Validity of the Cauchy-Born rule applied to discrete cellular-scale models of biological tissues

The development of new models of biological tissues that consider cells in a discrete manner is becoming increasingly popular as an alternative to PDE-based continuum methods, although formal relationships between the discrete and continuum frameworks remain to be established. For crystal mechanics, the discrete-to-continuum bridge is often made by assuming that local atom displacements can be mapped homogeneously from the mesoscale deformation gradient, an assumption known as the Cauchy-Born rule (CBR). Although the CBR does not hold exactly for non-crystalline materials, it may still be used as a first order approximation for analytic calculations of effective stresses or strain energies. In this work, our goal is to investigate numerically the applicability of the CBR to 2-D cellular-scale models by assessing the mechanical behaviour of model biological tissues, including crystalline (honeycomb) and non-crystalline reference states. The numerical procedure consists in precribing an affine deformation on the boundary cells and computing the position of internal cells. The position of internal cells is then compared with the prediction of the CBR and an average deviation is calculated in the strain domain. For centre-based models, we show that the CBR holds exactly when the deformation gradient is relatively small and the reference stress-free configuration is defined by a honeycomb lattice. We show further that the CBR may be used approximately when the reference state is perturbed from the honeycomb configuration. By contrast, for vertex-based models, a similar analysis reveals that the CBR does not provide a good representation of the tissue mechanics, even when the reference configuration is defined by a honeycomb lattice. The paper concludes with a discussion of the implications of these results for concurrent discrete/continuous modelling, adaptation of atom-to-continuum (AtC) techniques to biological tissues and model classification

Validity of the Cauchy-Born rule applied to discrete cellular-scale models of biological tissues.

The development of new models of biological tissues that consider cells in a discrete manner is becoming increasingly popular as an alternative to continuum methods based on partial differential equations, although formal relationships between the discrete and continuum frameworks remain to be established. For crystal mechanics, the discrete-to-continuum bridge is often made by assuming that local atom displacements can be mapped homogeneously from the mesoscale deformation gradient, an assumption known as the Cauchy-Born rule (CBR). Although the CBR does not hold exactly for noncrystalline materials, it may still be used as a first-order approximation for analytic calculations of effective stresses or strain energies. In this work, our goal is to investigate numerically the applicability of the CBR to two-dimensional cellular-scale models by assessing the mechanical behavior of model biological tissues, including crystalline (honeycomb) and noncrystalline reference states. The numerical procedure involves applying an affine deformation to the boundary cells and computing the quasistatic position of internal cells. The position of internal cells is then compared with the prediction of the CBR and an average deviation is calculated in the strain domain. For center-based cell models, we show that the CBR holds exactly when the deformation gradient is relatively small and the reference stress-free configuration is defined by a honeycomb lattice. We show further that the CBR may be used approximately when the reference state is perturbed from the honeycomb configuration. By contrast, for vertex-based cell models, a similar analysis reveals that the CBR does not provide a good representation of the tissue mechanics, even when the reference configuration is defined by a honeycomb lattice. The paper concludes with a discussion of the implications of these results for concurrent discrete and continuous modeling, adaptation of atom-to-continuum techniques to biological tissues, and model classification

Aerospace Medicine and Biology: A continuing bibliography (supplement 229)

This bibliography lists 109 reports, articles, and other documents introduced into the NASA scientific and technical information system in January 1982

MULTI-LENGTH SCALE MODELING OF THE HIGH-PRESSURE, LARGE-STRAIN, HIGH-STRAIN-RATE RESPONSE OF SODA-LIME GLASS

Development of new transparent armor systems is essential for the protection of the current and future US armed forces, especially in light of the recent military operations The Operation Iraqi Freedom in Iraq and The Operation Enduring Freedom in Afghanistan. These conflicts have introduced a new military theater without a well-defined battle front and new types of threats (e.g. improvised explosive devices, IEDs). Development and modeling of new transparent armor systems for use in numerous applications from vehicle windows to face shields is a current area of thrust aimed at addressing the shortcomings of existing systems in order to better protect US soldiers and align with the military\u27s goal of becoming more mobile, deployable, and sustainable. This dissertation is focused predominately on the computational modeling of transparent armor materials and structures. Glass remains the dominant constituent in many modern transparent armor systems for a number of performance and manufacturing related reasons and thus is the material of focus in the present work. The present work is concerned with the development and further enhancement of a continuum-level, physically-based, high strain-rate, large-strain, high-pressure mechanical material model for soda-lime (and borosilicate) glass. The model is being developed in attempt to capture the complex stochastic, pre-existing flaw-controlled damage nature of glass under blast and impact conditions and do so in a computationally efficient manner. Numerous finite element simulations were carried out using the computational code ABAQUS/Explicit to assess the utility of the model under physically realistic ballistic loading conditions, including multi-hit impact scenarios. Further enhancements of the glass material model are made with the inclusion of the following: (i) differentiation of the mechanical properties of the so-called air-side and tin-side of glass plates manufactured using the float glass process; and (ii) a damage tensor to produce an orthotropic macro-cracked material. In addition a multi-length scale modeling approach for glass is taken to elucidate phenomena at different length scales (e.g. glass irreversible densification, shock response, etc.) with the ultimate objective of enhancing the efficacy of the current continuum-level material model. The irreversible densification of glass under ballistic (shock) loading conditions is investigated at multiple length scales (atomistic-level and continuum-level) in order to understand its effect on the ballistic penetration resistance of glass. The findings related to the material shock response and irreversible densification of glass were subsequently included in the continuum-level glass material model equation of state to further increase its efficacy. The results from the various test scenarios and modifications to the continuum-level glass material models reveal that: (a) transient non-linear dynamics computational analyses, when utilizing the glass material model, have demonstrated to be a useful tool in understanding the multi-hit ballistic-protection performance of laminated glass/polycarbonate transparent armor systems. The loss of the ballistic-protection performance of the armor caused by a sequence of closely spaced bullet impacts has been observed and the results of these analyses are validated against their experimental counterparts; (b) while it was expected (based on quasi-static mechanical testing result) that orienting the borofloat tin-side as a three-layer laminate strike face would enhance its ballistic protection performance, experimental findings did not support this conjecture. Computational simulations of the laminate impact established the capability of the borosilicate glass material model to capture the prominent experimentally observed damage modes and the measured V50, reconfirming the experimental findings; and (c) a 2-4% (shock strength-dependent) irreversible density increase in glass is capture computationally at multiple lengths scales. Subsequent modifications of the continuum-level material model for glass to include the effect of irreversible-densification resulted in minor improvements in the ballistic-penetration resistance of glass and only for high projectile initial velocities

Shear-promoted drug encapsulation into red blood cells: a CFD model and μ-PIV analysis

The present work focuses on the main parameters that influence shear-promoted encapsulation of drugs into erythrocytes. A CFD model was built to investigate the fluid dynamics of a suspension of particles flowing in a commercial micro channel. Micro Particle Image Velocimetry (μ-PIV) allowed to take into account for the real properties of the red blood cell (RBC), thus having a deeper understanding of the process. Coupling these results with an analytical diffusion model, suitable working conditions were defined for different values of haematocrit

1992 NASA/ASEE Summer Faculty Fellowship Program

For the 28th consecutive year, a NASA/ASEE Summer Faculty Fellowship Program was conducted at the Marshall Space Flight Center (MSFC). The program was conducted by the University of Alabama and MSFC during the period June 1, 1992 through August 7, 1992. Operated under the auspices of the American Society for Engineering Education, the MSFC program, was well as those at other centers, was sponsored by the Office of Educational Affairs, NASA Headquarters, Washington, DC. The basic objectives of the programs, which are the 29th year of operation nationally, are (1) to further the professional knowledge of qualified engineering and science faculty members; (2) to stimulate and exchange ideas between participants and NASA; (3) to enrich and refresh the research and teaching activities of the participants' institutions; and (4) to contribute to the research objectives of the NASA centers