Hynek Chlup

Correlations between age, prestrain, diameter and atherosclerosis in the male abdominal aorta

The longitudinal prestrain of arteries facilitates their physiological function. Remodeling, adaptation and aging result in an age-dependent magnitude of the pretension. Although the phenomenon is known, detailed statistics, especially for human arteries, are lacking. This study was designed to propose the regression model capable of estimating the prestrain of the human abdominal aorta. The length of the abdominal aorta before, l, and after excision from the body, L, the diameter, heart weight, thickness of left ventricle and degree of atherosclerosis were collected in autopsies of 156 male cadavers of known age. Longitudinal prestrain was quantified by means of the stretch ratio λ=l/L. Statistical analysis revealed significant dependence between age, prestrain, diameter and atherosclerosis, which were best fitted to the power law equation. Longitudinal prestretch reduced with age significantly; λmean=1.30±0.07 for age<30 (n=29), whereas λmean=1.06±0.03 for age>59 (n=31) with p-value<0.0001. Raw data gave linear correlation coefficients as follows: λ-age (R=-0.842); l-age (R=0.023); L-age (R=0.476); (l-L)-age (R=-0.811). It was concluded that longitudinal prestrain decreases nonlinearly with age and both age and diameter are suitable predictors of the prestrain. Data suggests that unloaded length elongates with age in contrast to the elastic retraction.

Age-related distribution of longitudinal pre-strain in abdominal aorta with emphasis on forensic application.

It is a well-known fact that the length of an artery in situ and the length of an excised artery differs. Retraction of blood vessels is usually observed. This pre-tension plays crucial role in arterial biomechanics. It augments an artery wall load-bearing capacity. This paper presents the longitudinal pre-strain of the human aorta as an index of human age. The length of abdominal aortas was measured during autopsies before and after segment resection. The longitudinal pre-strain was calculated in 130 donors; 100 male and 30 female bodies. The pre-strain was defined as the ratio between in situ length and the length after the excision. The mean pre-strain was found to be 1.18±0.10 for male and 1.14±0.10 for female sample (mean±standard deviation). The age in the male group was 41.6±15.9 years; and 47.7±17.7 years in the female group. Statistical analysis revealed the correlation coefficient between age and pre-strain r=-0.821 and r=-0.839 in male and female group, respectively. The analysis also confirmed close correlation between aortic circumference and age; and between circumference and pre-strain. Linear and power law regression equations were employed and prediction intervals were computed. The power law estimates the age more accurately than linear one model. Nevertheless, especially for small values of the pre-strain (aged individuals) the linear model can be advantageous.

Constitutive Modeling of Human Saphenous Veins at Overloading Pressures

In the present study, inflation tests with free axial extension of 15 human vena saphena magna were conducted ex vivo to obtain data suitable for multi-axial constitutive modeling at overloading conditions (pressures up to approximately 15kPa). Subsequently the data were fitted with a hyperelastic, nonlinear and anisotropic constitutive model based on the theory of the closed thick-walled tube. It was observed that initial highly deformable behavior (up to approximately 2.5kPa) in the pressure-circumferential stretch response is followed by progressive large strain stiffening. Contrary to that, samples were much stiffer in longitudinal direction, where the observed stretches were in the range 0.98-1.03 during the entire pressurization in most cases. The effect of possible residual stress was evaluated in a simulation of the intramural stress distribution with the opening angle prescribed to 0°, 10°, 20°, 30°, 40°, and 50°. The result suggests that the optimal opening angle making the stress distribution through the wall thickness uniform is about 40°. The material parameters presented here are suitable for use in mechanobiological simulations describing the adaptation of the autologous vein wall after bypass surgery.

Remodelling of living bone induced by dynamic loading and drug delivery-Numerical modelling and clinical treatment

Remodelling is a dynamic process occurring during growth and it includes sensing of environmental changes, tissue resorbance, i.e. the removal of existing old bone, and formation of new tissue. The biomechanical remodelling process is relatively well formulated for bones and can be divided into three stages: (1) bone resorption based on the osteoclast activity, (2) bone deposition based on the osteoblast activity and (3) bone growth control established on RANK/RANKL/OPG pathway-RANKL/OPG balance. The main driving force of remodelling process is a dynamic loading (cyclic compression and expansion, e.g. walking or running), which strongly influences the rate of chemical reactions. The evolution from the homogeneous density distribution to the corticalis and cancellous bone formation is shown. An inevitable influence of a dynamic mechanical loading and osteoprotegerin (OPG) concentration is demonstrated. Deformations were calculated by commercial code ANSYS. The clinical experience indicates that the dynamic loading (above the threshold level 1500-2500microstains/s), especially walking with a characteristic time approximately 1s, influences the whole process of bone remodelling after a time period of approximately 3 months. The numerical simulation shows that the concentration of the new bone and the bone elastic constants substantially depend on history and intensity of the loading, drug delivery and nutrition.

Strain energy function for arterial walls based on limiting fiber extensibility

An anisotropic strain energy density function based on limiting fiber extensibility assumption was suggested. The function was deduced directly from isotropic Gent model. A material was modeled as a composite reinforced with two families of helical fibers. The anisotropy of the strain energy function was incorporated via pseudo-invariants I 4 and I 6. Mathematical expression includes three material parameters. Suitability of the model for a description of arterial mechanical response was verified by regression analysis of experimental data. Computational model based on a cylindrical thick-walled tube with residual strains was used to estimate material parameters. Identified material model fits pressure-radius data of an aortic inflation test successfully. Further upgrades of the model are discussed.

Constitutive Behavior of Coronary Artery Bypass Graft

Implantation of coronary artery bypass graft (CABG) is still one of frequent revascularization methods. Biomechanics of a CABG wall may significantly affect its successful function, nevertheless, papers which concern with a constitutive modeling of the CABG are lacking in literature. The purpose of this study is to describe a constitutive behavior of the CABG tissue. A sample of the CABG underwent three years of remodeling under arterial conditions. This sample was analyzed in an inflation–extension test (vertically aligned closed-end tube was loaded by an internal overpressure and by varying axial force). Displacements of the specimen were recorded by CCD cameras and subsequently evaluated by digital image cross-correlation. The experiment comprised preconditioning cycles and measurement periods. Mechanical response of the CABG was studied using four different values of an axial force (weight). A pressure – circumferential stretch and an axial force – axial stretch data are presented. Presence of the so called inversion point in the pressure – axial stretch data was observed, manifested by an elongation of a pressurized tube under some critical value of axial stretch and by a shortening as soon as the axial stretch exceeds the critical value. This interesting phenomenon was previously reported for iliac arteries. Now we may confirm it for saphenous vein graft also. Selected data were used to fit a material model. The tissue was modeled as a one-layered composite reinforced by two families of helical fibers. The material was assumed to be locally orthotropic, nonlinear, incompressible and hyperelastic. Material parameters were estimated for the strain energy function based on a limiting fiber extensibility assumption. Model parameters are fitted by optimization based on radial and axial equilibrium equation in the thick–walled tube. Material model fits selected data successfully. Further work will be aimed at extension of material model domain on all measured data.

Effect of Polyvinyl Alcohol Concentration on the Mechanical Properties of Collagen/Polyvinyl Alcohol Blends

The effects of the polyvinyl alcohol (PVA) concentration on mechanical properties of hydrogels based on blends of native or denatured collagen / PVA were examined. Blends of PVA with collagen were obtained by mixing the solutions in different ratios, using glycerol as a plasticizer. The solutions were cast on polystyrene plates and the solvent was allowed to evaporate at room temperature. Uniaxial tensile tests were performed in order to obtain the initial modulus of elasticity (up to deformation 0.1), the ultimate tensile stress and the deformation at failure of the material in the water-saturated hydrogel form. It was found that the material was elastic and the addition of PVA helped to enhance both the ultimate tensile stress and modulus of elasticity of the films. Samples prepared from denaturated collagen showed the higher ultimate tensile stress and the deformation at failure in comparison with those prepared from native collagen. The results suggest that we could expect successful application of the collagen/PVA biomaterial for tissue engineering.

Constitutive Modelling and Histology of Vena saphena

The inflation-extension test was performed in order to obtain the mechanical response (stress-strain curves) of the human vein - vena saphena magna (usually used for coronary artery bypass graft surgery). Tubular samples of the vein were inflated four times up to the pressure approx. 4 kPa (vein pressure) and then four times up to approx. 16 kPa (systolic pressure). The experiments were recorded by the CCD camera. The longitudinal and circumferential deformations of the tube were evaluated using the edge detection method. The experimental data were fitted by anisotropic, nonlinear, constitutive model in order to obtain model parameters, especially the parameter which can be explained as collagen fibres orientation approximation. This parameter was then compared with the findings from histology. The histology analyses based on label-free imaging were performed additionally to the mechanical testing. Collagen (most important load-bearing component of the vein wall) was visualized using second harmonic generation imaging (SHG, excitation at 860 nm by a tunable IR pulse laser, detection at 430±10 nm). This method enabled us to observe collagen through the vein wall. It was found that the collagen fibres are helically aligned within the vein at an angle 37±6° measured from circumferential axis. The results of collagen orientation angle show a good agreement of findings obtained from histology and from constitutive model.

INTEGRAL METHODS FOR DESCRIBING PULSATILE FLOW

This paper presents an approximate solution of the pulsatile flow of a Newtonian fluid in the laminar flow regime in a rigid tube of constant diameter. The model is represented by two ordinary differential equations. The first equation describes the time evolution of the total flow rate, and the second equation characterizes the reverse flow near the wall. These equations are derived from the momentum balance equation and from the kinetic energy equation, respectively. The accuracy of the derived equations is compared with a solution in which the finite difference method is applied to a partial differential equation.

The Influence of the Opening Angle on the Stress Distribution through the Saphenous Vein Wall

In the present study, the inflation test of human vena saphena magna was conducted to obtain data suitable for multi-axial constitutive modeling at overloading conditions (pressures up to approximately 18 kPa). Subsequently the data were fitted with a hyperelastic, nonlinear and anisotropic constitutive model based on the theory of the closed thick-walled tube. It was observed that initial highly deformable behavior in the pressure–circumferential stretch response is followed by progressive large strain stiffening, which is in contrast to the pressure–axial stretch response. The effect of possible residual stress was evaluated in a simulation of the intramural stress distribution with the opening angle prescribed to 0°, 10°, 20°, 30°, 40°, and 50°. The result suggests that the optimal opening angle making the stress distribution through the wall thickness uniform is about 20°.