Dr. Florian Fischer
The human brain is the most complex compact structure in the known universe on any temporo-spatial scale. It is therefore not surprising that many macroscopic metrics of its function exhibit features that intuitively evoke associations with properties of the phase space orbits typical for complex dynamic systems, such as attracting stable states and predictable periodical oscillations. The underlying complexity of the mutable elements of the brain and their likewise mutable interactions over various scales, from molecular to macroscopic, render the relating of neuropsychological phenomena to the relatively limited number of the brains measurable (in vivo) structural and functional features a daunting task. The situation is complicated even more by the conspicuous homeodynamic properties of the brain evident through copious documented cases of functional recovery and adaption after exo- and endogenous structural or functional insults, such as mechanically induced lesions, hemorrhagic insults and age associated forms of neurodegeneration.
The rapid development of in vivo brain imaging in the last decades has led to the successful identification of many structural and functional features of the brain that are associated with various neuropsychological outcome measures quantifying cognitive function and dysfunction. However, the underlying complexity of the brain as described above is a very probable reason for the unsatisfactory predictive value of isolated brain features for cognitive functioning in dynamic situations, such as ongoing adaption to various forms of neuropathology. Likewise, the mechanistic inferences that can be drawn from traditionally reductionist approaches in dynamic situations are relatively limited.
This is specifically the case in aging and its associated neurodegenerative disorders. Elderly persons are typically affected by various sometimes unassociated forms of neuropathology and more heterogeneously so with higher age, which individually is often not reflected in a straight forward linear fashion in cognitive functioning. Most prominently, neuropathology such as beta-amyloid deposits and grey matter atrophy that are present in the great majority of Alzheimer's disease patients can also be found in a large proportion of the cognitively healthy elderly. The reaction of the field to this puzzling finding has been twofold. First, the need to include brain features beyond present neuropathology as possible compensatory counteractive agents to the effects of neuropathology has been recognized and conceptualized as resilience or cognitive reserve, acknowledging thus the presumable dynamics as elaborated above. Second, the dimensionality of the acquired data has been enormously increased from molecular to microstructural, morphological and functional imaging as well as life-style related factors or other age-related comorbidities such as diabetes mellitus or hypertension, in order to identify potentially relevant measures of resilience or pathology. However, while doubtlessly necessary, this approach demonstrates two inherent issues. First, in many models an implicitly or explicitly linear interaction of the measured brain features is presumed. Second, the acquired data exacerbates the so-called 'curse of dimensionality', which states that the number of samples required to continuously map the parameter space increases exponentially with the number of dimensions. Due to logistical and financial constraints, the number of available data samples is still greatly limited in comparison to the available measurements.
However, both issues can be effectively addressed using recent advances in computer science as well as established mathematical methodology. Given the presumably complex and/or non-linear structuring of the data, linear statistical methods alone may be a rather ineffective tool to identify relevant associations due to their constraints regarding data distribution, power and nature of the modelled associations. In contrast, computer science offers a range of machine learning methods much less constrained by assumptions of data distribution and nature of its structuring, from simple clustering to deep learning. Thus, addressing the first issue cited above, these methods can be used for prior free discovery of complex patterns in the data that can help to form or adapt hypotheses as to the underlying mechanisms which are not apparent from exploratory visual or parametric statistical analyses. They have also been used successfully to improve the prediction of cognitive status in Alzheimer's disease based on multimodal neuroimaging data, although with limited success. Assuming that the available data contains the information needed for satisfactorily accurate predictions, a likely explanation for this shortfall is that many machine learning methods are also greatly constrained when investigating sparse data. In order to address this second of the two issues referred to above, on can make use of a combination of the great amount of knowledge from prior investigations that refer to the structure within the available data and the vast inventory of modelling tools provided by computer science and mathematics, effectively applying an informed dimensionality reduction. This method has been used by surprisingly few research groups to date. Those who did, however, showed astonishing results: e.g. Raj et al. were more recently able to demonstrate that the eigensystem decomposition of a molecular diffusion disease model constructed from structural connectivity networks corresponds to prevalence rates and temporo-spatial atrophy patterns of the most common neurodegenerative diseases. Put in a blunt way, this means that a relational structure within the imaging data (the reconstructed white matter network) explains a wide range of previously inexplicable temporo-spatial neuropathology distributions under a very simple and abstract disease diffusion process model!
To sum up, the analysis of the very high dimensional available imaging and non-imaging data referring to the brain and other factors relevant for cognitive functioning is extremely challenging due to its sparsity and prominent highly non-linear structuring. A combination of tailored machine learning methods for pattern identification and informed modelling of underlying mechanisms seems paramount to successfully improve the prediction of cognitive status and forming testable hypotheses as to the underlying mechanisms. My personal aim as member of the research group is accordingly to facilitate the use and adaption of these methods to the specific research questions in the field of neuroimaging and resilience in aging.