Accelerated Cardiac Diffusion Tensor Imaging Using Joint Low-Rank and Sparsity Constraints

Objective: The purpose of this manuscript is to accelerate cardiac diffusion tensor imaging (CDTI) by integrating low-rankness and compressed sensing. Methods: Diffusion-weighted images exhibit both transform sparsity and low-rankness. These properties can jointly be exploited to accelerate CDTI, especially when a phase map is applied to correct for the phase inconsistency across diffusion directions, thereby enhancing low-rankness. The proposed method is evaluated both ex vivo and in vivo, and is compared to methods using either a low-rank or sparsity constraint alone. Results: Compared to using a low-rank or sparsity constraint alone, the proposed method preserves more accurate helix angle features, the transmural continuum across the myocardium wall, and mean diffusivity at higher acceleration, while yielding significantly lower bias and higher intraclass correlation coefficient. Conclusion: Low-rankness and compressed sensing together facilitate acceleration for both ex vivo and in vivo CDTI, improving reconstruction accuracy compared to employing either constraint alone. Significance: Compared to previous methods for accelerating CDTI, the proposed method has the potential to reach higher acceleration while preserving myofiber architecture features which may allow more spatial coverage, higher spatial resolution and shorter temporal footprint in the future.Comment: 11 pages, 16 figures, published on IEEE Transactions on Biomedical Engineerin

Flux cost functions and the choice of metabolic fluxes

Metabolic fluxes in cells are governed by physical, biochemical, physiological, and economic principles. Cells may show "economical" behaviour, trading metabolic performance against the costly side-effects of high enzyme or metabolite concentrations. Some constraint-based flux prediction methods score fluxes by heuristic flux costs as proxies of enzyme investments. However, linear cost functions ignore enzyme kinetics and the tight coupling between fluxes, metabolite levels and enzyme levels. To derive more realistic cost functions, I define an apparent "enzymatic flux cost" as the minimal enzyme cost at which the fluxes can be realised in a given kinetic model, and a "kinetic flux cost", which includes metabolite cost. I discuss the mathematical properties of such flux cost functions, their usage for flux prediction, and their importance for cells' metabolic strategies. The enzymatic flux cost scales linearly with the fluxes and is a concave function on the flux polytope. The costs of two flows are usually not additive, due to an additional "compromise cost". Between flux polytopes, where fluxes change their directions, the enzymatic cost shows a jump. With strictly concave flux cost functions, cells can reduce their enzymatic cost by running different fluxes in different cell compartments or at different moments in time. The enzymactic flux cost can be translated into an approximated cell growth rate, a convex function on the flux polytope. Growth-maximising metabolic states can be predicted by Flux Cost Minimisation (FCM), a variant of FBA based on general flux cost functions. The solutions are flux distributions in corners of the flux polytope, i.e. typically elementary flux modes. Enzymatic flux costs can be linearly or nonlinearly approximated, providing model parameters for linear FBA based on kinetic parameters and extracellular concentrations, and justified by a kinetic model

Adapting the interior point method for the solution of LPs on serial, coarse grain parallel and massively parallel computers

In this paper we describe a unified scheme for implementing an interior point algorithm (IPM) over a range of computer architectures. In the inner iteration of the IPM a search direction is computed using Newton's method. Computationally this involves solving a sparse symmetric positive definite (SSPD) system of equations. The choice of direct and indirect methods for the solution of this system, and the design of data structures to take advantage of serial, coarse grain parallel and massively parallel computer architectures, are considered in detail. We put forward arguments as to why integration of the system within a sparse simplex solver is important and outline how the system is designed to achieve this integration