Experimental foundation for in vivo measurement of the elasticity of the aorta in computed tomography angiography

OBJECTIVE

This study was performed to determine the feasibility of measuring the elastic properties of the arterial wall in vivo. To prove this concept, elastic parameters were calculated from an aortic model of elastic behavior similar to a human aorta using computed tomography angiography (CTA) images.

METHODS

We first constructed an aortic model from polydimethylsiloxane (PDMS). This model was inserted into a pulsatile flow loop. The model was then placed inside a computed tomography scanner. To estimate the elasticity values, we measured the cross-sectional area and the pressure changes in the model during each phase of the simulated cardiac cycle. A discrete wavelet transform (DWT) algorithm was applied to the CTA data to calculate the geometric changes in the pulsatile model over a simulated cardiac cycle for various pulsatile rates and elasticity values of the PDMS material. The elastic modulus of the aortic model wall was derived from these geometric changes. The elastic moduli derived from the CTA data were compared with those obtained by testing strips of the same PDMS material in a tensile testing machine. Our two aortic models had elastic values at both extremes of those found in normal human aortas.

RESULTS

The results show a good comparison between the elastic values derived from the CTA data and those obtained in a tensile testing machine. In addition, the elasticity values were found to be independent of the pulsatile rate for mixing ratios of 6:1 and 9:1 (p = .12 and p = .22, respectively).

CONCLUSIONS

The elastic modulus of a pulsatile aortic model may be measured by electrocardiographically-gated multi-detector CTA protocol. This preliminary study suggests the possibility of determining non-invasively the elastic properties of a living, functioning aorta using CTA data.

How should we measure and report elasticity in aortic tissue?

BACKGROUND

Different stress-strain definitions are used in the literature to measure the elastic modulus in aortic tissue. There is no agreement as to which stress-strain definition should be implemented. The purpose of this study is to show how different results are given by the various definitions of stress-strain used and to recommend a specific definition when testing aortic tissues.

METHODS

Circumferential specimens from three patients with ascending thoracic aortic aneurysm (ATAA) were obtained from the greater curvature and their tensile properties were tested uniaxially. Three stress definitions (second Piola-Kirchhoff stress, engineering stress and true stress) and four strain definitions (Almansi-Hamel strain, Green-St. Venant strain, engineering strain and true strain) were used to determine the elastic modulus.

RESULTS

We found that the Almansi-Hamel strain definition exhibited the highest non-linear stress-strain relation and consequently may overestimate the elastic modulus when using different stress definitions (second Piola-Kirchhoff stress, engineering stress and true stress). The Green-St. Venant strain definition yielded the lowest non-linear stress-strain relation using different definitions of stress, which may underestimate the values of elastic modulus. Engineering stress and strain definitions are only valid for small strains and displacements, which make them impractical when analysing soft tissues. We show that the effect of varying the stress definition on the elastic modulus measurements is significant for maximum elastic modulus but not when calculating the hypertensive elastic modulus.

CONCLUSIONS

It is important to consider which stress-strain definition is employed when analysing soft tissues. Although the true stress-true strain definition exhibits a non-linear relation, we favour it in tissue mechanics because it gives more accurate measurements of the material's response using the instantaneous values.

In vitro characterisation of physiological and maximum elastic modulus of ascending thoracic aortic aneurysms using uniaxial tensile testing

OBJECTIVE

Ascending thoracic aortic aneurysms (ATAA) are a life-threatening condition due to the risk of rupture or dissection. This risk is increased in the presence of a bicuspid aortic valve (BAV). The purpose of this study was to provide data on the elastic modulus of aortic wall of ATAA using uniaxial tensile testing in two different areas of the stress-strain relationship: physiological and maximum range of stresses. The influence of tissue location, tissue orientation and valve type on these parameters was investigated.

MATERIALS AND METHODS

Tissues freshly excised from ATAA with bicuspid or tricuspid aortic valve were obtained from greater and lesser curvature (GC and LC) and the specimens were tested uniaxially in circumferential (CIRC) and longitudinal (LONG) orientation. Maximum elastic modulus (MEM) was given by the maximum slope of the stress-strain curve before failure. Physiological modulus (PM) was derived from the Laplace law and from ranges of pressure of 80-120 mmHg. Means of each group of specimen were compared using Student's t-test to assess the influence of location, orientation and valve type on each mechanical parameter.

RESULTS

PM was found to be significantly lower than the MEM (p < 0.001). The MEM and PM were significantly higher (p < 0.01) in the CIRC (n = 66) than in the LONG orientation (n = 42). The MEM was higher in the circumferential orientation in the BAV group (p < 0.001 in GC and p < 0.05 in LC). MEM and PM in GC specimens were higher in the longitudinal orientation than the LC specimens (p < 0.05).

CONCLUSION

This study demonstrates the anisotropy of the aortic wall in ATAA and provides data on the mechanical behaviour in the physiological range of pressure.

Computational modeling of cerebral diffusion-application to stroke imaging

Water diffusion within the structure of a brain extracellular space is analyzed numerically for various diffusion parameters of brain tissue namely extracellular space porosity and tortuosity. An algorithm for predicting diffusion pattern of water molecules within human brain considering the mechanics of water diffusion within porous media is developed. The extracellular space is modeled as a homogeneous porous medium with uniform porosity and permeability. Discretization of the fluid flow, heat transfer and mass transport equations is achieved using a finite element scheme based on the Galerkin method of weighted residuals. Concentration maps are developed in this study for various clinical conditions. The effect of the space porosity and the turtousity on the heat and mass transport within the extracellular space are found to be significant. The results presented in this work play an important role in producing more effective imaging techniques for brain injury based on the apparent diffusion coefficient.

Water diffusion in biomedical systems as related to magnetic resonance imaging

Water diffusion within the brain is studied numerically for various clinical conditions. The numerical procedure used in this work is based on the Galerkin weighted residual method of finite-element formulation. A wide range of pertinent parameters such as Lewis number, cell volume, and the buoyancy ratio are considered in the present study. Comparisons with previously published work show excellent agreement. The results show that the diffusion coefficient, cell volume, and the buoyancy ratio play significant roles on the characterization of the mass and heat transfer mechanisms within the cell. Concentration maps are developed for various clinical conditions. Pertinent results for the streamlines, isotherms and the mass and heat transfer rates in terms of the average Sherwood and Nusselt numbers are presented and discussed for different parametric values. Experimental tests are also conducted to produce an 8 Tesla image which is compared with our numerical simulation. The present study provides essential maps for brain disorders classified based on several pertinent clinical attributes.