These symposia explore the interface between macroscale function and microscale physiology with the perspective from the macroscale to the microscale. This theme includes the modulation and control of macroscale whole-organ-level function from its interactions with microscale muscle and neurophysiological processes, and the corresponding diseases associated with disruption between the micro and micro scale dynamics. It also includes systems level function from the integration of multiple microscale components. Modeling is from the macroscale to the microscale: macroscale function from microscale physiology. Modeling complexity involves both numerical and mathematical issues, and often the modeling integrates with data from imaging modalities.

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ABSTRACTS

• Trent Guess: Multiscale Simulation of the Musculoskeletal System using Surrogate Models of Tissue Behavior

Trent Guess(1), Mohammad Kia(1), Reza Derakhshani(2), Ganesh Thiagarajan(1)

(1) Department of Civil and Mechanical Engineering and (2) Department of Electrical Engineering, University of Missouri-Kansas City

The primary tools of computational biomechanics include multi-body dynamics at the body level and finite element methods at the organ level. The multi-body technique lacks the complexity to accurately capture tissue behavior and finite element models are typically too computationally intensive for body level simulations. Presented here is the use of computationally efficient surrogate models of tissue within a multi-body framework. The input-output relations of the surrogate models are derived from finite element solutions.

• Anil Misra: Microstructure and Composition Based Constitutive Relationships for Meniscus/Cartilage

Anil Misra (1), Viraj Sing (1), Trent Guess (2)

(1) Department of Civil, Environmental and Architectural Engineering, University of Kansas

(2) Department of Civil and Mechanical Engineering, University of Missouri-Kansas City

Objectives: To develop stress-strain relationship for modelling the deformation behavior of soft tissues, such as knee meniscus and cartilage, based upon their microstructure and composition. Methods: The knee meniscus and cartilage is considered to be composed of hydrated collagen fiber network, hydrated proteoglycan (PG) gel and free water. Consequently, we seek constitutive relationships of the type used in fluid saturated porous medium. The effective stress in this poroelastic constitutive law is obtained from a simple volume average of the stress on the non- fibrillar PG gel and the stress on the fibrillar network. The stress on the non- fibrillar PG gel is estimated using a modified neo-Hookean model. The stress tensor of the fibrillar network is obtained by considering the fiber orientations and fiber loading condition. The fiber network is considered to be under pre-tension that results from the swelling pressure caused by the PG gel hydration under a given ion concentration. At present, the pre-tension stress is estimated using the Donnan osmotic pressure model. Finally, we make the kinematic assumption that the strain in the non- fibrillar PG gel and the fibrillar network are the same. The resultant stress-strain relationship is used to perform parametric study of overall tissue behavior under various loading conditions. Using this approach we are able to obtain closed form expressions for overall stress-strain behavior under uniaxial compression and tension. For multiaxial loading cases, the stress-strain behaviors are evaluated numerically. Results: Stress-strain behavior under strain controlled uniaxial compression is found to be significantly affected by the fiber content, fiber network pre-tension and fiber stiffness. For large pre-tension, the overall behavior can show softening at intermediate strain-levels. For small pre-tension and fiber stiffness, the overall behavior is dominated by the non-fibrillar part.

• Dmitry Fedosov: Triple-Decker: Interfacing Atomistic-Mesoscopic-Continuum Flow Regimes in Biological Fluids

Dmitry A. Fedosov and George E. Karniadakis)

Division of Applied Mathematics, Brown University

Multiscale flow phenomena in microfluidic and biomedical applications require the use of heterogeneous modeling approaches. We present a hybrid method based on coupling the Molecular Dynamics (MD) method, the Dissipative Particle Dynamics (DPD) method, and the incompressible Navier-Stokes (NS) equations. MD, DPD, and NS are formulated in separate sub-domains and are coupled via an overlapping region by communicating state information at the sub-domain boundaries. Imposition of boundary conditions in the MD and DPD systems involves particle insertion and deletion, specular wall reflection and body force terms. The latter includes a boundary pressure force in order to minimize near-boundary density fluctuations, and an adaptive shear force which enforces the tangential velocity component of boundary conditions. The triple-decker algorithm is verified for prototype flows, including simple and multi-layer fluids (Couette, Poiseuille, and lid-driven cavity), using highly accurate reference solutions. A zero-thickness interface is also possible if it is aligned with the flow streamlines.

• Nicolas Smith:euHeartL: multi-scale computational models of the heart

University of Oxford, nic.smith@comlab.ox.ac.uk

Contraction of the heart is a fundamental whole organ phenomenon driven by cellular mechanisms. With each beat the myocytes in the heart generate tension and relax. This local cellular scale tension is transduced into a coordinated global whole heart deformation in a synchronous contraction resulting in an effective, organized and efficient system level pump function. This synchrony is achieved through the integrated effects of organ, tissue and cellular scale mechanisms. The importance of a synchronous contraction for cardiac pump function is well known, yet the role and relative importance of the underlying mechanisms responsible for achieving coordinated function remains unclear. In the healthy heart structural heterogeneities in the morphology, electrophysiology, metabolic and neural mechanisms provide a stable physiological framework that facilitates synchronous contraction. However, over shorter time scales, sub cellular mechanisms are the most likely candidates for regulating cardiac synchrony in the face of dynamic varying cardiac demand. Specifically, the sarcomeres themselves contain tension and deformation feedback (TDF) mechanisms that regulate the development of active tension based on the local tension, strain and strain rate. These provide a regulatory process to modulate deformation and tension signals experienced by the cell into a coordinated global response. To isolate and quantify the role of TDF in the synchronous contraction of the heart we have developed a multi-scale electromechanical model of the heart that incorporates the TDF mechanisms and fluid dynamics of the left ventricle. By comparing the synchrony of each phase of the heart beat in the absence of each of the TDF mechanisms we are able to quantify the effect of each of the TDF mechanisms on the synchrony of contraction and derive both the cell and tissue level mechanisms which are fundamental to efficient pump function.

• Gino Banco: Control of Macro-Scale Mixing and Transport in the Small Intestine: A Lattice-Boltzmann Model

Gino Banco (1), James G. Brasseur (1,2), Yanxing Wang (1), Amit Ailiani (2), Andrew G. Webb (2)

(1) Department of Mechanical Engineering and (2) Department of Bioengineering, Pennsylvania State University

The primary function of the small intestine is the absorption of nutrients through the epithelial surface into the blood stream. Two basic motility patterns are responsible for the transport: peristaltic contractions for axial transport, and repetitive segmental contractions of short sections of the gut for radial transport. We evaluate the relative contributions of peristaltic and segmental contractions to the absorption process using a two-dimensional model of flow and mixing of passive scalar using a lattice-Boltzmann model of small intestine motility with second-order moving boundary conditions for velocity and scalar. Mixes of segmental and peristaltic contractions are parameterized with magnetic resonance imaging (MRI) data from the rat intestine and nutrient uptake was quantified as surface scalar flux. We find that any level of peristaltic contribution degrades uptake, explaining radiologic observations where peristalsis is absent during the initial digestive period and appears only periodically later to transport chyme.

• Yanxing Wang: A Multiscale Lattice-Boltzmann Model of Macro-to-Micro Scale Couplings in the Small Intestine

Yanxing Wang (1), James G. Brasseur (1,2), Gino Banco (1), Andrew G. Webb (2), Amit Ailiani (2)

(1) Department of Mechanical Engineering and (2) Department of Bioengineering, Pennsylvania State University.

Nutrient and pharmaceutical absorption in the small intestine involve coupled multiscale transport and mixing processes that span several orders of magnitude. We have hypothesized that muscle-induced villi motions generate and control a "micro-mixing layer" that couples with macro-scale mixing to enhance molecular transport to and from the epithelium. To test this hypothesis, we developed a 2-D numerical method based on a multigrid strategy within the lattice-Boltzmann framework. Emphasis is placed on the treatment of moving boundaries with arbitrary curvatures for flow and scalar. We model a macro-scale cavity flow with microscale finger-like "villi" in pendular motion on the lower surface and evaluate the coupling between macro and micro-scale fluid motions, scalar mixing, and uptake of passive scalar at the villi surface. Results show that the moving villi can be effective mixers at the micro scale, especially when groups of villi move in a coordinated out-of-phase fashion. A time-evolving series of flow recirculation eddies are generated over the villi, which form a micro mixing layer. These eddies increase the transport of scalar from the macro eddy to the surface of villi by advection. Higher frequency of villi motions enhances scalar absorption. This enhancement of absorption is lower with smaller villous length.