# Mathematical description of brain plasticity

Advances in magnetic resonance imaging (MRI) and image processing have enabled quantitative volumetric studies of human brain morphology to assess abnormalities of regional brain structures in diseases. Volumetric MRI has been used to study the temporal dynamics of brain morphology in human development, ...

Advances in magnetic resonance imaging (MRI) and image processing have enabled quantitative volumetric studies of human brain morphology to assess abnormalities of regional brain structures in diseases. Volumetric MRI has been used to study the temporal dynamics of brain morphology in human development, aging, brain diseases (such as Alzheimer’s disease, mild cognitive impairment etc) and brain recovery from a chronic insult (such as recovery from alcohol or illicit substance use). With the use of MRI volumetric group data and statistical analyses, non-linear temporal trajectories of regional brain morphology have been reported in the developing brain and in brain recovery from chronic insults, such as alcoholism. Though statistical analysis of group data can distinguish abnormal brain morphology from normal morphology, statistical analysis reveals only the general pattern of brain volume change for a given sample but does not help to describe the temporal course of regional brain volumes in individuals. The knowledge of individual regional brain volume trajectories during development, normal aging, neurodegeneration or recovery from disease will help assess individual brain tissue change rates and determine if such a rate is normal or abnormal. Recently, a mathematical formula that describes a square root dependence of individual brain tissue volume recovery on time was reported in abstinent alcohol dependent individuals (Mon et al. 2011). The mechanisms mediating brain tissue regeneration in alcohol or other substance use disorders are thought to reflect general mechanisms involved in brain growth. It will therefore be interesting to see if the said mathematical formula also describes individual brain development (i.e., tissue volume increases as well as myelination) in children. Also, non-linear courses of brain tissue volume loss due to diseases have been reported, and a reverse of the recently proposed formula was said (by the authors) to have predicted individual brain tissue volume losses over two years on a test sample of individuals with Alzheimer’s disease. There is a further need to test the applicability of the formula for predicting brain tissue volume losses in larger samples of brain volume data from Alzheimer’s disease patients. This research topic therefore seeks to review abstracts on the use of the mathematical formula or similar mathematical formulations for predicting individual brain development, regeneration (after a chronic insult) or degeneration in dementia or mild cognitive impairment using longitudinal neuroimaging volumetric data. Abstracts on the application of the formula or similar mathematical formulations for prediction of individual brain tissue loss in other brain diseases, such as licit and illicit substance use disorders well as psychiatric diseases that are associated with brain volume changes with time are also welcomed.
For details on the derivation of the formula see Mon et al., Psychiatry Research: Neuroimaging 194: 198 – 204 (2011).

Anderson Mon and Dieter J. Meyerhoff

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