Fig 1.
a. When MS patients experience relapses, there is a spike in their clinical disability.
In addition to these inflammatory events, the underlying accumulation of permanent damage results in decreased brain volume as there is a gradual increase of lesion volume (subclinical disease). b. MRI scans serve as both a diagnostic tool and an ongoing measure of disease progression. Here we show a cartoon map depicting a typical axial slice of a patient’s MRI data. Lesions are shown as white areas of demyelination. c. In MS, the demyelination of nerve axons is driven by immune cells such as activated T cells. Myelin is a membrane extension of oligodendrocytes, which are cells that undertake remyelination to maintain proper nerve signalling. Myelin loss in MS patients removes the protective insulation of nerve cells, causing oligodendrocyte loss and symptom onset subject to lesion location (recall b).
Table 1.
Abbreviations of key terminology.
Fig 2.
On the left we show a simplification of MS immunology.
Following priming in the periphery, autoreactive T cells migrate within blood and then cross the blood-brain barrier to enter the perivascular space. Perivascular macrophages present myelin antigens to T cells resulting in their re-activation and entry into the brain parenchyma. The accumulation of myelin loss and the death of myelin-synthesising cells called oligodendroctyes gives rise to lesion formation. This simplified physiology is translated to a mathematical model, shown on the right (not to scale). A square lattice is divided into regions of peripheral blood (red), perivascular space (blue), and parenchyma (white). Agent populations include primed T cells (yellow), perivascular macrophages (purple), reactivated T cells (blue), myelin (grey) and oligodendrocytes (outlined grey boxes).
Fig 3.
a. Cells are centred on square lattice sites.
Primed T cells (yellow) and PVMs (purple) undertake unbiased migration, with an equal probability of migrating north, south, east or west from their current position to a neighbouring lattice site. b. The occupation of a lattice site is not mutually exclusive. Same-site occupation of a lattice site by a T cell and a PVM is recorded as activation of that primed T cell, so that it becomes a reactivated T cell (blue), and the PVM remains. c. The reactivated T cells (blue) are incentivised to undertaken biased random movement towards the nearest myelinated lattice site. The strength of the bias in a reactivated T cell’s movement increases as the cell becomes closer to the myelin (brown). d. The model is simulated over three hundred days, with three relapse events that are one hundred days apart and four weeks in duration. During each relapse, the inflow of primed T cells is increased, and when these cells enter the PVS there is a delayed increase in the reactivated T cell population.
Fig 4.
a. To reconcile the spatial discrepancy between the size of oligodendrocytes and the size of the immune cell populations, we model each oligodendrocyte as a 5 by 5 block of myelinated lattice sites.
b. When a myelinated lattice site is occupied by a reactivated T cell, it is progressively degraded until it is fully demyelinated. If the myelinated lattice site resides in a block associated with an oligodendrocyte that can undertake myelin synthesis, the site is remyelinated over a series of time steps. c. The extent of demyelination within an oligodendrocyte block determines the extent to which the oligodendrocyte undertakes its typical physiological functions. When the number of completely demyelinated sites σ exceeds the first threshold ω, the oligodendrocyte loses the ability to remyelinate. Once the total damage σ exceed the second threshold λ, the oligodendrocyte undergoes apoptosis and all of the associated myelin is removed from its designated myelin sites.
Table 2.
Summary of the five agent populations and the three key parameters identified to model treatment effects.
Fig 5.
The averaged results across 40 simulations with and
.
These results represent the expected disease course of an untreated patient. The extremes across the 40 simulations are indicated by the shading around each averaged result. The three relapse events, each 4 weeks in duration, are indicated by the grey shading. a. The average population of primed T cells (yellow), perivascular macrophages (purple) and reactivated T cells (blue). b. The proportion of the myelin population that is fully intact (light green), partially damaged (green) and fully damaged (dark green). c. The proportion of oligodendrocytes that are myelinating (pink), nonmyelinating (dark pink), and have undergone apoptosis (purple).
Fig 6.
Spatial and intracellular insights from an individual simulation.
a. Shown at Day 10 and Day 20, the model produces a rightward-progressing lesion (light blue). The progression and heterogeneity of the lesion boundary are driven by the reactivated T cell population (yellow). The insets show a closeup of Day 20, where reactivated T cells create paths of intermediate damage (blue) in the densely myelinated region (dark blue). b. The interrelationship between the level of myelin damage and the behaviour of oligodendrocytes. In bi. we show the individual state of a myelin agent within a given oligodendrocyte (green region depicted in the inset of a). The number of healthy myelin sites within this oligodendrocyte is shown in bii., alongside the reductions in healthy myelin that cause the oligodendrocyte to stop myelinating and undergo apoptosis. Note that the tolerances depicted (red dashed lines at 15 and 11) against the healthy myelin count are 25-ω and 25-λ, since and
describe the total of damaged myelin. The behaviour of the oligodendrocyte is shown in biii., where it switches from myelinating to nonmyelinating and then undergoes apoptosis once ω and λ are triggered.
Fig 7.
Investigation of the impact of the BBB permeability, bR on the agent-based model.
a. Heatmaps corresponding to the number of reactivated T cells (left), and percentage of lost myelin (middle and right) as a function of time (days) and BBB permeability bR. Note the timescales for the myelin heatmaps range from 300 days (middle) to 28 days (right). b. Correlation between the number of reactivated T cells and the lost myelin percentage for the varying BBB permeabilities bR directly after each relapse (top row) and during each non-relapse period (second row). The linear correlation, R, is given for each.
Fig 8.
Investigation of the impact of the oligodendrocyte stress tolerances, ω and λ (recall Fig 4).
a. Heatmaps corresponding to the number of oligodendrocytes performing each behaviour (myelinating, nonmyelinating, undergone apoptosis) over the 300 day simulation. We show normalised ‘area under the curve’ data averaged across 20 simulations. The values of ω and λ range from 1-25, representing the damage required before oligodendrocytes stop myelinating and undergo apoptosis, respectively. b. Swarm charts of select parameter pairs highlighted in (a) (green squares). We show collective data across the same 20 simulations of the frequency of oligodendrocyte time spent performing each behaviour.
Fig 9.
Comparison of BBB targeted treatment timing (delayed versus immediate).
a. Reactivated T cell populations under DMT treatment effects. While the typical BBB permeability is simulated as bR = 0.1, the BBB targeted treatment reduces it to bR = 0.025. The delayed treatment (dark blue) reduces the cell population from Day 80 onward, while the immediate treatment (light blue) reduces the cell population from the simulation onset. b. The proportion of the myelin population that remains intact under the two different treatment scenarios: delayed (light green) and immediate (dark green).
Fig 10.
a. Comparison of myelinating oligodendrocyte agent population across the three treatment strategies.
b. Comparison of fully intact myelin agent population across the three treatment strategies. We first simulate under the untreated parameter scheme ( and
), and show results averaged over 40 simulations. The three treatment strategies commence at Day 80. The first strategy (1) restores oligodendrocytes (and myelin). While this restores the myelin (light green) and oligodendrocyte (light pink) populations back to 100%, they rapidly decline with the next relapses. Enhancing the resilience of existing oligodendrocytes through
and
under treatment (2) stabilises myelin loss (green) through the prevention of oligodendrocyte loss (dark pink). Combining these ideas in (3), we see that the intensity of the first relapse event still leads to notable myelin loss, given the abundance of potential myelin to destroy remains high.
Fig 11.
Simulation of a combined treatment approach achieving suppressed immune activity through a DMT, and the promotion of remyelination by oligodendrocyte replenishment and increases in their innate resilience.
a. Breakdown of the oligodendrocyte agent population into myelinating, nonmyelinating and having undergone apoptosis. b. Breakdown of the myelin agent population by its level of damage (fully intact, partially damaged, fully damaged). Initially we show an untreated case where and
. Rapid myelin loss motivates the treatment intervention at Day 80, where in addition to restoring the myelin and oligodendrocyte populations we simulate under
and
.
Fig 12.
Proportion of myelinating oligodendrocytes remaining by Day 300 for untreated and treated scenarios.
We model the effects of disease modifying therapies targeting the BBB, as well as oligodendrocyte therapies enhancing their resilience (ISR targeting) and re-establishing their numbers (stem cell therapies). From left to right, we show the untreated case (A), delayed DMT targeting the BBB (B), immediate DMT targeting the BBB (C), and 100% re-establishment of the oligodendrocyte population (D), enhancement of oligodendrocyte resilience (E), 100% re-establishment and enhancement of the oligodendrocyte resilience (F). We also show the impact of combining the DMT and oligodendrocyte therapies, assuming 100%, 75%, 50% and 25% success in reestablishing myelinating oligodendrocytes (G, H, I, J respectively).