An in silico validation framework for quantitative DCE-MRI techniques based on a dynamic digital phantom.

Quantitative evaluation of an image processing method to perform as designed is central to both its utility and its ability to guide the data acquisition process. Unfortunately, these tasks can be quite challenging due to the difficulty of experimentally obtaining the "ground truth" data to which the output of a given processing method must be compared. One way to address this issue is via "digital phantoms", which are numerical models that provide known biophysical properties of a particular object of interest.  In this contribution, we propose an in silico validation framework for dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) acquisition and analysis methods that employs a novel dynamic digital phantom. The phantom provides a spatiotemporally-resolved representation of blood-interstitial flow and contrast agent delivery, where the former is solved by a 1D-3D coupled computational fluid dynamic system, and the latter described by an advection-diffusion equation. Furthermore, we establish a virtual simulator which takes as input the digital phantom, and produces realistic DCE-MRI data with controllable acquisition parameters. We assess the performance of a simulated standard-of-care acquisition (Protocol A) by its ability to generate contrast-enhanced MR images that separate vasculature from surrounding tissue, as measured by the contrast-to-noise ratio (CNR). We find that the CNR significantly decreases as the spatial resolution (SRA, where the subscript indicates Protocol A) or signal-to-noise ratio (SNRA) decreases. Specifically, with an SNRA / SRA = 75 dB / 30 µm, the median CNR is 77.30, whereas an SNRA / SRA = 5 dB / 300 µm reduces the CNR to 6.40. Additionally, we assess the performance of simulated ultra-fast acquisition (Protocol B) by its ability to generate DCE-MR images that capture contrast agent pharmacokinetics, as measured by error in the signal-enhancement ratio (SER) compared to ground truth (PESER). We find that PESER significantly decreases the as temporal resolution (TRB) increases. Similar results are reported for the effects of spatial resolution and signal-to-noise ratio on PESER. For example, with an SNRB / SRB / TRB = 5 dB / 300 µm / 10 s, the median PESER is 21.00%, whereas an SNRB / SRB / TRB = 75 dB / 60 µm / 1 s, yields a median PESER of 0.90%. These results indicate that our in silico framework can generate virtual MR images that capture effects of acquisition parameters on the ability of generated images to capture morphological or pharmacokinetic features. This validation framework is not only useful for investigations of perfusion-based MRI techniques, but also for the systematic evaluation and optimization new MRI acquisition, reconstruction, and image processing techniques.

A Highly-Efficient Implementation of the Doktorov Recurrence Equations for Franck-Condon Calculations.

In this paper, a new algorithm for computing Franck-Condon overlaps using the Doktorov recurrence equations is proposed. One of the major computational stresses of using the recurrence equations arises from searching data structures for overlaps that are stored in memory. The proposed algorithm alleviates this problem by tracking, throughout the algorithm, the locations in memory of overlaps that are required to use the recurrence relations. The tracking procedure helps to significantly reduce the run time of the algorithm compared to existing implementations.

Parallelization strategy for large-scale vibronic coupling calculations.

The vibronic coupling model of Köppel, Domcke, and Cederbaum is a powerful means to understand, predict, and analyze electronic spectra of molecules, especially those that exhibit phenomena that involve breakdown of the Born-Oppenheimer approximation. In this work, we describe a new parallel algorithm for carrying out such calculations. The algorithm is conceptually founded upon a "stencil" representation of the required computational steps, which motivates an efficient strategy for coarse-grained parallelization. The equations involved in the direct-CI type diagonalization of the model Hamiltonian are presented, the parallelization strategy is discussed in detail, and the method is illustrated by calculations involving direct-product basis sets with as many as 17 vibrational modes and 130 billion basis functions.