Smoothed particle hydrodynamics simulation of biphasic soft tissue and its medical applications.

Modeling the coupled fluid and elastic mechanics of blood perfused soft tissues is important for medical applications. In particular, the current study aims to capture the effect of tissue swelling and the transport of blood through damaged tissue under bleeding or hemorrhaging conditions. The soft tissue is considered a dynamic poro-hyperelastic material with blood-filled voids. A biphasic formulation-effectively, a generalization of Darcy's law-is utilized, treating the phases as occupying fractions of the same volume. A Stokes-like friction force and a pressure that penalizes deviations from volume fractions summing to unity serve as the interaction force between solid and liquid phases. The resulting equations for both phases are discretized with the method of smoothed particle hydrodynamics (SPH). The solver is validated separately on each phase and demonstrates good agreement with exact solutions in test problems. Simulations of oozing, hysteresis, swelling, drying and shrinkage, and tissue fracturing and hemorrhage are shown in the paper. Graphical Abstract In the paper, a new methodology for the numerical simulation of the full dynamic response of blood-perfused soft tissues was developed.

A simplified computational model of possible hydrodynamic interactions between respiratory and swimming-related water flows in labriform-swimming fishes.

Hydrodynamic interactions in bony fishes between respiratory fluid flows leaving the opercular openings and simultaneous flows generated by movements of downstream pectoral fins are both poorly understood and likely to be complex. Labriform-swimming fishes that swim primarily by moving only their pectoral fins are good subjects for these studies. We performed a computational fluid dynamics investigation of a simplified 2D model of these interactions based on previously published experimental observations of both respiratory and pectoral fin movements under both resting and slow, steady swimming conditions in two similar labriform swimmers: the bluegill sunfish (L. macrochirus) and the largemouth bass (M. salmoides). We carried out a parametric study investigating the effects that swimming speed, strength of opercular flow and phase difference between the pectoral fin motion and the opercular opening and closing have on the thrust and sideslip forces generated by the pectoral fins during both the abduction and adduction portions of the fin movement cycle. We analyzed pressure distributions on the fin surface to determine physical differences in flows with and without opercular jets. The modeling indicates that complex flow structures emerge from the coupling between the opercular jets and vortex shedding from pectoral fins. The jets from the opercular openings appear to exert significant influence on the forces generated by the fins; they are potentially significant in the maneuverability of at least some labriform swimmers. The numerical simulations and the analysis establish a framework for the study of these interactions in various labriform swimmers in a variety of flow regimes. Similar situations in groups of fishes using other swimming modes should also be investigated.

Model of Left Ventricular Contraction: Validation Criteria and Boundary Conditions.

Computational models of cardiac contraction can provide critical insight into cardiac function and dysfunction. A necessary step before employing these computational models is their validation. Here we propose a series of validation criteria based on left ventricular (LV) global (ejection fraction and twist) and local (strains in a cylindrical coordinate system, aggregate cardiomyocyte shortening, and low myocardial compressibility) MRI measures to characterize LV motion and deformation during contraction. These validation criteria are used to evaluate an LV finite element model built from subject-specific anatomy and aggregate cardiomyocyte orientations reconstructed from diffusion tensor MRI. We emphasize the key role of the simulation boundary conditions in approaching the physiologically correct motion and strains during contraction. We conclude by comparing the global and local validation criteria measures obtained using two different boundary conditions: the first constraining the LV base and the second taking into account the presence of the pericardium, which leads to greatly improved motion and deformation.

Characterization of perfused and sectioned liver tissue in a full indentation cycle using a visco-hyperelastic model.

Realistic modeling of biologic material is required for optimizing fidelity in computer-aided surgical training and assistance systems. The modeling of liver tissue has remained challenging due to its nonlinear viscoelastic properties and high hysteresis of the stress-strain relation. While prior studies have described the behavior of liver tissue during the loading status (in elongation, compression, or indentation tests) or unloading status (in stress relaxation or creep tests), a hysteresis curve with both loading and unloading processes was incompletely defined. We seek to use a single material model to characterize the mechanical properties of liver tissue in a full indentation cycle ex vivo perfused and then sectioned. Based on measurements taken from ex-vivo perfused porcine livers, we converted force-displacement curves to stress-strain curves and developed a visco-hyperelastic constitutive model to characterize the liver's mechanical behavior at different locations under various rates of indentation (1, 2, 5, 10, and 20 mm/s). The proposed model is a mixed visco-hyperelastic model with up to 6 coefficients. The normalized root mean square standard deviations of fitted curves are less than 5% and 10% in low (<0.05) and high strain (>0.3) conditions respectively.

A regulated multiscale closed-loop cardiovascular model, with applications to hemorrhage and hypertension.

A computational tool is developed for simulating the dynamic response of the human cardiovascular system to various stressors and injuries. The tool couples 0-dimensional models of the heart, pulmonary vasculature, and peripheral vasculature to 1-dimensional models of the major systemic arteries. To simulate autonomic response, this multiscale circulatory model is integrated with a feedback model of the baroreflex, allowing control of heart rate, cardiac contractility, and peripheral impedance. The performance of the tool is demonstrated in 2 scenarios: neurogenic hypertension by sustained stimulation of the sympathetic nervous system and an acute 10% hemorrhage from the left femoral artery.

Visualization of vascular injuries in extremity trauma.

A tandem of particle-based computational methods is adapted to simulate injury and hemorrhage in the human body. In order to ensure anatomical fidelity, a three-dimensional model of a targeted portion of the human body is reconstructed from a dense sequence of CT scans of an anonymized patient. Skin, bone and muscular tissue are distinguished in the imaging data and assigned with their respective material properties. An injury geometry is then generated by simulating the mechanics of a ballistic projectile passing through the anatomical model with the material point method. From the injured vascular segments identified in the resulting geometry, smoothed particle hydrodynamics (SPH) is employed to simulate bleeding, based on inflow boundary conditions obtained from a network model of the systemic arterial tree. Computational blood particles interact with the stationary particles representing impermeable bone and skin and permeable muscular tissue through the Brinkman equations for porous media. The SPH results are rendered in post-processing for improved visual fidelity. The overall simulation strategy is demonstrated on an injury scenario in the lower leg.

Current Methods and Advances in Simulation of Hemorrhage after Trauma.

As animal models fall out of favor, there is demand for simulators to train medical personnel in the management of trauma and hemorrhage. Realism is essential to the development of simulators for training in the management of trauma and hemorrhage, but is difficult to achieve because it is difficult to create models that accurately represent bleeding organs. We present a simulation platform that uses real-time mathematical modeling of hemodynamics after hemorrhage and trauma and visually represents the injury described by the model. Using patient-specific imaging, 3D-mesh representations of the liver were created and merged with an anatomically accurate vascular tree. By using anatomically accurate representations of the vasculature, we were able to model the cardiovascular response to hemorrhage in a specific artery. The incorporation of autonomic tone allowed for the calculation of bleeding rate and aortic pressures. The 3D-mesh representation of the liver allowed us to simulate blood flow from the liver after trauma. For the first time, we have successfully incorporated tissue modeling and fluid dynamics with a model of the cardiovascular system to create a simulator. These simulations may aid in the creation of realistic virtual environments for training.

Theoretical and experimental study of the dynamic response of absorber-based, micro-scale, oscillatory probes for contact sensing applications.

This paper presents two models for predicting the frequency response of micro-scale oscillatory probes. These probes are manufactured by attaching a thin fiber to the free end of one tine of a quartz tuning fork oscillator. In these studies, the attached fibers were either 75 µm diameter tungsten or 7 µm diameter carbon with lengths ranging from around 1 to 15 mm. The oscillators used in these studies were commercial 32.7 kHz quartz tuning forks. The first theoretical model considers lateral vibration of two beams serially connected and provides a characteristic equation from which the roots (eigenvalues) are extracted to determine the natural frequencies of the probe. A second, lumped model approximation is used to derive an approximate frequency response function for prediction of tine displacements as a function of a modal force excitation corresponding to the first mode of the tine in the absence of a fiber. These models are used to evaluate the effect of changes in both length and diameter of the attached fibers. Theoretical values of the natural frequencies of different modes show an asymptotic relationship with the length and a linear relationship with the diameter of the attached fiber. Similar results are observed from experiment, one with a tungsten probe having an initial fiber length of 14.11 mm incrementally etched down to 0.83 mm, and another tungsten probe of length 8.16 mm incrementally etched in diameter, in both cases using chronocoulometry to determine incremental volumetric material removal. The lumped model is used to provide a frequency response again reveals poles and zeros that are consistent with experimental measurements. Finite element analysis shows mode shapes similar to experimental microscope observations of the resonating carbon probes. This model provides a means of interpreting measured responses in terms of the relative motion of the tine and attached fibers. Of particular relevance is that, when a "zero" is observed in the response of the tine, one mode of the fiber is matched to the tine frequency and is acting as an absorber. This represents an optimal condition for contact sensing and for transferring energy to the fiber for fluid mixing, touch sensing, and surface modification applications.

GPU-Based Parallelized Solver for Large Scale Vascular Blood Flow Modeling and Simulations.

Cardio-vascular blood flow simulations are essential in understanding the blood flow behavior during normal and disease conditions. To date, such blood flow simulations have only been done at a macro scale level due to computational limitations. In this paper, we present a GPU based large scale solver that enables modeling the flow even in the smallest arteries. A mechanical equivalent of the circuit based flow modeling system is first developed to employ the GPU computing framework. Numerical studies were employed using a set of 10 million connected vascular elements. Run-time flow analysis were performed to simulate vascular blockages, as well as arterial cut-off. Our results showed that we can achieve ~100 FPS using a GTX 680m and ~40 FPS using a Tegra K1 computing platform.

Transport of inertial particles by viscous streaming in arrays of oscillating probes.

A mechanism for the transport of microscale particles in viscous fluids is demonstrated. The mechanism exploits the trapping of such particles by rotational streaming cells established in the vicinity of an oscillating cylinder, recently analyzed in previous work. The present work explores a strategy of transporting particles between the trapping points established by multiple cylinders undergoing oscillations in sequential intervals. It is demonstrated that, by controlling the sequence of oscillation intervals, an inertial particle is effectively and predictably transported between the stable trapping points. Arrays of cylinders in various arrangements are investigated, revealing a technique for constructing arbitrary particle trajectories. It is found that the domain from which particles can be transported and trapped by an oscillator is extended, even to regions in which particles are shielded, by the presence of other stationary cylinders. The timescales for transport are examined, as are the mechanisms by which particles are drawn away from an obstacle toward the trapping point of an oscillator.

Evaluation of the Upper Airway Morphology: The Role of Cone Beam Computed Tomography.

Cone beam computed tomography (CBCT) has several applications in dentomaxillofacial diagnosis. Frequently, the imaged volume encompasses the upper airway. This article provides a systematic approach to airway analysis and the implications of the anatomic and pathologic alterations. It discusses the role of CBCT in management of obstructive sleep apnea (OSA) patients. This paper also highlights technological advances that combine CBCT imaging with computational modeling of the airway and the potential clinical applications of such technologies.

Cardiovascular blood flow analysis under normal and open injury conditions.

The aim of this paper is to enable a simulation tool for cardiovascular blood flow in order to better understand normal and hemorrhage conditions. A second order partial differential model for cardiovascular blood flow is employed. The individual components of the model is represented as an RLC circuit representation. Injury behavior is simulated by varying the circuit system parameters for the section representing different arterial levels. Our results show that significant changes in the blood flow inside the cardiovascular system can be observed when different injury conditions are modeled.

A computational study of the flow through a vitreous cutter.

Vitrectomy is an ophthalmic microsurgical procedure that removes part or all of the vitreous humor from the eye. The procedure uses a vitreous cutter consisting of a narrow shaft with a small orifice at the end through which the humor is aspirated by an applied suction. An internal guillotine oscillates back and forth across the orifice to alter the local shear response of the humor. In this work, a computational study of the flow in a vitreous cutter is conducted in order to gain better understanding of the vitreous behavior and provide guidelines for a new vitreous cutter design. The flow of a Newtonian surrogate of vitreous in a two-dimensional analog geometry is investigated using a finite difference-based immersed boundary method with an algebraically formulated fractional-step method. A series of numerical experiments is performed to evaluate the impact of cutting rate, aspiration pressure, and opening/closing transition on the vitreous cutter flow rate and transorifice pressure variation during vitrectomy. The mean flow rate is observed to increase approximately linearly with aspiration pressure and also increase nearly linearly with duty cycle. A study of time-varying flow rate, velocity field, and vorticity illuminates the flow behavior during each phase of the cutting cycle and shows that the opening/closing transition plays a key role in improving the vitreous cutter's efficacy and minimizing the potential damage to surrounding tissue. The numerical results show similar trend in flow rate as previous in vitro experiments using water and balanced saline solution and also demonstrate that high duty cycle and slow opening/closing phases lead to high flow rate and minor disturbance to the eye during vitrectomy, which are the design requirements of an ideal vitreous cutter.

Fluid transport and coherent structures of translating and flapping wings.

The Lagrangian coherent structures (LCSs) of simple wing cross sections in various low Reynolds number motions are extracted from high-fidelity numerical simulation data and examined in detail. The entrainment process in the wake of a translating ellipse is revealed by studying the relationship between attracting structures in the wake and upstream repelling structures, with the help of blocks of tracer particles. It is shown that a series of slender lobes in the repelling LCS project upstream from the front of the ellipse and "pull" fluid into the wake. Each lobe is paired with a corresponding wake vortex, into which the constituent fluid particles are folded. Flexible and rigid foils in flapping motion are studied, and the resulting differences in coherent structures are used to elucidate their differences in force generation. The clarity with which these flow structures are revealed, compared to the vorticity or velocity fields, provides new insight into the vortex shedding mechanisms that play an important role in unsteady aerodynamics.

Lagrangian coherent structures in low Reynolds number swimming.

This work explores the utility of the finite-time Lyapunov exponent (FTLE) field for revealing flow structures in low Reynolds number biological locomotion. Previous studies of high Reynolds number unsteady flows have demonstrated that ridges of the FTLE field coincide with transport barriers within the flow, which are not shown by a more classical quantity such as vorticity. In low Reynolds number locomotion (O(1)-O(100)), in which viscous diffusion rapidly smears the vorticity in the wake, the FTLE field has the potential to add new insight to locomotion mechanics. The target of study is an articulated two-dimensional model for jellyfish-like locomotion, with swimming Reynolds number of order 1. The self-propulsion of the model is numerically simulated with a viscous vortex particle method, using kinematics adapted from previous experimental measurements on a live medusan swimmer. The roles of the ridges of the computed forward- and backward-time FTLE fields are clarified by tracking clusters of particles both backward and forward in time. It is shown that a series of ridges in front of the jellyfish in the forward-time FTLE field transport slender fingers of fluid toward the lip of the bell orifice, which are pulled once per contraction cycle into the wake of the jellyfish, where the fluid remains partitioned. A strong ridge in the backward-time FTLE field reveals a persistent barrier between fluid inside and outside the subumbrellar cavity. The system is also analyzed in a body-fixed frame subject to a steady free stream, and the FTLE field is used to highlight differences in these frames of reference.

Numerical simulations of undulatory swimming at moderate Reynolds number.

We perform numerical simulations of the swimming of a three-linkage articulated system in a moderately viscous regime. The computational methodology focuses on the creation, diffusion and transport of vorticity from the surface of the bodies into the fluid. The simulations are dynamically coupled, in that the motion of the three-linkage swimmer is computed simultaneously with the dynamics of the fluid. The novel coupling scheme presented in this work is the first to exploit the relationship between vorticity creation and body dynamics. The locomotion of the system, when subject to undulatory inputs of the hinges, is computed at Reynolds numbers of 200 and 1000. It is found that the forward swimming speed increases with the Reynolds number, and that in both cases the swimming is slower than in an inviscid medium. The vortex shedding is examined, and found to exhibit behavior consistent with experimental flow visualizations of fish.