Analysis of the distribution of the EDSS time series.

<p>A) Distribution of the time intervals between the clinical relapses. The distribution is derived from the experimental data of the EDSS time series (orange), simulations from the ODE model of T cell cross-regulation [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005757#pcbi.1005757.ref004" target="_blank">4</a>] (light blue) and the results from the GEV distribution model (red line). B-C) Examples of the analysis of the EDSS time-series in patients with MS. Incremental changes in EDSS over time in the experimental series for (B) PPMS and (C) SPMS. The onset of ΔEDSS is marked with an asterisk.</p

Dynamics of the clinical and pathogenic processes in MS.

<p>The upper panel shows the evolution of relapsing-remitting MS (RRMS) and its transition to secondary-progressive MS (SPMS), while the bottom panel shows the evolution of primary-progressive MS (PPMS). The autoimmune process starts in the peripheral immune system, inducing episodes of CNS inflammation (red line) that subsequently provokes demyelination (blue line) and then axon degeneration (dark green line). Although inflammation and demyelination may experience remissions, axon degeneration accumulates over time, as does chronic compartmentalized inflammation (orange line). If inflammatory infiltrates affect eloquent CNS regions and exceed damage thresholds, they manifest as clinical relapses. Alternatively, when cumulative axon degeneration surpasses the capacity of the functional CNS reserve, permanent neurological disability arises (light blue line) and there is a transition to the progressive disease. The decrease in brain volume over time is more severe at the beginning of the disease, in parallel with more intense inflammatory activity, and it continues steadily as the disease evolves. PPMS follows the same processes but the inflammatory relapses are not translated into clinical relapses, either because they are less frequent, less severe or they affect silent (non-eloquent) areas. Only when axon degeneration reaches a clinical threshold is disability manifested as progressive. Therefore, there are no differences between SPMS and PPMS except for the relative clinical impact (relapses) of acute inflammatory activity.</p

The ODE model of CNS damage in MS.

<p>A) The model represents the volume occupied by axons and myelin: Right, the healthy CNS is composed of myelinated axons (<i>A</i>_<i>m</i>); Center, inflammatory attack is represented by the time-dependent parameter λ(t), which arises from the Generalized Extreme Value (GEV) distribution of the EDSS time-series, producing either demyelination (right) or degeneration of axons (bottom); Left, demyelinated axons (<i>A</i>_<i>d</i>) can be remyelinated with myelin produced by oligodendrocytes (<i>M)</i>, as a function of the parameters <i>km</i> and <i>q</i>; Bottom, myelinated or demyelinated axons can be lost by either acute axon transection or degeneration (<i>D)</i>, according to the parameters <i>kmd</i> or <i>kd</i> respectively. B) Clustering MS patients based on the EDSS time series. The horizontal axes correspond to the time in months (maximum = 16 months), while the vertical axes correspond to the patients. Each line represents the EDSS of a given patient over time, using a color scale to reflect the EDSS. Clusters 1 and 2 include patients that maintain an intermediate short term EDSS and that reach a high EDSS in the long term. Cluster 3 includes patients that maintain a low short term EDSS and that achieve an intermediate EDSS in the long term. Cluster 4 represents a more heterogeneous group.</p

Model parameters for the studied disease subtypes.

<p>Parameter distribution for the different disease subtypes were analyzed through pairwise Wilcoxon tests (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005757#pcbi.1005757.s004" target="_blank">S2 Table</a>).</p

Sensitivity analysis of the model’s parameters.

<p>A) A sensitivity analysis showing the effects of the uncertainties in parameters on the model’s behavior (output variables: EDSS and brain volume—BV). The extended version of a Fourier amplitude sensitivity test (eFAST) was used to quantify the relative importance of the input factors. Pink line indicates the sensitivity level of a dummy parameter that does not occur in any of the equations. Sensitivities below this line should not be considered significantly different from zero. B) Simulations of brain volume in MS. Median occurrence and interquartile range (IQR) for the correlation coefficients between the experimental and simulated BVs in the validation cohort. Pearson correlation coefficients: cluster 1, 0.93; cluster 2, 0.94; cluster 3, 0.86; and cluster 4, 0.87.</p

The distribution of the model’s parameters calculated for the four clusters.

<p>Each boxplot shows the distribution of each parameter in the model for each of the clusters: <i>km</i>, <i>kmd</i>, <i>kd</i>, <i>q</i>, and <i>δ</i>.</p

Comparison of the EDSS time-series and model simulations.

<p>Comparison of the EDSS scores from all the patients in the longitudinal cohort as a function of their cluster (each patient from the discovery cohort is shown separately and identified with a cluster-specific color: red, cluster 1; green, cluster 2; blue, cluster 3 and black, cluster 4) and in accordance with the model’s predictions (grey lines, each line corresponds to an individual simulation).</p

Proportion of each MS subtype in the clusters identified in the discovery cohort.

<p>Proportion of each MS subtype in the clusters identified in the discovery cohort.</p

Model parameters.

<p>Model parameters.</p

Multivariate linear regression analysis between the clinical variables and visual outcomes.

<p>The variables included are described in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0195856#pone.0195856.t001" target="_blank">Table 1</a>. The variables were selected using the stepwise method. To analyze visual acuity, the retinal layer thickness was multiplied by 10 to readily visualize the values.</p