### Abstract

To characterize the interaction between mechanical and fluid transport properties in hypertension, we measured in vivo elastic material constants and hydraulic conductivity in intact segments of carotid arteries in normal and spontaneously hypertensive rats (SHR). With the use of a finite element model, the arterial wall was modeled as a large-deformation, two-phase (solid/fluid) medium, which accounts for the existence and motion of the tissue fluid. Measurements of internal diameter and transmural pressures were obtained during continuous increases in pressure from 0 to 200 mm Hg. Strain and stress components were calculated based on a pseudostrain exponential energy density function. To measure the hydraulic conductivity, segments of the carotid artery were isolated, filled with a 4% oxygenated albumin-Tyrode's solution, and connected to a capillary tube. The movement of the meniscus of the capillary tube represented the fluid filtration across the artery. To study the influence of transmural pressure on hydraulic conductivity, measurement of fluid filtration across the arterial wall was obtained at transmural pressures of 50 and 100 mm Hg. The material constants in the SHR (n=9) were higher (p<0.05 for all variables) than in normal rats (n=10): c=1,343+96 versus 1,158±65 mm Hg, b_{1}=1.84+0.24 versus 1.22+0.22, b_{2}=0.769±0.114 versus 0.616±0.11, b_{3}=0.017±0.005 versus 0.0065±0.002, b_{4}=0.206±0.04 versus 0.083±0.03, b_{5}=0.0594±0.007 versus 0.0217+0.006, and b_{6}=0.22±0.09 versus 0.123±0.02, respectively. The hydraulic conductivity of the total wall, calculated from the filtration data, was lower (p<0.05) at both 50 and 100 mm Hg in the SHR (n=6) compared with normal rats (n=7): 1.12±0.31×10^{-8} and 0.72±0.23×10^{-8} versus 1.95±0.53×10^{-8} and 1.35±0.47×10^{-8} cm/(sec·mm Hg), respectively. The intergroup comparisons between 50 and 100 mm Hg in both SHR and normal rats were also different (p<0.05). The finite element model was used to predict tissue fluid pressure distribution, tissue fluid velocity distribution, and total Cauchy stress gradients developed in the arterial wall during fluid pressurization in both species. From these results, we conclude that 1) it is not adequate to treat the arterial wall as a single-phase, incompressible material because fluid moves across the boundaries of the arterial wall, resulting in a change in tissue volume; therefore, the incompressibility assumption is not valid; 2) hydraulic conductivity is dependent on pressure and may be a function of altered wall strain; 3) measurements of material constants and hydraulic conductivity can define differences in the physical properties of the arterial wall between SHR and normal rats; and 4) finite element models based on large-deformation, materially nonlinear, two-phase theory accurately reproduced the nonlinear stiffening response and the creep response under constant transmural pressure, which was observed experimentally in both species.

Original language | English (US) |
---|---|

Pages (from-to) | 145-158 |

Number of pages | 14 |

Journal | Circulation Research |

Volume | 71 |

Issue number | 1 |

State | Published - Jul 1992 |

### Fingerprint

### Keywords

- Finite element models
- Hydraulic conductivity
- Large deformation
- Pseudostrain energy function
- Two-phase media

### ASJC Scopus subject areas

- Physiology
- Cardiology and Cardiovascular Medicine

### Cite this

*Circulation Research*,

*71*(1), 145-158.

**Arterial mechanics in spontaneously hypertensive rats : Mechanical properties, hydraulic conductivity, and two-phase (solid/fluid) finite element models.** / Gaballa, Mohamed A.; Raya, Thomas E.; Simon, Bruce R.; Goldman, Steven.

Research output: Contribution to journal › Article

*Circulation Research*, vol. 71, no. 1, pp. 145-158.

}

TY - JOUR

T1 - Arterial mechanics in spontaneously hypertensive rats

T2 - Mechanical properties, hydraulic conductivity, and two-phase (solid/fluid) finite element models

AU - Gaballa, Mohamed A.

AU - Raya, Thomas E.

AU - Simon, Bruce R.

AU - Goldman, Steven

PY - 1992/7

Y1 - 1992/7

N2 - To characterize the interaction between mechanical and fluid transport properties in hypertension, we measured in vivo elastic material constants and hydraulic conductivity in intact segments of carotid arteries in normal and spontaneously hypertensive rats (SHR). With the use of a finite element model, the arterial wall was modeled as a large-deformation, two-phase (solid/fluid) medium, which accounts for the existence and motion of the tissue fluid. Measurements of internal diameter and transmural pressures were obtained during continuous increases in pressure from 0 to 200 mm Hg. Strain and stress components were calculated based on a pseudostrain exponential energy density function. To measure the hydraulic conductivity, segments of the carotid artery were isolated, filled with a 4% oxygenated albumin-Tyrode's solution, and connected to a capillary tube. The movement of the meniscus of the capillary tube represented the fluid filtration across the artery. To study the influence of transmural pressure on hydraulic conductivity, measurement of fluid filtration across the arterial wall was obtained at transmural pressures of 50 and 100 mm Hg. The material constants in the SHR (n=9) were higher (p<0.05 for all variables) than in normal rats (n=10): c=1,343+96 versus 1,158±65 mm Hg, b1=1.84+0.24 versus 1.22+0.22, b2=0.769±0.114 versus 0.616±0.11, b3=0.017±0.005 versus 0.0065±0.002, b4=0.206±0.04 versus 0.083±0.03, b5=0.0594±0.007 versus 0.0217+0.006, and b6=0.22±0.09 versus 0.123±0.02, respectively. The hydraulic conductivity of the total wall, calculated from the filtration data, was lower (p<0.05) at both 50 and 100 mm Hg in the SHR (n=6) compared with normal rats (n=7): 1.12±0.31×10-8 and 0.72±0.23×10-8 versus 1.95±0.53×10-8 and 1.35±0.47×10-8 cm/(sec·mm Hg), respectively. The intergroup comparisons between 50 and 100 mm Hg in both SHR and normal rats were also different (p<0.05). The finite element model was used to predict tissue fluid pressure distribution, tissue fluid velocity distribution, and total Cauchy stress gradients developed in the arterial wall during fluid pressurization in both species. From these results, we conclude that 1) it is not adequate to treat the arterial wall as a single-phase, incompressible material because fluid moves across the boundaries of the arterial wall, resulting in a change in tissue volume; therefore, the incompressibility assumption is not valid; 2) hydraulic conductivity is dependent on pressure and may be a function of altered wall strain; 3) measurements of material constants and hydraulic conductivity can define differences in the physical properties of the arterial wall between SHR and normal rats; and 4) finite element models based on large-deformation, materially nonlinear, two-phase theory accurately reproduced the nonlinear stiffening response and the creep response under constant transmural pressure, which was observed experimentally in both species.

AB - To characterize the interaction between mechanical and fluid transport properties in hypertension, we measured in vivo elastic material constants and hydraulic conductivity in intact segments of carotid arteries in normal and spontaneously hypertensive rats (SHR). With the use of a finite element model, the arterial wall was modeled as a large-deformation, two-phase (solid/fluid) medium, which accounts for the existence and motion of the tissue fluid. Measurements of internal diameter and transmural pressures were obtained during continuous increases in pressure from 0 to 200 mm Hg. Strain and stress components were calculated based on a pseudostrain exponential energy density function. To measure the hydraulic conductivity, segments of the carotid artery were isolated, filled with a 4% oxygenated albumin-Tyrode's solution, and connected to a capillary tube. The movement of the meniscus of the capillary tube represented the fluid filtration across the artery. To study the influence of transmural pressure on hydraulic conductivity, measurement of fluid filtration across the arterial wall was obtained at transmural pressures of 50 and 100 mm Hg. The material constants in the SHR (n=9) were higher (p<0.05 for all variables) than in normal rats (n=10): c=1,343+96 versus 1,158±65 mm Hg, b1=1.84+0.24 versus 1.22+0.22, b2=0.769±0.114 versus 0.616±0.11, b3=0.017±0.005 versus 0.0065±0.002, b4=0.206±0.04 versus 0.083±0.03, b5=0.0594±0.007 versus 0.0217+0.006, and b6=0.22±0.09 versus 0.123±0.02, respectively. The hydraulic conductivity of the total wall, calculated from the filtration data, was lower (p<0.05) at both 50 and 100 mm Hg in the SHR (n=6) compared with normal rats (n=7): 1.12±0.31×10-8 and 0.72±0.23×10-8 versus 1.95±0.53×10-8 and 1.35±0.47×10-8 cm/(sec·mm Hg), respectively. The intergroup comparisons between 50 and 100 mm Hg in both SHR and normal rats were also different (p<0.05). The finite element model was used to predict tissue fluid pressure distribution, tissue fluid velocity distribution, and total Cauchy stress gradients developed in the arterial wall during fluid pressurization in both species. From these results, we conclude that 1) it is not adequate to treat the arterial wall as a single-phase, incompressible material because fluid moves across the boundaries of the arterial wall, resulting in a change in tissue volume; therefore, the incompressibility assumption is not valid; 2) hydraulic conductivity is dependent on pressure and may be a function of altered wall strain; 3) measurements of material constants and hydraulic conductivity can define differences in the physical properties of the arterial wall between SHR and normal rats; and 4) finite element models based on large-deformation, materially nonlinear, two-phase theory accurately reproduced the nonlinear stiffening response and the creep response under constant transmural pressure, which was observed experimentally in both species.

KW - Finite element models

KW - Hydraulic conductivity

KW - Large deformation

KW - Pseudostrain energy function

KW - Two-phase media

UR - http://www.scopus.com/inward/record.url?scp=0026766775&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0026766775&partnerID=8YFLogxK

M3 - Article

C2 - 1535029

AN - SCOPUS:0026766775

VL - 71

SP - 145

EP - 158

JO - Circulation Research

JF - Circulation Research

SN - 0009-7330

IS - 1

ER -