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ARTERIAL REMODELING IN RESPONSE TO A SUSTAINED INCREASE IN FLOW USING A CONSTITUENT-BASED MODEL
Presentation O-39
S42
Arterial Wall Mechanics: Simulation
ARTERIAL REMODELING IN RESPONSE TO A SUSTAINED INCREASE IN FLOW USING A CONSTITUENT-BASED MODEL Alkiviadis Tsamis, Nikos Stergiopulos
Laboratory of Hemodynamics and Cardiovascular Technology École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland
Methods We assume that smooth muscle is fully relaxed and media remodels to alter the resting arterial radius. We use the SEF W proposed by Zulliger [2007]: W = felastWelast + fcollWcoll
2.4 68 2.2
celast [kPa]
ri [mm]
2.0 1.8 0
10
20
30
N
H N
(2)
where the mismatch in shear stress decreases celast. tC is a time constant and superscripts N and H refer to normal and high flow, respectively. Wall stress restoration is based on geometrical remodeling with the remodeling rate eqs. taken from [Tsamis, 2007].
Results and Discussion Literature data were used to qualitatively study the effect of a 2-fold increase in flow. In Fig. 1, the Journal of Biomechanics 41(S1)
56 52 0
40
10
20
30
40
10
20
30
40
0.9
0.7 0.6 0
10
20
30
[kPa]
110
0.8
100 90
40
80 0
Dimensionless Time
Figure 1: Mechanical and geometrical adaptation. In Fig. 2 left, the P-ri curve shifts leftward, also in agreement with experimental data [Prior, 2004] (Fig. 2 right). Compliance CA may increase if remodeling takes place at low pressure P, and may decrease for high P. Indeed, CA increased in [Prior, 2004] and decreased in [Matsumoto, 2005]. Model results agree overall with experimental findings.
ri [mm]
2.5
celast decreases CA
2.0
CA
1.5 1.0 0
50
100 150 200 250
P [mm Hg]
Relat. Lum. Diameter
3.0
1 tC
60
(1)
where Welast = celast(I1-3)3/2 is the SEF of elastin and the parameter celast describes the elastic properties of elastin. See [Zulliger, 2007] for more details. We hypothesize that elastin fenestrations result in a decrease in effective elastic constant celast and, in consequence, to an increase in wall compliance and lumen. Thus, we postulate the remodeling rate eq. H celast d , N dt celast
64
,av
Changes in medial elastin are critical to arterial remodeling following a sustained increase in flow, wherein the lumen enlarges in two phases tending to restore intimal shear stress to control: 1st, via rapid smooth muscle relaxation and, 2nd, via wall reconstruction and thickening [Langille, 1995]. The 2nd phase implicates enzymatic digestion of elastin fibers. Fenestrations of elastin are an important consideration in this regard, because they increase wall compliance and consequently lumen radius. Rachev [2000] proposed a theoretical model of global geometrical adaptation of arteries caused by changes in flow. However, the model employed a phenomenological strain energy function (SEF) and material properties were considered constant. Here we propose a constituent-based model of flowinduced remodeling by extending our prior model of hypertension-induced remodeling [Tsamis, 2007] to account for the effect of elastin fenestrations.
deformed inner radius ri increases as celast decreases to restore . Wall thickness H at the zero-stress state increases to restore the mean circumferential stress ,av in qualitative agreement with [Tulis, 1998].
H [mm]
Introduction
1.0 0.8 0.6 0.4 0.2
Exercised Sedentary Non-ligated
0.0 10 30 50 70 90 Intraluminal Pressure [cm H20]
Figure 2: Model predictions versus experiments.
References Langille, Flow-dependent Regulation of Vascular Function, Oxford University Press:277-299, 1995. Matsumoto et al, JSME International Journal Series C, 48:477-483, 2005. Prior et al, Am J Physiol Heart Circ Physiol, 287:H2434-H2447, 2004. Rachev, J Elasticity, 61:83-111, 2000. Tsamis et al, Am J Physiol Heart Circ Physiol, 293:H3130-H3139, 2007. Tulis et al, Am J Physiol, 274:H874-H882, 1998. Zulliger et al, J Biomech, 40:3061-3069, 2007.
16th ESB Congress, Oral Presentations, Monday 7 July 2008
S42
Arterial Wall Mechanics: Simulation
ARTERIAL REMODELING IN RESPONSE TO A SUSTAINED INCREASE IN FLOW USING A CONSTITUENT-BASED MODEL Alkiviadis Tsamis, Nikos Stergiopulos
Laboratory of Hemodynamics and Cardiovascular Technology École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland
Methods We assume that smooth muscle is fully relaxed and media remodels to alter the resting arterial radius. We use the SEF W proposed by Zulliger [2007]: W = felastWelast + fcollWcoll
2.4 68 2.2
celast [kPa]
ri [mm]
2.0 1.8 0
10
20
30
N
H N
(2)
where the mismatch in shear stress decreases celast. tC is a time constant and superscripts N and H refer to normal and high flow, respectively. Wall stress restoration is based on geometrical remodeling with the remodeling rate eqs. taken from [Tsamis, 2007].
Results and Discussion Literature data were used to qualitatively study the effect of a 2-fold increase in flow. In Fig. 1, the Journal of Biomechanics 41(S1)
56 52 0
40
10
20
30
40
10
20
30
40
0.9
0.7 0.6 0
10
20
30
[kPa]
110
0.8
100 90
40
80 0
Dimensionless Time
Figure 1: Mechanical and geometrical adaptation. In Fig. 2 left, the P-ri curve shifts leftward, also in agreement with experimental data [Prior, 2004] (Fig. 2 right). Compliance CA may increase if remodeling takes place at low pressure P, and may decrease for high P. Indeed, CA increased in [Prior, 2004] and decreased in [Matsumoto, 2005]. Model results agree overall with experimental findings.
ri [mm]
2.5
celast decreases CA
2.0
CA
1.5 1.0 0
50
100 150 200 250
P [mm Hg]
Relat. Lum. Diameter
3.0
1 tC
60
(1)
where Welast = celast(I1-3)3/2 is the SEF of elastin and the parameter celast describes the elastic properties of elastin. See [Zulliger, 2007] for more details. We hypothesize that elastin fenestrations result in a decrease in effective elastic constant celast and, in consequence, to an increase in wall compliance and lumen. Thus, we postulate the remodeling rate eq. H celast d , N dt celast
64
,av
Changes in medial elastin are critical to arterial remodeling following a sustained increase in flow, wherein the lumen enlarges in two phases tending to restore intimal shear stress to control: 1st, via rapid smooth muscle relaxation and, 2nd, via wall reconstruction and thickening [Langille, 1995]. The 2nd phase implicates enzymatic digestion of elastin fibers. Fenestrations of elastin are an important consideration in this regard, because they increase wall compliance and consequently lumen radius. Rachev [2000] proposed a theoretical model of global geometrical adaptation of arteries caused by changes in flow. However, the model employed a phenomenological strain energy function (SEF) and material properties were considered constant. Here we propose a constituent-based model of flowinduced remodeling by extending our prior model of hypertension-induced remodeling [Tsamis, 2007] to account for the effect of elastin fenestrations.
deformed inner radius ri increases as celast decreases to restore . Wall thickness H at the zero-stress state increases to restore the mean circumferential stress ,av in qualitative agreement with [Tulis, 1998].
H [mm]
Introduction
1.0 0.8 0.6 0.4 0.2
Exercised Sedentary Non-ligated
0.0 10 30 50 70 90 Intraluminal Pressure [cm H20]
Figure 2: Model predictions versus experiments.
References Langille, Flow-dependent Regulation of Vascular Function, Oxford University Press:277-299, 1995. Matsumoto et al, JSME International Journal Series C, 48:477-483, 2005. Prior et al, Am J Physiol Heart Circ Physiol, 287:H2434-H2447, 2004. Rachev, J Elasticity, 61:83-111, 2000. Tsamis et al, Am J Physiol Heart Circ Physiol, 293:H3130-H3139, 2007. Tulis et al, Am J Physiol, 274:H874-H882, 1998. Zulliger et al, J Biomech, 40:3061-3069, 2007.
16th ESB Congress, Oral Presentations, Monday 7 July 2008