Optimizing the Porohyperelastic Response of a Layered Compliance Matched Vascular Graft to Promote Luminal Self-Cleaning.

Thrombosis and intimal hyperplasia have remained the major failure mechanisms of small-diameter vascular grafts used in bypass procedures. While most efforts to reduce thrombogenicity have used a biochemical surface modification approach, the use of local mechanical phenomena to aid in this goal has received somewhat less attention. In this work, the mechanical, fluid transport, and geometrical properties of a layered and porous vascular graft are optimized within a porohyperelastic finite element framework to maximize self-cleaning via luminal reversal fluid velocity (into the lumen). This is expected to repel platelets as well as inhibit the formation of and/or destabilize adsorbed protein layers thereby reducing thrombogenic potential. A particle swarm optimization algorithm was utilized to maximize luminal reversal fluid velocity while also compliance matching our graft to a target artery (rat aorta). The maximum achievable luminal reversal fluid velocity was approximately 246 µm/s without simultaneously optimizing for host compliance. Simultaneous optimization of reversal flow and compliance resulted in a luminal reversal fluid velocity of 59 µm/s. Results indicate that a thick highly permeable compressible inner layer and a thin low permeability incompressible outer layer promote intraluminal reversal fluid velocity. Future research is needed to determine the feasibility of fabricating such a layered and optimized graft and verify its ability to improve hemocompatibility.

A Finite Element Model for Mixed Porohyperelasticity with Transport, Swelling, and Growth.

The purpose of this manuscript is to establish a unified theory of porohyperelasticity with transport and growth and to demonstrate the capability of this theory using a finite element model developed in MATLAB. We combine the theories of volumetric growth and mixed porohyperelasticity with transport and swelling (MPHETS) to derive a new method that models growth of biological soft tissues. The conservation equations and constitutive equations are developed for both solid-only growth and solid/fluid growth. An axisymmetric finite element framework is introduced for the new theory of growing MPHETS (GMPHETS). To illustrate the capabilities of this model, several example finite element test problems are considered using model geometry and material parameters based on experimental data from a porcine coronary artery. Multiple growth laws are considered, including time-driven, concentration-driven, and stress-driven growth. Time-driven growth is compared against an exact analytical solution to validate the model. For concentration-dependent growth, changing the diffusivity (representing a change in drug) fundamentally changes growth behavior. We further demonstrate that for stress-dependent, solid-only growth of an artery, growth of an MPHETS model results in a more uniform hoop stress than growth in a hyperelastic model for the same amount of growth time using the same growth law. This may have implications in the context of developing residual stresses in soft tissues under intraluminal pressure. To our knowledge, this manuscript provides the first full description of an MPHETS model with growth. The developed computational framework can be used in concert with novel in-vitro and in-vivo experimental approaches to identify the governing growth laws for various soft tissues.

A porohyperelastic finite element model of the eye: the influence of stiffness and permeability on intraocular pressure and optic nerve head biomechanics.

Progressively deteriorating visual field is a characteristic feature of primary open-angle glaucoma (POAG), and the biomechanics of optic nerve head (ONH) is believed to be important in its onset. We used porohyperelasticity to model the complex porous behavior of ocular tissues to better understand the effect variations in ocular material properties can have on ONH biomechanics. An axisymmetric model of the human eye was constructed to parametrically study how changes in the permeabilities of retina-Bruch's-choroid complex (k(RBC)), sclera k(sclera), uveoscleral pathway (k(UVSC)) and trabecular meshwork k(TM) as well as how changes in the stiffness of the lamina cribrosa (LC) and sclera affect IOP, LC strains, and translaminar interstitial pressure gradients (TLIPG). Decreasing k(RBC) from 5 × 10(- 12) to 5 × 10(- 13) m/s increased IOP and LC strains by 17%, and TLIPG by 21%. LC strains increased by 13% and 9% when the scleral and LC moduli were decreased by 48% and 50%, respectively. In addition to the trabecular meshwork and uveoscleral pathway, the retina-Bruch's-choroid complex had an important effect on IOP, LC strains, and TLIPG. Changes in k(RBC) and scleral modulus resulted in nonlinear changes in the IOP, and LC strains especially at the lowest k(TM) and k(UVSC). This study demonstrates that porohyperelastic modeling provides a novel method for computationally studying the biomechanical environment of the ONH. Porohyperelastic simulations of ocular tissues may help provide further insight into the complex biomechanical environment of posterior ocular tissues in POAG.

A finite element study on variations in mass transport in stented porcine coronary arteries based on location in the coronary arterial tree.

Drug-eluting stents have a significant clinical advantage in late-stage restenosis due to the antiproliferative drug release. Understanding how drug transport occurs between coronary arterial locations can better help guide localized drug treatment options. Finite element models with properties from specific porcine coronary artery sections (left anterior descending (LAD), right (RCA); proximal, middle, distal regions) were created for stent deployment and drug delivery simulations. Stress, strain, pore fluid velocity, and drug concentrations were exported at different time points of simulation (0-180 days). Tests indicated that the highest stresses occurred in LAD sections. Higher-than-resting homeostatic levels of stress and strain existed at upwards of 3.0 mm away from the stented region, whereas concentration of species only reached 2.7 mm away from the stented region. Region-specific concentration showed 2.2 times higher concentrations in RCA artery sections at times corresponding to vascular remodeling (peak in the middle segment) compared to all other segments. These results suggest that wall transport can occur differently based on coronary artery location. Awareness of peak growth stimulators and where drug accumulation occurs in the vasculature can better help guide local drug delivery therapies.

Deformationally dependent fluid transport properties of porcine coronary arteries based on location in the coronary vasculature.

OBJECTIVE: Understanding coronary artery mass transport allows researchers to better comprehend how drugs or proteins move through, and deposit into, the arterial wall. Characterizing how the convective component of transport changes based on arterial location could be useful to better understand how molecules distribute in different locations in the coronary vasculature. METHODS AND RESULTS: We measured the mechanical properties and wall fluid flux transport properties of de-endothelialized (similar to post-stenting or angioplasty) left anterior descending (LADC) and right (RC) porcine coronary arteries along their arterial lengths. Multiphoton microscopy was used to determine microstructural differences. Proximal LADC regions had a higher circumferential stiffness than all other regions. Permeability decreased by 198% in the LADC distal region compared to other LADC regions. The RC artery showed a decrease of 46.9% from the proximal to middle region, and 51.7% from the middle to distal regions. The porosity increased in the intima between pressure states, without differences through the remainder of the arterial thickness. CONCLUSIONS: We showed that the permeabilities and mechanical properties do vary in the coronary vasculature. With variations in mechanical properties, overexpansion of stents can occur more easily while variations in permeability may lead to altered transport based on location.

Location-dependent coronary artery diffusive and convective mass transport properties of a lipophilic drug surrogate measured using nonlinear microscopy.

PURPOSE: Arterial wall mass transport properties dictate local distribution of biomolecules or locally delivered dugs. Knowing how these properties vary between coronary artery locations could provide insight into how therapy efficacy is altered between arterial locations. METHODS: We introduced an indocarbocyanine drug surrogate to the lumens of left anterior descending and right coronary (LADC; RC) arteries from pigs with or without a pressure gradient. Interstitial fluorescent intensity was measured on live samples with multiphoton microscopy. We also measured binding to porcine coronary SMCs in monoculture. RESULTS: Diffusive transport constants peaked in the middle sections of the LADC and RC arteries by 2.09 and 2.04 times, respectively, compared to the proximal and distal segments. There was no statistical difference between the average diffusivity value between LADC and RC arteries. The convection coefficients had an upward trend down each artery, with the RC being higher than the LADC by 3.89 times. CONCLUSIONS: This study demonstrates that the convective and diffusive transport of lipophilic molecules changes between the LADC and the RC arteries as well as along their length. These results may have important implications in optimizing drug delivery for the treatment of coronary artery disease.

Wall stress reduction in abdominal aortic aneurysms as a result of polymeric endoaortic paving.

Polymeric endoaortic paving (PEAP) may improve endovascular repair of abdominal aortic aneurysms (AAA) since it has the potential to treat patients with complex AAA geometries while reducing the incidence of migration and endoleak. Polycaprolactone (PCL)/polyurethane (PU) blends are proposed as PEAP materials due to their range of mechanical properties, thermoformability, and resistance to biodegradation. In this study, the reduction in AAA wall stress that can be achieved using PEAP was estimated and compared to that resulting from stent-grafts. This was accomplished by mechanically modeling the anisotropic response of PCL/PU blends and implementing these results into finite element model (FEM) simulations. We found that at the maximum diameter of the AAA, the 50/50 and 10/90 PCL/PU blends reduced wall stress by 99 and 98%, respectively, while a stent-graft reduced wall stress by 99%. Our results also show that wall stress reduction increases with increasing PEAP thickness and PCL content in the blend ratio. These results indicate that PEAP can reduce AAA wall stress as effectively as a stent-graft. As such, we propose that PEAP may provide an improved treatment alternative for AAA, since many of the limitations of stent-grafts have the potential to be solved using this approach.

Porohyperelastic finite element modeling of abdominal aortic aneurysms.

Abdominal aortic aneurysm (AAA) is the gradual weakening and dilation of the infrarenal aorta. This disease is progressive, asymptomatic, and can eventually lead to rupture--a catastrophic event leading to massive internal bleeding and possibly death. The mechanical environment present in AAA is currently thought to be important in disease initiation, progression, and diagnosis. In this study, we utilize porohyperelastic (PHE) finite element models (FEMs) to investigate how such modeling can be used to better understand the local biomechanical environment in AAA. A 3D hypothetical AAA was constructed with a preferential anterior bulge assuming both the intraluminal thrombus (ILT) and the AAA wall act as porous materials. A parametric study was performed to investigate how physiologically meaningful variations in AAA wall and ILT hydraulic permeabilities affect luminal interstitial fluid velocities and wall stresses within an AAA. A corresponding hyperelastic (HE) simulation was also run in order to be able to compare stress values between PHE and HE simulations. The effect of AAA size on local interstitial fluid velocity was also investigated by simulating maximum diameters (5.5 cm, 4.5 cm, and 3.5 cm) at the baseline values of ILT and AAA wall permeability. Finally, a cyclic PHE simulation was utilized to study the variation in local fluid velocities as a result of a physiologic pulsatile blood pressure. While the ILT hydraulic permeability was found to have minimal affect on interstitial velocities, our simulations demonstrated a 28% increase and a 20% decrease in luminal interstitial fluid velocity as a result of a 1 standard deviation increase and decrease in AAA wall hydraulic permeability, respectively. Peak interstitial velocities in all simulations occurred on the luminal surface adjacent to the region of maximum diameter. These values increased with increasing AAA size. PHE simulations resulted in 19.4%, 40.1%, and 81.0% increases in peak maximum principal wall stresses in comparison to HE simulations for maximum diameters of 35 mm, 45 mm, and 55 mm, respectively. The pulsatile AAA PHE FEM demonstrated a complex interstitial fluid velocity field the direction of which alternated in to and out of the luminal layer of the ILT. The biomechanical environment within both the aneurysmal wall and the ILT is involved in AAA pathogenesis and rupture. Assuming these tissues to be porohyperelastic materials may provide additional insight into the complex solid and fluid forces acting on the cells responsible for aneurysmal remodeling and weakening.

Drained secant modulus for human and porcine peripapillary sclera using unconfined compression testing.

Glaucoma is an ocular disease characterized by damage of the optic nerve head (ONH) resulting in blindness. Recent research has identified the material properties of the sclera as being an important factor in the biomechanics of major load bearing tissues near the ONH. Most mechanical investigations performed on sclera have focused on the tensile behavior of this tissue, neglecting its compressive stiffness. The present study characterized the compressive moduli of peripapillary sclera using an unconfined compression (UCC) technique, for both human and porcine sources. UCC stress-relaxation tests were performed on human and porcine peripapillary scleral samples at 5%, 10% and 15% sequential compressive strain. Our results indicate a linearly decreasing drained equilibrium stress (at 5%) with age in male human samples, ranging from 79.4 Pa at 78 yrs to 40.1 Pa at 89 yrs of age. The drained secant modulus (E(5)) of human and porcine sclera was found to be 1.1 +/- 0.08 kPa and 3.9 +/- 0.57 kPa, respectively. Our experimental results also reveal a non-linear increase in drained equilibrium stress with increasing compressive strain. The compressive stiffness of sclera, as reported here, provides important information on the mechanical response of peripapillary ocular tissues. This information will be useful in future computational simulations of the sclera, especially as they relate to understanding mechanical damage near the ONH. Furthermore, our results indicate that age-related changes in the biomechanical response of the sclera occur, suggesting that these factors may be playing a role in the increasing prevalence of glaucoma with age.

Compressive mechanical properties of the intraluminal thrombus in abdominal aortic aneurysms and fibrin-based thrombus mimics.

An intraluminal thrombus (ILT) forms in the majority of abdominal aortic aneurysms (AAAs). While the ILT has traditionally been perceived as a byproduct of aneurysmal disease, the mechanical environment within the ILT may contribute to the degeneration of the aortic wall by affecting biological events of cells embedded within the ILT. In this study, the drained secant modulus (E(5) approximately modulus at 5% strain) of ILT specimens (luminal, medial, and abluminal) procured from elective open repair was measured and compared using unconfined compression. Five groups of fibrin-based thrombus mimics were also synthesized by mixing various combinations of fibrinogen, thrombin, and calcium. Drained secant moduli were compared to determine the effect of the components' concentrations on mimic stiffness. The stiffness of mimics was also compared to the native ILT. Preliminary data on the water content of the ILT layers and mimics was measured. It was found that the abluminal layer (E(5)=19.3kPa) is stiffer than the medial (2.49kPa) and luminal (1.54kPa) layers, both of which are statistically similar. E(5) of the mimics (0.63, 0.22, 0.23, 0.87, and 2.54kPa) is dependent on the concentration of all three components: E(5) decreases with a decrease in fibrinogen (60-20 and 20-15mg/ml) and a decrease in thrombin (3-0.3 units/ml), and E(5) increases with a decrease in calcium (0.1-0.01M). E(5) from two of the mimics were not statistically different than the medial and luminal layers of ILT. A thrombus mimic with similar biochemical components, structure, and mechanical properties as native ILT would provide an appropriate test medium for AAA mechanobiology studies.

Toward a model for local drug delivery in abdominal aortic aneurysms.

The formation of an abdominal aortic aneurysm (AAA) may eventually result in rupture, an event associated with a 50% mortality rate. This work represents a first step toward improving current stress estimation techniques and local transport simulations in AAA. Toward this aim, a computational parametric study was performed on an axisymmetric cylindrical FEM of a 5 cm AAA with a 1.5 cm thick intraluminal thrombus (ILT). Both the AAA wall and ILT were modeled as porohyperelastic PHE materials using estimated values of AAA wall and ILT permeability. While no values for AAA wall permeability could be found in the literature, the value of ILT permeability was taken from a previous investigation by Adolph et al.(7) Peak stresses, fluid velocities, and local pore pressure values within the ILT and wall were recorded and analyzed as a function of the cardiac cycle. While peak wall stress values for the PHE models did not largely differ from corresponding solid finite element simulations (186.2 N/cm(2) vs. 186.5 N/cm(2)), the stress in the abluminal region of the ILT increased by 17.4% (7.7 N/cm(2) vs. 6.5 N/cm(2)). Pore pressure values were relatively constant through the ILT while there were significant pore pressure gradients present in the AAA wall. The magnitude of fluid velocities varied in magnitude and direction throughout the cardiac cycle with large fluctuations occurring on the luminal surface. The combination of the patient-specific PHE AAA FEMs with mass transport simulations will result in spatially and time-varying concentration distributions within AAA, which may benefit future pharmaceutical treatments of AAA.