Literature Survey for In-Vivo Reynolds and Womersley Numbers of Various Arteries and Implications for Compliant In-Vitro Modelling

PURPOSE

In-vitro modelling can be used to investigate haemodynamics of arterial geometry and stent implants. However, in-vitro model fidelity relies on precise matching of in-vivo conditions. In pulsatile flow, velocity distribution and wall shear stress depend on compliance, and the Reynolds and Womersley numbers. However, matching such values may lead to unachievable tolerances in phantom fabrication.

METHODS

Published Reynolds and Womersley numbers for 14 major arteries in the human body were determined via a literature search. Preference was given to in-vivo publications but in-vitro and in-silico values were presented when in-vivo values were not found. Subsequently ascending aorta and carotid artery case studies were presented to highlight the limitations dynamic matching would apply to phantom fabrication.

RESULTS

Seven studies reported the in-vivo Reynolds and Womersley numbers for the aorta and two for the carotid artery. However, only one study each reported in-vivo numbers for the remaining ten arteries. No in-vivo data could be found for the femoral, superior mesenteric and renal arteries. Thus, information derived in-vitro and in-silico were provided instead. The ascending aorta and carotid artery models required scaling to 1.5× and 3× life-scale, respectively, to achieve dimensional tolerance restrictions. Modelling the ascending aorta with the comparatively high viscosity water/glycerine solution will lead to high pump power demands. However, all the working fluids considered could be dynamically matched with low pump demand for the carotid model.

CONCLUSION

This paper compiles available human haemodynamic information, and highlights the paucity of information for some arteries. It also provides a method for optimal in-vitro experimental configuration.

On the mechanical significance of vascular imprints of the human neurocranium when impacted at 11 m/s

The course of the middle meningeal vessels can be traced through imprints on the inner table of the human neurocranium. It is as yet unexplored whether these notches lower the load-bearing capacity of the bone when compared to areas that are free of vascular imprints. Here, 310 temporo-parietal samples with and without vascular imprints, from 52 human Crosado-embalmed cadavers, were tested in a three-point bending setup with a half-cylindrical impactor (1 mm radius of curvature) contacting the sample at 11 m/s. The maximum forces before breaking, and the thicknesses of the samples, were statistically compared, including comparing the avascular group to several groups with vascular imprints of different orientations. Furthermore, the influence of sample length and impact location were investigated. To investigate structure and mechanical function of vascular imprints concomitantly, scanning electron microscopy was performed on selected samples in two different planes. The results showed that avascular samples were on average thicker (p < 0.001) and stronger (p ≤ 0.050) compared to samples with vascular imprints. When only thickness-matched samples were analysed, the observed maximum forces of vascular and avascular samples were statistically similar (p ≥ 0.531). Regarding the load-bearing capacity of samples with vascular imprints, it was irrelevant whether the imprint was placed parallel to and directly underneath the impactor, parallel to and offset from the impactor, or perpendicular to the impactor (p > 0.999). The overall results of this study were statistically unrelated to both sample length (p ≥ 0.720) and impact location (p > 0.999). Scanning electron microscopy revealed that vascular imprints are formed through a curve of the inner table. Perforating holes of the inner table are present in avascular areas, however, they are considerably larger in size and higher in number within vascular imprints. In conclusion, vascular imprints are formed through curving of the inner table. In numerical models of human head mechanics, vascular imprints can be accounted for through a simple thinning of the bone assuming the same load-bearing capacity as for the surrounding imprint-free areas.

Hydrodynamic control of titania nanotube formation on Ti-6Al-4V alloys enhances osteogenic differentiation of human mesenchymal stromal cells

In order to obtain bioactive bone-implant interfaces with enhanced osteogenic capacity, various approaches have been developed to modify surface physicochemical properties of bio-inert titanium and titanium alloys. One promising strategy involves fabricating highly ordered nanotubes (NT) on implant surfaces via electrochemical anodization. However, few studies have applied this technique to Ti-6Al-4V alloys most commonly adopted for the fabrication of osteo-integrated surfaces on orthopedic implants. In this study, we investigated the influence of electrolyte hydrodynamics to NT fabrication on Ti-6Al-4V in ethylene glycol based electrolyte and evaluated the osteogenic differentiation capacity of human mesenchymal stromal cells (hMSCs) on different diameter NT surfaces. Computational Fluid Dynamics (CFD) analysis was used to simulate electrolyte flow profiles under various stirring conditions (e.g. stirrer bar location and flow direction) and their correlation to NT formation. Polished Ti-6Al-4V disks (240 grit) were anodized at 20 and 40 V under optimal electrolyte flow conditions for comparison of NT diameter-controlled osteogenic differentiation and mineralization potential of hMSCs over 21 days culture in osteogenic media. Ti-6Al-4V surfaces anodized with 20 and 40 V resulted with NTs diameter approx. 39 and 83 nm, respectively. Electrolyte hydrodynamics (flow profile) significantly influenced the uniformity of NT formation. Here, a uniform velocity and shear stress profile at the surface promoted homogeneous NT growth, whereas large variation in either flow velocity or shear stress to the surface impaired mature NT formation. After 21 days of culture, fluorescence staining demonstrated significantly greater osteocalcin and osteopontin expression, and increased mineralized deposits (xylenol orange staining) on fluctuating NT surfaces anodized under 20 V (Ø 39 nm) relative to flat NT layer anodized with 40 V (Ø 83 nm) and polished controls. This study provides a systematic investigation of NT formation with respect to the electrolyte hydrodynamic effects to NT growth on Ti-6Al-4V alloys, demonstrating the feasibility of a one-step anodization process for generating uniform NT under optimal hydrodynamics. Optimized wavy micro-/nano-topography with Ø 39 nm NT stimulated osteogenic differentiation capacity of hMSCs on Ti-6Al-4V alloys and confirmed the potential application of anodization to improve osteo-integrative surfaces in orthopedic implants.

PIV Analysis of Stented Haemodynamics in the Descending Aorta

Cardiovascular diseases (CVD) are the leading cause of death in the developed world and aortic aneurysm is a key contributor. Aortic aneurysms typically occur in the thoracic aorta and can extend into the descending aorta. The Frozen Elephant Trunk stent (FET) is one of the leading treatments for the aneurysms extending into the descending aorta. This study focuses on the in-vitro experimentation of a stented descending aorta, investigating the haemodynamics in a compliant phantom. A silicone phantom of the descending aorta was manufactured using a lost core casting method. A PVC stent was manufactured using the same mould core. Particle Image Velocimetry (PIV) was used for pulsatile studies, focusing specifically on the passive fixation at the distal end of the FET. The results showed an apparent expansion in the diastolic period that was identified to be a collapse in the lateral plane. Flow recirculation regions were identified during the collapse. The collapse was attributed to low upstream and high downstream pressures causing a vacuum effect. The findings may imply a potential risk introduced by the FET stent that requires further investigation.