Numerical accuracy of floating point computation is a well studied topic which has not made its way to the end-user in scientific computing. Yet, it has become a critical issue with the recent requirements for code modernization to harness new highly parallel hardware and perform higher resolution computation. To democratize numerical accuracy analysis, it is important to propose tools and methodologies to study large use cases in a reliable and automatic way. In this paper, we propose verificarlo, an extension to the LLVM compiler to automatically use Monte Carlo Arithmetic in a transparent way for the end-user. It supports all the major languages including C, C++, and Fortran. Unlike source-tosource approaches, our implementation captures the influence of compiler optimizations on the numerical accuracy. We illustrate how Monte Carlo Arithmetic using the verificarlo tool outperforms the existing approaches on various use cases and is a step toward automatic numerical analysis.

With an increase in awareness regarding a troubling lack of reproducibility in analytical software tools, the degree of validity in scientific derivatives and their downstream results has become unclear. The nature of reproducibility issues may vary across domains, tools, data sets, and computational infrastructures, but numerical instabilities are thought to be a core contributor. In neuroimaging, unexpected deviations have been observed when varying operating systems, software implementations, or adding negligible quantities of noise. In the field of numerical analysis, these issues have recently been explored through Monte Carlo Arithmetic, a method involving the instrumentation of floating-point operations with probabilistic noise injections at a target precision. Exploring multiple simulations in this context allows the characterization of the result space for a given tool or operation. In this article, we compare various perturbation models to introduce instabilities within a typical neuroimaging pipeline, including (i) targeted noise, (ii) Monte Carlo Arithmetic, and (iii) operating system variation, to identify the significance and quality of their impact on the resulting derivatives. We demonstrate that even low-order models in neuroimaging such as the structural connectome estimation pipeline evaluated here are sensitive to numerical instabilities, suggesting that stability is a relevant axis upon which tools are compared, alongside more traditional criteria such as biological feasibility, computational efficiency, or, when possible, accuracy. Heterogeneity was observed across participants which clearly illustrates a strong interaction between the tool and data set being processed, requiring that the stability of a given tool be evaluated with respect to a given cohort. We identify use cases for each perturbation method tested, including quality assurance, pipeline error detection, and local sensitivity analysis, and make recommendations for the evaluation of stability in a practical and analytically focused setting. Identifying how these relationships and recommendations scale to higher order computational tools, distinct data sets, and their implication on biological feasibility remain exciting avenues for future work.

• MRI assessment of CSF volume is feasible in healthy volunteers/hydrocephalus patients. • CSF volume can be obtained on a whole-body scale. • The ratio of subarachnoid and ventricular CSF is constant in healthy volunteers. • CSF linear discriminant analysis can distinguish between patients and healthy volunteers. • Entire CSF volume imaging is useful for diagnosing and following hydrocephalus.

In this paper we analyze volumes of the cerebrospinal fluid spaces for the diagnosis of hydrocephalus, which are served as reference values for future studies. We first present an automatic method to estimate those volumes from a new three-dimensional whole body magnetic resonance imaging sequence. This enables us to statistically analyze the fluid volumes, and to show that the ratio of subarachnoid volume to ventricular one is a proportionality constant for healthy adults (= 10.73), while in range [0.63, 4.61] for hydrocephalus patients. This indicates that a robust distinction between pathological and healthy cases can be achieved by using this ratio as an index.

The assessment of CSF spaces volume and distribution may help to characterise hydrocephalus.