The pathogenesis of concentric sclerosis is a medical enigma. In a recent review1 summarizing the different hypotheses for periodic demyelination, our mathematical model2 is described in a way that requires further clarification.
In all forms of multiple sclerosis, a front of an unknown 'demyelinating molecule' is supposed to diffuse from a blood vessel located in the center of the developing lesion. In the classical theories proposed to explain the genesis of Baló's sclerosis, including the recent preconditioning theory,3 pattern formation occurs at the edge of this propagating front analogous to the accrual of the rings of a tree trunk. A 'protective' substance is supposed to inhibit demyelination at a limited distance ahead of the front. As the front crosses this protected region, demyelination restarts, and the cycle begins again.
Our conception of ring formation in Baló's sclerosis is very different. We consider the forming lesion as a field of microglial cells involved in attractive chemotactic interactions, and we show that these cells can spontaneously self-organize into concentric rings. Periodic demyelination is an indirect consequence of this self-organization. Two molecular factors are needed to create the pattern: first, an activator, which triggers the autoimmune reaction and has the same role as the demyelinating front in the previous theories, and second, a nonspecific microglial chemoattractant secreted by the microglial cell itself. Ring formation thus occurs behind the propagating front as a secondary self-organization phenomenon. The transition between homogeneous and concentric demyelination depends on a critical parameter that takes into account the number of microglial cells and the strength of the chemoattraction. In fact, many microglial cells involved in intense chemotaxis are likely to induce concentric demyelination. A major characteristic of our model is that no protection factor is required to explain the persistence of nondemyelinated zones behind the front: as the total number of microglial cells is fixed, demyelination only occurs where the microglial cells aggregate.
Interestingly, an analogy between Baló's sclerosis and the Liesegang periodic precipitation phenomenon has been repeatedly reported in the medical litterature for more than 70 years4 without rigorous re-examination. Periodic precipitation is a striking chemical process in which periodic rings of precipitate appear after the diffusion of a homogeneous front in a homogeneous gel. Despite their superficial similarities, we show that, according to numerical and theoretical data, these two processes share very little in the way of common mechanisms. The only theories for Liesegang ring formation that might be applicable to concentric demyelination are the postnucleation theories,5 in which ring formation occurs behind the diffusion front by self-organization. Even in these cases, it is not possible to draw a direct analogy with the biological phenomenon.
Our model for concentric sclerosis is both indirect and secondary. The mechanism of ring formation behind the front is inspired by the basic concepts of postnucleation theories for Liesegang rings. In addition, the structure of our critical parameter allows us to draw an interesting correlation between disease aggressivity and concentric pattern formation.
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Khonsari, R., Calvez, V. Concentric demyelination by self-organization: a new hypothesis for Baló's sclerosis. Nat Rev Neurol 3, E1 (2007). https://doi.org/10.1038/ncpneuro0619
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