An invariant-based damage model for human and animal skins

Constitutive modelling of skins that account for damage effects is important to provide insight for various clinical applications, such as skin trauma and injury, artificial skin design, skin aging, disease diagnosis, surgery, as well as comparative studies of skin biomechanics between species. In this study, a new damage model for human and animal skins is proposed for the first time. The model is nonlinear, anisotropic, invariant-based, and is based on the Gasser–Ogden–Holzapfel constitutive law initially developed for arteries. Taking account of the mean collagen fibre orientation and its dispersion, the new model can describe a wide range of skins with damage. The model is first tested on the uniaxial test data of human skin and then applied to nine groups of uniaxial test data for the human, swine, rabbit, bovine and rhino skins. The material parameters can be inversely estimated based on uniaxial tests using the optimization method in MATLAB with a root mean square error ranged between 2.15% and 12.18%. A sensitivity study confirms that the fibre orientation dispersion and the mean fibre angle are among the most important factors that influence the behaviour of the damage model. In addition, these two parameters can only be reliably estimated if some histological information is provided. We also found that depending on the location of skins, the tissue damage may be brittle controlled by the fibre breaking limit (i.e., when the fibre stretch is greater than 1.13–1.32, depending on the species), or ductile (due to both the fibre and the matrix damages). The brittle damages seem to occur mostly in the back, and the ductile damages are seen from samples taken from the belly. The proposed constitutive model may be applied to various clinical applications that require knowledge of the mechanical response of human and animal skins

Constitutive laws with damage effect for the human great saphenous vein

Strain energy-based constitutive laws with damage effect were proposed by using existing both uniaxial tensile test and tubular biaxial inflation test data on the human great saphenous vein (GSV) segments. These laws were applied into GSV coronary artery bypass grafts (CABG) by employing a thin-walled vessel model to evaluate their passive biomechanical performance under coronary artery physiological conditions at a fixed axial pre-stretch. At a peak systolic pressure in 100-150 mmHg, a 20-33% GSV diameter dilation was predicted with the law based on tubular biaxial inflation test data and agreed well with 25% dilation in clinical observation in comparison with as small as 2-4% dilation estimated with the law based on uniaxial tensile test data. The constitutive law generated by tubular biaxial inflation test data was mostly suitable for GSV CABG under coronary artery physiological conditions than that based on uniaxial tensile test results. With these laws, the fibre ultimate stretch was extracted from uniaxial tensile test data and the structural sub-failure/damage threshold of 1.0731 was decided for the human GSV. GSV fibres could exhibit damage effect but unlikely undergo a structure failure/break, suggesting a damage factor might exist during CABG arterialization. The damage in GSV tissue might initiate or contribute to early remodelling of CABG after implantation. [Abstract copyright: Copyright © 2018 Elsevier Ltd. All rights reserved.

Constitutive law of healthy gallbladder walls in passive state with damage effect

Biomechanical properties of human gallbladder (GB) wall in passive state can be valuable to diagnosis of GB diseases. In the article, an approach for identifying damage effect in GB walls during uniaxial tensile test was proposed and a strain energy function with the damage effect was devised as a constitutive law phenomenologically. Scalar damage variables were introduced respectively into the matrix and two families of fibres to assess the damage degree in GB walls. The parameters in the constitutive law with the damage effect were determined with a custom MATLAB code based on two sets of existing uniaxial tensile test data on human and porcine GB walls in passive state. It turned out that the uniaxial tensile test data for GB walls could not be fitted properly by using the existing strain energy function without the damage effect, but could be done by means of the proposed strain energy function with the damage effect involved. The stresses and Young moduli developed in two families of fibres were more than thousands higher than the stresses and Young’s moduli in the matrix. According to the damage variables estimated, the damage effect occurred in two families of fibres only. Once the damage occurs, the value of the strain energy function will decrease. The proposed constitutive laws are meaningful for finite element analysis on human GB walls

Ultrasound image based human gallbladder 3D modelling along with volume and stress level assessment

Purpose: Three-dimensional (3D) gallbladder (GB) geometrical models are essential to GB motor function evaluation and GB wall biomechanical property identification by employing finite element analysis (FEA) in GB disease diagnosis with ultrasound systems. Methods for establishing such 3D geometrical models based on static two-dimensional (2D) ultrasound images scanned along the long-axis/sagittal and short-axis/transverse cross-sections in routine GB disease diagnosis at the beginning of emptying phase have not been documented in the literature so far. Methods: Based on two custom MATLAB codes composed, two images were segmented manually to secure two sets of the scattered points for the long- and short-axis GB cross-section edges; and the points were best fitted with a piecewise cubic spline function, and the short-axis cross-section edges were lofted along the long-axis to yield a 3D geometrical model, then GB volume of the model was figured out. The model was read into SolidWorks for real surface generation and involved in ABAQUS for FEA. Results: 3D geometrical models of seven typical GB samples were established. Their GB volumes are with 15.5% and − 4.4% mean errors in comparison with those estimated with the ellipsoid model and sum-of-cylinders method but can be correlated to the latter very well. The maximum first principal in-plane stress in the 3D models is higher than in the ellipsoid model by a factor of 1.76. Conclusions: A numerical method was put forward here to create 3D GB geometrical models and can be applied to GB disease diagnosis and GB shape analysis with principal component method potentially in the future

Rôle of contrast media viscosity in altering vessel wall shear stress and relation to the risk of contrast extravasations

Iodinated contrast media (CM) are the most commonly used injectables in radiology today. A range of different media are commercially available, combining various physical and chemical characteristics (ionic state, osmolality, viscosity) and thus exhibiting distinct in vivo behaviour and safety profiles. In this paper, numerical simulations of blood flow with contrast media were conducted to investigate the effects of contrast viscosity on generated vessel wall shear stress and vessel wall pressure to elucidate any possible relation to extravasations. Five different types of contrast for Iodine fluxes ranging at 1.5–2.2 gI/s were modelled through 18 G and 20 G cannulae placed in an ideal vein at two different orientation angles. Results demonstrate that the least viscous contrast media generate the least maximum wall shear stress as well as the lowest total pressure for the same flow rate. This supports the empirical clinical observations and hypothesis that more viscous contrast media are responsible for a higher percentage of contrast extravasations. In addition, results support the clinical hypothesis that a catheter tip directed obliquely to the vein wall always produces the highest maximum wall shear stress and total pressure due to impingement of the contrast jet on the vessel wall

Primes in the intersection of two Piatetski-Shapiro sets

Let $\pi(x;\gamma_1,\gamma_2)$ denote the number of primes $p$ with $p\leqslant x$ and $p=\lfloor n^{1/\gamma_1}_1\rfloor=\lfloor n^{1/\gamma_2}_2\rfloor$, where $\lfloor t\rfloor$ denotes the integer part of $t\in\mathbb{R}$ and $1/2<\gamma_2<\gamma_1<1$ are fixed constants. In this paper, we show that $\pi(x;\gamma_1,\gamma_2)$ holds an asymptotic formula for $21/11<\gamma_1+\gamma_2<2$, which constitutes an improvement upon the previous result of Baker [1].Comment: 13 page

A waste heat-driven cooling system based on combined organic Rankine and vapour compression refrigeration cycles

In this paper, a heat driven cooling system that essentially integrated an organic Rankine cycle power plant with a vapour compression cycle refrigerator was investigated, aiming to provide an alternative to absorption refrigeration systems. The organic Rankine cycle (ORC) subsystem recovered energy from the exhaust gases of internal combustion engines to produce mechanical power. Through a transmission unit, the produced mechanical power was directly used to drive the compressor of the vapour compression cycle system to produce a refrigeration effect. Unlike the bulky vapour absorption cooling system, both the ORC power plant and vapour compression refrigerator could be scaled down to a few kilowatts, opening the possibility for developing a small-scale waste heat-driven cooling system that can be widely applied for waste heat recovery from large internal combustion engines of refrigerated ships, lorries, and trains. In this paper, a model was firstly established to simulate the proposed concept, on the basis of which it was optimized to identify the optimum operation condition. The results showed that the proposed concept is very promising for the development of heat-driven cooling systems for recovering waste heat from internal combustion engines’ exhaust gas