Ishani Roy

Verification of cardiac tissue electrophysiology simulators using an N-version benchmark

Ongoing developments in cardiac modelling have resulted, in particular, in the development of advanced and increasingly complex computational frameworks for simulating cardiac tissue electrophysiology. The goal of these simulations is often to represent the detailed physiology and pathologies of the heart using codes that exploit the computational potential of high-performance computing architectures. These developments have rapidly progressed the simulation capacity of cardiac virtual physiological human style models; however, they have also made it increasingly challenging to verify that a given code provides a faithful representation of the purported governing equations and corresponding solution techniques. This study provides the first cardiac tissue electrophysiology simulation benchmark to allow these codes to be verified. The benchmark was successfully evaluated on 11 simulation platforms to generate a consensus gold-standard converged solution. The benchmark definition in combination with the gold-standard solution can now be used to verify new simulation codes and numerical methods in the future.

An accurate, fast and robust method to generate patient-specific cubic Hermite meshes.

In-silico continuum simulations of organ and tissue scale physiology often require a discretisation or mesh of the solution domain. Cubic Hermite meshes provide a smooth representation of anatomy that is well-suited for simulating large deformation mechanics. Models of organ mechanics and deformation have demonstrated significant potential for clinical application. However, the production of a personalised mesh from patients anatomy using medical images remains a major bottleneck in simulation workflows. To address this issue, we have developed an accurate, fast and automatic method for deriving patient-specific cubic Hermite meshes. The proposed solution customises a predefined template with a fast binary image registration step and a novel cubic Hermite mesh warping constructed using a variational technique. Image registration is used to retrieve the mapping field between the template mesh and the patient images. The variational warping technique then finds a smooth and accurate projection of this field into the basis functions of the mesh. Applying this methodology, cubic Hermite meshes are fitted to the binary description of shape with sub-voxel accuracy and within a few minutes, which is a significant advance over the existing state of the art methods. To demonstrate its clinical utility, a generic cubic Hermite heart biventricular model is personalised to the anatomy of four patients, and the resulting mechanical stability of these customised meshes is successfully demonstrated.

Resonant Scattering and Lyα Radiation Emergent from Neutral Hydrogen Halos

With a state-of-the-art numerical method used for solving the integral-differential equation of radiative transfer, we investigate the flux of the Lyα photon ν0 emergent from an optically thick halo containing a central light source. Our focus is on the time-dependent effects of the resonant scattering. We first show that the frequency distribution of photons in the halo is quickly approaching a locally thermalized state around the resonant frequency, even when the mean intensity of the radiation is highly time dependent. Since initial conditions are forgotten during the thermalization, some features of the flux, such as the two-peak structure of its profile, are actually independent of the intrinsic width and time behavior of the central source, if the emergent photons are mainly from photons in the thermalized state. In this case, the difference |ν± – ν0|, where ν± are the frequencies of the two peaks of the flux, cannot be less than 2 times the Doppler broadening. We then study the radiative transfer in the case where the light emitted from the central source is a flash. We calculate the light curves of the flux from the halo. It shows that the flux is still a flash. The time duration of the flash for the flux, however, is independent of the original time duration of the light source but depends on the optical depth of the halo. Therefore, the spatial transfer of resonant photons is a diffusion process, even though it is not a purely Brownian diffusion. This property enables an optically thick halo to trap and store thermalized photons around ν0 for a long time after the cessation of the central source emission. The photons trapped in the halo can yield delayed emission, of which the profile also shows typical two-peak structure as that from locally thermalized photons. Possible applications of these results are addressed.

TIME EVOLUTION OF WOUTHUYSEN-FIELD COUPLING

We study the Wouthuysen-Field (W-F) coupling at early universe with numerical solutions of the integrodifferential equation describing the kinetics of photons undergoing resonant scattering. The numerical solver is developed based on the weighted essentially nonoscillatory (WENO) scheme for the Boltzmann-like integrodifferential equation. This method has perfectly passed the tests of the analytic solution and conservation property of the resonant scattering equation. We focus on the time evolution of the Wouthuysen-Field (W-F) coupling in relation to the 21 cm emission and absorption at the epoch of reionization. We especially pay attention to the formation of the local Boltzmann distribution, , of photon frequency spectrum around resonant frequency ν0 within width ν l , i.e., |ν – ν0| ≤ ν l . We show that a local Boltzmann distribution will be formed if photons with frequency ~ν0 have undergone a 10,000 or more times of scattering, which corresponds to the order of 103 yr for neutral hydrogen density of the concordance ΛCDM model. The time evolution of the shape and width of the local Boltzmann distribution actually do not depend on the details of atomic recoil, photon sources, or initial conditions very much. However, the intensity of photon flux at the local Boltzmann distribution is substantially time dependent. The timescale of approaching the saturated intensity can be as long as 105-106 yr for typical parameters of the ΛCDM model. The intensity of the local Boltzmann distribution at time less than 105 yr is significantly lower than that of the saturation state. Therefore, it may not be always reasonable to assume that the deviation of the spin temperature of 21 cm energy states from cosmic background temperature is mainly due to the W-F coupling if first stars or their emission/absorption regions evolved with a timescale equal to or less than Myr.

Toward GPGPU accelerated human electromechanical cardiac simulations

In this paper, we look at the acceleration of weakly coupled electromechanics using the graphics processing unit (GPU). Specifically, we port to the GPU a number of components of Heart—a CPU-based finite element code developed for simulating multi-physics problems. On the basis of a criterion of computational cost, we implemented on the GPU the ODE and PDE solution steps for the electrophysiology problem and the Jacobian and residual evaluation for the mechanics problem. Performance of the GPU implementation is then compared with single core CPU (SC) execution as well as multi-core CPU (MC) computations with equivalent theoretical performance. Results show that for a human scale left ventricle mesh, GPU acceleration of the electrophysiology problem provided speedups of 164 × compared with SC and 5.5 times compared with MC for the solution of the ODE model. Speedup of up to 72 × compared with SC and 2.6 × compared with MC was also observed for the PDE solve. Using the same human geometry, the GPU implementation of mechanics residual/Jacobian computation provided speedups of up to 44 × compared with SC and 2.0 × compared with MC.

THE ANGULAR DISTRIBUTION OF Lyα RESONANT PHOTONS EMERGING FROM AN OPTICALLY THICK MEDIUM

We investigate the angular distribution of Lyα photons scattering or emerging from an optically thick medium. Since the evolution of specific intensity I in frequency space and angular space are coupled with each other, we first develop the WENO numerical solver to find the time-dependent solutions of the integro-differential equation of I in frequency and angular space simultaneously. We first show that the solutions with the Eddington approximation, which assume that I is linearly dependent on the angular variable μ, yield similar frequency profiles of the photon flux as those without the Eddington approximation. However, the solutions of the μ distribution evolution are significantly different from those given by the Eddington approximation. First, the angular distribution of I is found to be substantially dependent on the frequency of the photons. For photons with the resonant frequency ν0, I contains only a linear term of μ. For photons with frequencies at the double peaks of the flux, the μ-distribution is highly anisotropic; most photons are emitted radially forward. Moreover, either at ν0 or at the double peaks, the μ distributions actually are independent of the initial μ distribution of photons of the source. This is because the photons with frequencies either at ν0 or the double peaks undergo the process of forgetting their initial conditions due to resonant scattering. We also show that the optically thick medium is a collimator of photons at the double peaks. Photons from the double peaks form a forward beam with a very small opening angle.