Multiscale homogenization of aluminum honeycomb structures: Thermal analysis with orthotropic representative volume element and finite element method.

This study develops a thermal homogenization model for an aluminum honeycomb panel using the representative volume element (RVE) concept, considering the orthotropic nature of the structure. The RVE thermal homogenization method is a numerical approach for analyzing heterogeneous materials. It employs a constitutive model based on RVE performance to represent thermal behavior. Effective parameters are determined through averaging techniques, and the finite element method solves the thermal problem, accounting for structure topology and material behavior. The resulting heat conduction problem is solved using the finite element method (FEM) to evaluate the effective thermal characteristics. A 3D RVE is generated based on the honeycomb panel's geometry, evaluating thermal conductivity tensor and describing the medium's thermal performance. Numerical tests validate the model by comparing it with the real honeycomb structure under sinusoidal heat flux. Results show good correlation, with maximum temperatures of 1101.9 °C in the real structure and 1096.4 °C in the medium. The homogeneous medium is further used to investigate thermal performance under convective conditions with varying panel thicknesses, achieving over 77 °C temperature reduction with the thickest panel. Natural vibration behavior is considered, demonstrating strong correlation between modal responses and natural frequencies. This modeling approach efficiently analyzes thermal behavior in large honeycomb structures, reducing computational time significantly.

Advancing Front Oxygen Transfer Model for the Design of Microchannel Artificial Lungs.

Microchannel artificial lungs may provide highly efficient, long-term respiratory support, but a robust predictive oxygen transfer (VO2) model is needed to better design them. To meet this need, we first investigated the predictive accuracy of Mikic, Benn, and Drinker's advancing front (AF) oxygen transfer theory by applying it to previous microchannel lung studies. Here, the model that included membrane resistance showed no bias toward overprediction or underprediction of VO2 (median error: -1.13%, interquartile range: [-26.9%, 19.2%]) and matched closely with existing theory. Next, this theory was expanded into a general model for investigating a family of designs. The overall model suggests that, for VO2 = 100 ml/min, fraction of delivered oxygen (FDO2) = 40%, wall shear stress ((Equation is included in full-text article.)) = 30 dyn/cm, and blood channel height = 20-50 µm, a compact design can be achieved with priming volume ((Equation is included in full-text article.)) = 5.8-32 ml; however, manifolding may be challenging to satisfy the rigorous total width ((Equation is included in full-text article.)) requirement ((Equation is included in full-text article.)= 76-475 m). In comparison, 100-200 µm heights would yield larger dimensions ((Equation is included in full-text article.)122-478 ml) but simpler manifolding ((Equation is included in full-text article.)4.75-19.0 m). The device size can be further adjusted by varying FDO2, (Equation is included in full-text article.), or VO2. This model may thus serve as a simple yet useful tool to better design microchannel artificial lungs.

Correlation between MMP and TIMP levels and elastic moduli of ascending thoracic aortic aneurysms.

OBJECTIVE: The objective of this preliminary investigation is to determine if there is a relation between the biological levels of matrix metalloproteinases and tissue inhibitor of matrix metalloproteinase (TIMP) and the elastic moduli of the ascending aortic wall in patients with ascending thoracic aortic aneurysms (ATAA). METHODS: Circumferential specimens from twelve patients with ATAA were obtained from the greater curvature and their tensile properties (maximum elastic modulus) were tested uniaxially. The levels of MMP1, 2, 3, 8, and 9 as well as TIMP1 and 2 were determined in these aortic wall specimens using MMP/TIMP antibodies array. RESULTS: Direct relations were found between MMP2 and the elastic modulus of the ascending aorta wall (R2 = 0.52) and between MMP9 and TIMP1 (R2 = 0.63). However, weak positive relation was found between MMP2 and TIMP2 (R2 = 0.23). We found inverse relations between MMP3 and MMP8 levels and the elastic module. There were no relations between MMP1 and MMP9 levels and the elastic modulus of aortic wall. CONCLUSIONS: This preliminary study looks at the relationship between the elastic modulii and the MMPs/TIMPs levels found in aortic wall specimens. Given that the value of the elastic moduli can be obtained non-invasively, a close relation might permit to infer the value of MMPs and TIMPs levels from the non-invasive determination of the elasticity of the aortic wall. By allowing the non-invasive determination of the mechanical and biological properties of the aorta in in-vivo, the method proposed here might improve the prediction of outcomes of ascending aortic aneurysms. This is a very preliminary study (small sample size) and the outcomes of this study cannot be used as final conclusions and should be verified in further studies with larger sample of patients.

Organization of Endothelial Cells, Pericytes, and Astrocytes into a 3D Microfluidic in Vitro Model of the Blood-Brain Barrier.

The endothelial cells lining the capillaries supplying the brain with oxygen and nutrients form a formidable barrier known as the blood-brain barrier (BBB), which exhibits selective permeability to small drug molecules and virtually impermeable to macromolecular therapeutics. Current in vitro BBB models fail to replicate this restrictive behavior due to poor integration of the endothelial cells with supporting cells (pericytes and astrocytes) following the correct anatomical organization observed in vivo. We report the coculture of mouse brain microvascular endothelial cells (b.End3), pericytes, with/without C8-D1A astrocytes in layered microfluidic channels forming three-dimensional (3D) bi- and triculture models of the BBB. The live/dead assay indicated high viability of all cultured cells up to 21 days. Trans-endothelial electrical resistance (TEER) values confirmed the formation of intact monolayers after 3 days in culture and showed statistically higher values for the triculture model compared to the single and biculture models. Screening the permeability of [(14)C]-mannitol and [(14)C]-urea showed the ability of bi- and triculture models to discriminate between different markers based on their size. Further, permeability of [(14)C]-mannitol across the triculture model after 18 days in culture matched its reported permeability across the BBB in vivo. Mathematical calculations also showed that the radius of the tight junctions pores (R) in the triculture model is similar to the reported diameter of the BBB in vivo. Finally, both the bi- and triculture models exhibited functional expression of the P-glycoprotein efflux pump, which increased with the increase in the number of days in culture. These results collectively indicate that the triculture model is a robust in vitro model of the BBB.

Experimental and clinical evidence supporting septectomy in the primary treatment of acute type B thoracic aortic dissection.

BACKGROUND: We reviewed the mechanics involved in the aneurysmal dilatation of the false lumen (FL) in type B aortic dissection and the experimental and clinical evidence supporting the proposition that the main agent for this dilatation is a differential of pressure between the false and true lumena. This difference in pressure is the consequence of a restricted outflow of the FL. Our aim was to study the relationship between the size of a septectomy that increases the outflow of the FL and its effect on the values of the differential of pressure. METHODS: A bench-top model of aortic dissection was used to determine the relationship between the area of the tears and the value of the pressure differential. A range of tear sizes was tested. RESULTS: The highest differential of pressure (6.77 mm Hg) was found with a single proximal tear. The addition of a distal tear decreases the pressure difference. The greater the sum of the areas of proximal and distal tears, the lower the pressure difference between true lumen and FL. This pressure difference approached zero, as the sum of the areas approached 250 mm(2). CONCLUSIONS: A septectomy of at least 250 mm(2), initiated from the distal tear to the proximal aorta of an area, should be part of the initial treatment of acute aortic dissection. Concomitant with it, the proximal tear should be occluded with either a bare stent or a stent graft.

Sources of error in the measurement of aortic diameter in computed tomography scans.

OBJECTIVE: This study was conducted to determine the differences in the diameter of the thoracic aorta when measured from electrocardiographic (ECG)-gated and nongated computed tomography (CT) angiography. Another aim was to define the difference in the aortic diameter when it is measured at peak systole and end diastole in ECG-gated scans. METHODS: The gated and nongated CT angiograms of 27 patients (mean age, 58 ± 16 standard deviation [SD] years) obtained on a 256-slice multidetector CT scanner were used. The transverse and anteroposterior diameters and the lumen areas were measured at 1, 4, and 8 cm below the origin of the left subclavian artery. RESULTS: There was a significant difference in the aortic measurements of diameter between gated and nongated scans found in samples taken at 1, 4, and 8 cm distal to the left subclavian artery (P < .0001). We found a considerable difference between the systolic and diastolic diameters (P < .0001). The maximum change in diameter between systole and diastole was 2.9 ± 0.9 (SD) mm (14.5%, P < .0001) at 1 cm, 5.4 mm (22.6%; median, 1.7 mm; P < .0001) at 4 cm, and 4.4 mm (16.9%; median, 1.3 mm; P < .0001) at 8 cm. There was a significant difference between the transverse and anteroposterior diameters in systole and diastole at all locations (P < .0001): The maximum change in diameter between transverse and anteroposterior diameters in systole was 5.4 ± 1.1 (SD) mm (15.7%, P < .0001) at 1 cm, 5.8 mm (19%; median, 1.4 mm; P < .0001) at 4 cm, and 5 mm (15%; median, 1.02 mm; P < .0001) at 8 cm. There was also a substantial difference between measuring the transverse diameter directly and deriving it from the lumen area (P < .0001). CONCLUSIONS: Our results showed an important difference between systolic and diastolic diameters measurements in ECG-gated scans. The standard protocol for measuring aortic diameters in gated scans of the thoracic aorta uses images at end diastole because the lack of wall motion at this time provides better resolution. This is likely to result in undersizing that, in some instances, may threaten stability and the proper seal of the stent graft. The dimensions of the aorta in a gated CT should be measured at peak systole rather than the conventional end diastole used today. Most medical centers use nongated CT or gated CT scans in end diastole to calculate sizes of endografts. In view of our findings, the latter method could result in potential complications.

Design and in vitro assessment of an improved, low-resistance compliant thoracic artificial lung.

Current thoracic artificial lungs (TALs) have blood flow impedances greater than the natural lungs, which can result in abnormal pulmonary hemodynamics. This study investigated the impedance and gas transfer performance of a compliant TAL (cTAL). Fluid-structure interaction analysis was performed using ADINA (ADINA R&D Inc., Watertown, MA) to examine the effect of the inlet and outlet expansion angle, θ, on device impedance and blood flow patterns. Based on the results, the θ = 45° model was chosen for prototyping and in vitro testing. Glycerol was pumped through this cTAL at 2, 4, and 6 L/min at 80 and 100 beats/min, and the zeroth and first harmonic impedance moduli, Z(0) and Z(1), were calculated. Gas transfer testing was conducted at blood flow rates of 3, 5, and 7 L/min. Fluid-structure interaction results indicated that the 45° model had an ideal combination of low impedance and even blood flow patterns and was thus chosen for prototyping. In vitro, Z(0) = 0.53 ± 0.06 mm Hg/(L/min) and Z(1) = 0.86 ± 0.08 mm Hg/(L/min) at 4 L/min and 100 beats/min. Outlet PO(2) and SO(2) values were above 200 mm Hg and 99.5%, respectively, at each flow rate. Thus, the cTAL had lower impedance than hard shell TALs and excellent gas transfer.

Thoracic artificial lung impedance studies using computational fluid dynamics and in vitro models.

Current thoracic artificial lungs (TALs) possess blood flow impedances greater than the natural lungs, resulting in abnormal pulmonary hemodynamics when implanted. This study sought to reduce TAL impedance using computational fluid dynamics (CFD). CFD was performed on TAL models with inlet and outlet expansion and contraction angles, θ, of 15°, 45°, and 90°. Pulsatile blood flow was simulated for flow rates of 2-6 L/min, heart rates of 80 and 100 beats/min, and inlet pulsatilities of 3.75 and 2. Pressure and flow data were used to calculate the zeroth and first harmonic impedance moduli, Z(0) and Z(1), respectively. The 45° and 90° models were also tested in vitro under similar conditions. CFD results indicate Z(0) increases as stroke volume and θ increase. At 4 L/min, 100 beats/min, and a pulsatility of 3.75, Z(0) was 0.47, 0.61, and 0.79 mmHg/(L/min) for the 15°, 45°, and 90° devices, respectively. Velocity band and vector plots also indicate better flow patterns in the 45° device. At the same conditions, in vitro Z (0) were 0.69 ± 0.13 and 0.79 ± 0.10 mmHg/(L/min), respectively, for the 45° and 90° models. These Z(0) are 65% smaller than previous TAL designs. In vitro, Z(1) increased with flow rate but was small and unlikely to significantly affect hemodynamics. The optimal design for flow patterns and low impedance was the 45° model.

THE ROLE OF POROUS MEDIA IN MODELING FLUID FLOW WITHIN HOLLOW FIBER MEMBRANES OF THE TOTAL ARTIFICIAL LUNG.

A numerical study was conducted to analyze fluid flow within hollow fiber membranes of the artificial lungs. The hollow fiber bundle was approximated using a porous media model. In addition, the transport equations were solved using the finite-element formulation based on the Galerkin method of weighted residuals. Comparisons with previously published work on the basis of special cases were performed and found to be in excellent agreement. A Newtonian viscous fluid model for the blood was used. Different flow models for porous media, such as the Brinkman-extended Darcy model, Darcy's law model, and the generalized flow model, were considered. Results were obtained in terms of streamlines, velocity vectors, and pressure distribution for various Reynolds numbers and Darcy numbers. The results from this investigation showed that the pressure drop across the artificial lung device increased with an increase in the Reynolds number. In addition, the pressure drop was found to increase significantly for small Darcy numbers.

An Investigation of Pulsatile Flow Past Two Cylinders as a Model of Blood Flow in an Artificial Lung.

Pulsatile flow across two circular cylinders with different geometric arrangements is studied experimentally using the particle image velocimetry method and numerically using the finite element method. This investigation is motivated the need to optimize gas transfer and fluid mechanical impedance for a total artificial lung, in which the right heart pumps blood across a bundle of hollow microfibers. Vortex formation was found to occur at lower Reynolds numbers in pulsatile flow than in steady flow, and the vortex structure depends strongly on the geometric arrangement of the cylinders and on the Reynolds and Stokes numbers.

Determination of the elastic modulus of ascending thoracic aortic aneurysm at different ranges of pressure using uniaxial tensile testing.

OBJECTIVE: The purpose of this study is to provide measurements of the elastic modulus of the aortic wall of ascending thoracic aortic aneurysms for different ranges of pressure (physiologic, hypertensive). In addition, pre-failure stress, taken as the peak stress obtained before specimen failure, was recorded for each test. METHODS: Ninety-seven aortic samples freshly excised from 13 patients with ascending thoracic aortic aneurysms were obtained from greater and lesser curvatures and tested uniaxially in circumferential and longitudinal orientations. RESULTS: The maximum elastic moduli, overall, and particularly in the lesser curvature were significantly higher in the circumferential orientation (9.19 MPa) than in the longitudinal (3.13 MPa). Results of peak stress showed positive correlation with maximum elastic modulus and inverse correlation with tissue wall thickness. CONCLUSIONS: This study provides new data on the elastic modulus in the physiologic and hypertensive range that can be used in computational analysis and the design of bench-top models. The accuracy of computational analysis and bench-top models strongly depends on the knowledge of the elastic properties of the aortic wall. The mechanical properties presented in this study, with specific values for 2 locations (greater and lesser curvature) and 2 directions (circumferential, longitudinal), will increase our understanding of the mechanisms that precede rupture of an ascending aortic aneurysm.

Quantitative evaluation of the effect of poly(amidoamine) dendrimers on the porosity of epithelial monolayers.

Poly(amidoamine) (PAMAM) dendrimers are a family of water-soluble polymers with a characteristic tree-like branching architecture and a large number of surface groups, which have been used to immobilize a variety of therapeutic molecules for targeted drug delivery. Earlier studies showed that small cationic PAMAM-NH2 and selected anionic PAMAM-COOH dendrimers permeate across in vitro models of the small intestinal epithelium by paracellular and transcellular transport mechanisms. The focus of this research is to mathematically calculate the effect of cationic, anionic, and neutral PAMAM dendrimers on the porosity of epithelial tight junctions as a function of dendrimers concentration, incubation time, generation number, and charge density. Results show that the increase in the concentration, incubation time and generation number of cationic G0-G2 PAMAM-NH2 and anionic G2.5 and G3.5 PAMAM-COOH dendrimers caused a corresponding increase in the porosity of Caco-2 cell monolayers. Neutral G2-G4 PAMAM-OH dendrimers had no effect on the porosity of intestinal cells. These results provide quantitative evidence that the observed increase in permeability of PAMAM dendrimers across Caco-2 cell monolayers is due to their effect on the organization of the tight junctions and the associated increase in membrane porosity. Furthermore, these results emphasize the potential of cationic PAMAM-NH2 and anionic PAMAM-COOH dendrimers to function as carriers for controlled oral drug delivery.

Fluid-structure interaction analysis of turbulent pulsatile flow within a layered aortic wall as related to aortic dissection.

Turbulent pulsatile flow and wall mechanics were studied numerically in an axisymmetric three-layered wall model of a descending aorta. The transport equations were solved using the finite element formulation based on the Galerkin method of weighted residuals. A fully-coupled fluid-structure interaction (FSI) analysis was utilized in this investigation. We calculated Von Mises wall stress, streamlines and fluid pressure contours. The findings of this study show that peak wall stress and maximum shear stress are highest in the media layer. The difference in the elastic properties of contiguous layers of the wall of the aorta probably determines the occurrence of dissection in the media layer. Moreover, the presence of aortic intramural hematoma is found to have a significant effect on the peak wall stress acting on the inner layer.

Effects of strain rate, mixing ratio, and stress-strain definition on the mechanical behavior of the polydimethylsiloxane (PDMS) material as related to its biological applications.

Tensile tests on Polydimethylsiloxane (PDMS) materials were conducted to illustrate the effects of mixing ratio, definition of the stress-strain curve, and the strain rate on the elastic modulus and stress-strain curve. PDMS specimens were prepared according to the ASTM standards for elastic materials. Our results indicate that the physiological elastic modulus depends strongly on the definition of the stress-strain curve, mixing ratio, and the strain rate. For various mixing ratios and strain rates, true stress-strain definition results in higher stress and elastic modulus compared with engineering stress-strain and true stress-engineering strain definitions. The elastic modulus increases as the mixing ratio increases up-to 9:1 ratio after which the elastic modulus begins to decrease even as the mixing ratio continues to increase. The results presented in this study will be helpful to assist the design of in vitro experiments to mimic blood flow in arteries and to understand the complex interaction between blood flow and the walls of arteries using PDMS elastomer.

Tear size and location impacts false lumen pressure in an ex vivo model of chronic type B aortic dissection.

BACKGROUND: Follow-up mortality is high in patients with type B aortic dissection (TB-AD) approaching one in four patients at 3 years. A predictor of increased mortality is partial thrombosis of the false lumen which may occlude distal tears. The hemodynamic consequences of differing tear size, location, and patency within the false lumen is largely unknown. We examined the impact of intimal tear size, tear number, and location on false lumen pressure. METHODS: In an ex-vivo model of chronic type B aortic dissection connected to a pulsatile pump, simultaneous pressures were measured within the true and false lumen. Experiments were performed in different dissection models with tear sizes of 6.4 mm and 3.2 mm in the following configurations; model A: proximal and distal tear simulating the most common hemodynamic state in patients with TB-AD; model B: proximal tear only simulating patients with partial thrombosis and occlusion of distal tear; and model C: distal tear only simulating patients sealed proximally via a stent graft with persistent distal communication. To compare false lumen diastolic pressure between models, a false lumen pressure index (FPI%) was calculated for all simulations as FPI% = (false lumen diastolic pressure/true lumen diastolic pressure) x 100. RESULTS: In model A, the systolic pressure was slightly lower in the false lumen compared with the true lumen while the diastolic pressure (DP) was slightly higher in the false lumen (DP 66.45 +/- 0.16 mm Hg vs 66.20 +/- 0.12 mm Hg, P < .001, FPI% = 100.4%). In the absence of a distal tear (model B), diastolic pressure was elevated within the false lumen compared with the true lumen (58.95 +/- 0.10 vs 54.66 +/- 0.17, P < .001, FPI% = 107.9%). The absence of a proximal tear in the presence of a distal tear (model C) diastolic pressure was also elevated within the false lumen versus the true lumen (58.72 +/- 0.24 vs 56.15 +/- 0.16, P < .001, FPI% 104.6%). The difference in diastolic pressure was greatest with a smaller tear (3.2 mm) in model B. In model B, DBP increased by 13.9% (P < .001, R(2) 0.69) per 10 beat per minute increase in heart rate (P < .001) independent of systolic pressure. CONCLUSIONS: In this model of chronic type B aortic dissection, diastolic false lumen pressure was the highest in the setting of smaller proximal tear size and the lack of a distal tear. These determinants of inflow and outflow may impact false lumen expansion and rupture during the follow-up period.

Turbulence significantly increases pressure and fluid shear stress in an aortic aneurysm model under resting and exercise flow conditions.

The numerical models of abdominal aortic aneurysm (AAA) in use do not take into account the non-Newtonian behavior of blood and the development of local turbulence. This study examines the influence of pulsatile, turbulent, non-Newtonian flow on fluid shear stresses and pressure changes under rest and exercise conditions. We numerically analyzed pulsatile turbulent flow, using simulated physiological rest and exercise waveforms, in axisymmetric-rigid aortic aneurysm models (AAMs). Discretization of governing equations was achieved using a finite element scheme. Maximum turbulence-induced shear stress was found at the distal end of an AAM. In large AAMs (dilated to undilated diameter ratio = 3.33) at peak systolic flow velocity, fluid shear stress during exercise is 70.4% higher than at rest. Our study provides a numerical, noninvasive method for obtaining detailed data on the forces generated by pulsatile turbulent flow in AAAs that are difficult to study in humans and in physical models. Our data suggest that increased flow turbulence results in increased shear stress in aneurysms. While pressure readings are fairly uniform along the length of an aneurysm, the kinetic energy generated by turbulence impacting on the wall of the distal half of the aneurysm increases fluid and wall shear stress at this site. If the increased fluid shear stress results in further dilation and hence further turbulence, wall stress may be a mechanism for aneurysmal growth and eventual rupture.

Refinements in mathematical models to predict aneurysm growth and rupture.

The growth of aneurysms and eventually their likelihood of rupture depend on the determination of the stress and strain within the aneurysm wall and the exact reproduction of its geometry. A numerical model is developed to analyze pulsatile flow in abdominal aortic aneurysm (AAA) models using real physiological resting and exercise waveforms. Both laminar and turbulent flows are considered. Interesting features of the flow field resulting from using realistic physiological waveforms are obtained for various parameters using finite element methods. Such parameters include Reynolds number, size of the aneurysm (D/d), and flexibility of the aneurysm wall. The effect of non-Newtonian behavior of blood on hemodynamic stresses is compared with Newtonian behavior, and the non-Newtonian effects are demonstrated to be significant in realistic flow situations. Our results show that maximum turbulent fluid shear stress occurs at the distal end of the AAA model. Furthermore, turbulence is found to have a significant effect on the pressure distribution along AAA wall for both physiological waveforms. Related experimental work in which a bench top aneurysm model is developed is also discussed. The experimental model provides a platform to validate the numerical model. This work is part of our ongoing development of a patient-specific tool to guide clinician decision making and to elucidate the contribution of blood flow-induced stresses to aneurysm growth and eventual rupture. These studies indicate that accurately modeling the physiologic features of real aneurysms and blood is paramount to achieving our goal.

Modeling pulsatile flow in aortic aneurysms: effect of non-Newtonian properties of blood.

Pulsatile flow in an axisymmetric rigid-walled model of an abdominal aorta aneurysm was analyzed numerically for various aneurysm dilations using physiologically realistic resting waveform at time-averaged Reynolds number of 300 and peak Reynolds number of 1607. Discretization of the governing equations was achieved using a finite element scheme based on the Galerkin method of weighted residuals. Comparisons with previously published work on the basis of special cases were performed and found to be in excellent agreement. Our findings indicate that the velocity fields are significantly affected by non-Newtonian properties in pathologically altered configurations. Non-Newtonian fluid shear stress is found to be greater than Newtonian fluid shear stress during peak systole. Further, the maximum shear stress is found to occur near the distal end of AAA during peak systole. The impact of non-Newtonian blood flow characteristics on pressure compared to Newtonian model is found insignificant under resting conditions. Viscous and inertial forces associated with blood flow are responsible for the changes in the wall that result in thrombus deposition and dilation while rupture of AAA is more likely determined by much larger mechanical stresses imposed by pulsatile pressure on the wall of AAA.