Discretization of continuous convolution operators for accurate modeling of wave propagation in digital holography.

Discretization of continuous (analog) convolution operators by direct sampling of the convolution kernel and use of fast Fourier transforms is highly efficient. However, it assumes the input and output signals are band-limited, a condition rarely met in practice, where signals have finite support or abrupt edges and sampling is nonideal. Here, we propose to approximate signals in analog, shift-invariant function spaces, which do not need to be band-limited, resulting in discrete coefficients for which we derive discrete convolution kernels that accurately model the analog convolution operator while taking into account nonideal sampling devices (such as finite fill-factor cameras). This approach retains the efficiency of direct sampling but not its limiting assumption. We propose fast forward and inverse algorithms that handle finite-length, periodic, and mirror-symmetric signals with rational sampling rates. We provide explicit convolution kernels for computing coherent wave propagation in the context of digital holography. When compared to band-limited methods in simulations, our method leads to fewer reconstruction artifacts when signals have sharp edges or when using nonideal sampling devices.

Developmental Alterations in Heart Biomechanics and Skeletal Muscle Function in Desmin Mutants Suggest an Early Pathological Root for Desminopathies.

Desminopathies belong to a family of muscle disorders called myofibrillar myopathies that are caused by Desmin mutations and lead to protein aggregates in muscle fibers. To date, the initial pathological steps of desminopathies and the impact of desmin aggregates in the genesis of the disease are unclear. Using live, high-resolution microscopy, we show that Desmin loss of function and Desmin aggregates promote skeletal muscle defects and alter heart biomechanics. In addition, we show that the calcium dynamics associated with heart contraction are impaired and are associated with sarcoplasmic reticulum dilatation as well as abnormal subcellular distribution of Ryanodine receptors. Our results demonstrate that desminopathies are associated with perturbed excitation-contraction coupling machinery and that aggregates are more detrimental than Desmin loss of function. Additionally, we show that pharmacological inhibition of aggregate formation and Desmin knockdown revert these phenotypes. Our data suggest alternative therapeutic approaches and further our understanding of the molecular determinants modulating Desmin aggregate formation.