A mathematical model for this rare disease was presented in a paper by Khonsari and Calvez in the journal PLoS ONE, abbreviated as [KC] from now on) and this is my primary source of information for this post. In addition I have used the standard work ‘McAlpine’s Multiple Sclerosis‘ as a reference. The disease was first described by Balo in 1927 and he himself already mentioned a possible connection to Liesegang rings. It is relatively common in the Philippines compared to other parts of the world. The model proposed in [KC] is a system of PDE similar to those used to describe chemotaxis, e.g. the Keller-Segel model. An important difference from reaction diffusion equations is the presence of cross diffusion, i.e. the flux of one diffusive species depends on the gradient of another. The system of [KC] also contains an ODE describing the density of oligodendocytes (the cells responsible for production and maintenance of myelin) which is analogous to the equation describing the formation of a precipitate in certain models of Liesegang rings. Computer simulations using this model show the production of rings for certain values of the parameters involved and not for others. The authors of [KC] compare their model to one based on another mechanism (which has discontinuous coefficients) and argue that their model performs better.
In considering the relation of Balo’s disease to MS an interesting related question is whether MS is one disease or many. A classification into four types has been suggested with different pathological mechanisms. Balo’s disease most closely resembles Type III. If this distinction could be pushed further it might lead to a global increase in understanding. Perhaps different forms require different therapies. Characteristic features of Type III include destruction of oligodendrocytes and signs that the oxygen supply in the area where damage is taking place is not sufficient. Two different general pictures of the formation of the rings of demyelinated tissue have been proposed in the literature. In one of these the demyelination only takes place in certain rings while in the other there is demyelination everywhere followed by remyelination in certainrings. Remyelination, a process by which the myelin sheaths of nerve cells are repaired is known to play an important role in MS. The quality of the new coatings is generally poorer than that of the original ones. Understanding the dynamics of the interplay of demyelination and remyelination is a crucial issue in understanding the progression of MS.
Another disease related to MS (or a special form of it, the question arises here too, it resembles Type II) is neuromyelitis optica (NMO), also known as Devic’s disease. This disease is automimmune in nature and a specific target of autoimmune attacks has been identified, the protein aquaporin 4. This knowledge is useful in distinguishing NMO from typical MS by determining the concentration of antibodies against aquaporin 4 in the blood. For more details see this article in PloS Medicine.