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Spreading of pathological proteins through brain networks: a case study for Alzheimers disease

G. Landi, A. Scaravelli, M. C. Tesi, C. Testa

Abstract

Mathematical modeling offers a valuable approach to understanding Alzheimers disease (AD) given its complexity, unknown causes, and lack of effective treatments. Models, once validated, offer a powerful tool to test medical hypotheses that are otherwise difficult to verify directly. Our focus here is on elucidating the spread of misfolded tau protein, a critical hallmark of AD alongside Abeta protein, taking also into account the synergistic interaction between the two proteins. We consider distinct modelling choices, all employing network frameworks for protein evolution, differentiated by their network architecture and diffusion operators. By carefully comparing these models against clinical tau concentration data, gathered through advanced multimodal analysis techniques, we show that certain models replicate better the proteins dynamics. This investigation underscores a crucial insight: in modeling complex pathologies, the precision with which the mathematical framework is chosen is crucial, especially when validation against clinical data is considered decisive.

Spreading of pathological proteins through brain networks: a case study for Alzheimers disease

Abstract

Mathematical modeling offers a valuable approach to understanding Alzheimers disease (AD) given its complexity, unknown causes, and lack of effective treatments. Models, once validated, offer a powerful tool to test medical hypotheses that are otherwise difficult to verify directly. Our focus here is on elucidating the spread of misfolded tau protein, a critical hallmark of AD alongside Abeta protein, taking also into account the synergistic interaction between the two proteins. We consider distinct modelling choices, all employing network frameworks for protein evolution, differentiated by their network architecture and diffusion operators. By carefully comparing these models against clinical tau concentration data, gathered through advanced multimodal analysis techniques, we show that certain models replicate better the proteins dynamics. This investigation underscores a crucial insight: in modeling complex pathologies, the precision with which the mathematical framework is chosen is crucial, especially when validation against clinical data is considered decisive.
Paper Structure (9 sections, 11 equations, 1 figure, 6 tables)

This paper contains 9 sections, 11 equations, 1 figure, 6 tables.

Table of Contents

  1. Introduction
  2. The mathematical model
  3. Proteins spreading through brain's connectomes
  4. Materials and methods
  5. Results
  6. Experimental setting
  7. Clinical Deterioration Pattern and Model Evaluation
  8. Numerical Results
  9. Discussion and conclusion

Figures (1)

  • Figure 1: Mean $\tau$ concentration values $w^{(*)}_T,\, w^{(*)}_O,\, w^{(*)}_L,\, w^{(*)}_F$ in the temporal, occipital, fusiform and limbic networks as listed in Table \ref{['tab:signif']}. The colorbar reflects the ordering of $\tau$ values, from high (dark red) to low (yellow). A: 3D view of the brain and the corresponding sagittal plane. B: 3D view of the brain and the corresponding sagittal plane. C: corresponding axial and coronal view.