Diffusion-based microstructure models in brain tumours: Fitting in presence of a model-microstructure mismatch

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We analyzed the performance of NODDI, SMT and DKI inside the tumoral lesion.

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Goodness of fit were comparable to normal tissue, for DKI and NODDI.

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Parameter precision was similar to normal tissues for all quantified metrics.

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Parameters should not be given their healthy physiological meaning in the tumour.

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The three models are usable as signal representations of the tumoral tissue.

Diffusion-based biophysical models have been used in several recent works to study the microenvironment of brain tumours. While the pathophysiological interpretation of the parameters of these models remains unclear, their use as signal representations may yield useful biomarkers for monitoring the treatment and the progression of this complex and heterogeneous disease. Up to now, however, no study was devoted to assessing the mathematical stability of these approaches in cancerous brain regions. To this end, we analyzed in 11 brain tumour patients the fitting results of two microstructure models (Neurite Orientation Dispersion and Density Imaging and the Spherical Mean Technique) and of a signal representation (Diffusion Kurtosis Imaging) to compare the reliability of their parameter estimates in the healthy brain and in the tumoral lesion. The framework of our between-tissue analysis included the computation of 1) the residual sum of squares as a goodness-of-fit measure 2) the standard deviation of the models’ derived metrics and 3) models’ sensitivity functions to analyze the suitability of the employed protocol for parameter estimation in the different microenvironments. Our results revealed no issues concerning the fitting of the models in the tumoral lesion, with similar goodness of fit and parameter precisions occurring in normal appearing and pathological tissues. Lastly, with the aim of highlight possible biomarkers, in our analysis we briefly discuss the correlation between the metrics of the three techniques, identifying groups of indices which are significantly collinear in all tissues and thus provide no additional information when jointly used in data-driven analyses.

Quantification of plasma cell dynamics using mathematical modelling

Plasma cells (PCs) are the main antibody-producing cells in humans. They are long-lived so that specific antibodies against either pathogens or vaccines are produced for decades. PC longevity is attributed to specific areas within the bone marrow micro-environment, the so-called 'niche', providing the cells with required growth and survival factors. With antigen encounters, e.g. infection or vaccination, new PCs are generated and home to the bone marrow where they compete with resident PCs for the niche. We propose a parametrized mathematical model describing healthy PC dynamics in the bone marrow. The model accounts for competition for the niche between newly produced PCs owing to vaccination and resident PCs. Mathematical analysis and numerical simulations of the model allow explanation of the recovery of PC homoeostasis after a vaccine-induced perturbation, and the fraction of vaccine-specific PCs inside the niche. The model enables quantification of the niche-related dynamics of PCs, i.e. the duration of PC transition into the niche and the impact of different rates for PC transitions into and out of the niche on the observed cell dynamics. Ultimately, it provides a potential basis for further investigations in health and disease.

Illustration of sampling-based methods for uncertainty and sensitivity analysis

A sequence of linear, monotonic, and nonmonotonic test problems is used to illustrate sampling-based uncertainty and sensitivity analysis procedures. Uncertainty results obtained with replicated random and Latin hypercube samples are compared, with the Latin hypercube samples tending to produce more stable results than the random samples. Sensitivity results obtained with the following procedures and/or measures are illustrated and compared: correlation coefficients (CCs), rank correlation coefficients (RCCs), common means (CMNs), common locations (CLs), common medians (CMDs), statistical independence (SI), standardized regression coefficients (SRCs), partial correlation coefficients (PCCs), standardized rank regression coefficients (SRRCs), partial rank correlation coefficients (PRCCs), stepwise regression analysis with raw and rank-transformed data, and examination of scatter plots. The effectiveness of a given procedure and/or measure depends on the characteristics of the individual test problems, with (1) linear measures (i.e., CCs, PCCs, SRCs) performing well on the linear test problems, (2) measures based on rank transforms (i.e., RCCs, PRCCs, SRRCs) performing well on the monotonic test problems, and (3) measures predicated on searches for nonrandom patterns (i.e., CMNs, CLs, CMDs, SI) performing well on the nonmonotonic test problems.