over a length of 6.6 mm) and the time course (over a period of 56 days) of structural diameter changes in a single artery after partial interruption of blood flow. A striking feature of the results is that the mouse gracilis artery is capable of relatively rapid remodeling in a spatially heterogeneous manner (Fig. 7A). Some variation in diameters over time also was seen in the untreated arteries, particularly at day 56 after treatment (Fig. 4). This may reflect normal developmental changes with age. The time courses (Fig. 5) are presented in terms of normalized diameters so that variations in diameter with time reflect changes in diameter of treated arteries relative to untreated arteries at corresponding time points. In the part of the artery near the point of resection, the normalized diameter shows a slight decline in the first 2 days, a large increase at days 14–28, and a decrease toward the initial value at day 56. A similar transient increase in diameter was seen in the middle region but not in the region farthest from the point of resection, which remained almost constant in diameter. Although small arteries (including the gracilis artery) in the hindlimb of the mouse were previously reported to have remodeled outward after femoral artery occlusion or removal (5, 11, 32, 37, 38), such regional heterogeneity within a single artery, including a spatially dependent transient increase in diameter, was not reported before.

Structural remodeling during the process of ischemic revascularization depends on hemodynamic stimuli (shear stress and circumferential stress), cell-derived factors (inflammatory cytokines, growth factors, proteolytic enzymes), and the metabolic state of the affected tissue (4, 28, 31). The effects of these factors are difficult to study independently of each other in an experimental setting. We therefore developed integrative theoretical models to simulate the process. Such models of complex biological phenomena inevitably involve a number of simplifying assumptions but can provide a quantitative framework for testing hypotheses regarding the factors involved. For example, in the present study, a previously developed model incorporating responses to wall shear stress, intravascular pressure, and metabolic stimuli was found to be unable to predict the observed behavior. This led to the new hypothesis that a time-delayed remodeling stimulus is involved in the observed structural adaptation.

In previous studies, models of structural adaptation were used to predict steady-state distributions of vessel diameters in vascular networks. Satisfactory agreement with experimental observations was found with the use of a model including effects of shear stress, intravascular pressure, metabolic state of the tissue, and conducted responses (26). The present study presents the first comparison between predictions of this model as a function of time with observations of structural adaptation following a reduction in blood supply. The previous model, without a delayed response, predicted the gradual steady-state increase of diameter seen up to day 7 but failed to predict the transient outward remodeling of the SA section close to resected blood supply at later times (Fig. 7B).

The observed variation of diameter with time led us to hypothesize that a time-delayed remodeling stimulus is generated in the region near the cut end of the vessel, which experiences hypoxia and inflammation. This was represented in the model by assuming that a drop in TA flow below a critical level at any instant caused the generation of a time-delayed stimulus that reached a maximum and then decayed as a lognormal function of time. Best agreement between model predictions and experimental results was obtained when the stimulus reached a peak after a time delay of 7.3 days.

The hypothesized behavior is consistent with published data showing a delayed peak of arteriolar diameter adaptation following an ischemic event (32). This suggests that local production of growth factors and other cytokines (4, 13, 37) in response to ischemia or hypoxia may mediate the response. Recent evidence has shown that outward remodeling after reduction in blood flow in the mouse hindlimb is significantly reduced in the absence of cytokines such as monocyte chemoattractant protein-1, the CD44 glycoproteins, or leptin (10, 29, 41). The present model does not depend on any assumptions regarding the specific cytokines involved and does not exclude the possibility that other physical factors participate in the observed structural changes. For example, the reversal of flow in the region near the cut end may stimulate structural reorganization. Other modes of information transfer along flow pathways, such as arteriovenous communication, may be involved (33).

Measured and simulated diameters in the present study refer to conditions of maximal vasodilation. Small arteries and arterioles in skeletal muscle normally exhibit significant tone, which depends on blood flow and metabolic status. The conditions leading to structural increase in vessel diameter, such as increased shear stress and high metabolic demand, also cause vasodilation. Therefore, outward remodeling is most likely to occur when vessels are dilated, as considered in the present model. Conversely, however, inward remodeling would occur under vasoconstricted conditions (1), which are not explicitly represented in our model. Indeed, this may be one reason that the model does not give accurate predictions of the observed inward remodeling (Fig. 5D). Further work is required to explore the relationship between changes in tone and structural adaptation.

Structural adaptation of existing flow pathways is essential for collateral formation during ischemic revascularization. The present results are consistent with the hypothesis that time-delayed effects of cytokine release, resulting from hypoxia and inflammation, stimulate transient diameter increase in the affected regions. Such a response has the important consequence of transiently increasing blood flows to levels substantially higher than those that are reached in the eventual equilibrium state. Transient overperfusion could be important in accelerating the recovery of the tissue from ischemic damage.


   GRANTS
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 ABSTRACT
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 GRANTS
REFERENCES
 
This work was supported by American Heart Association Grant 0010189Z and National Heart, Lung, and Blood Institute Grants HL-34555 and HL-63732.


   FOOTNOTES
 

Address for reprint requests and other correspondence: T. W. Secomb, Dept. of Physiology, Univ. of Arizona, Tucson, AZ 85724-5051 (E-mail: secomb{at}u.arizona.edu)

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.


   REFERENCES
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 ABSTRACT
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 GRANTS
 REFERENCES
 

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