The influence of spatial patterns of capillary networks on transverse relaxation.

Tissue-inherent relaxation parameters offer valuable information about the arrangement of capillaries: in an external field, capillaries act as magnetic perturbers to generate local inhomogeneous fields due to the susceptibility difference of deoxygenated blood and the surrounding tissue. These field inhomogeneities influence the free induction decay in a characteristic way, and, conversely, the above tissue parameters can be recovered by multi-parametric fits of adequate theoretical models to experimentally sampled free induction decays. In this work we study the influence of different spatial patterns of capillary positions on the free induction decay. Starting from the standard single capillary approximation (Krogh cylinder) for a symmetric array of capillaries, the free induction decay is analyzed for increasingly random capillary positions, using a previously described Gibbs point field model. The effects of diffusion are implemented with a flexible and fast random walk simulation. We find that the asymmetric form of the obtained frequency distribution is more robust against variations of capillary radii than against shifts of capillary positions, and further that, for an inclusion of diffusion effects, the single capillary approximation models the uniform alignment of capillaries in the hexagonal lattice to great accuracy. An increase in randomization of capillary positions then leads to a significant change in relaxation times. This effect, however, is found less pronounced than that of changes in the off-resonance field strengths which are controlled by the oxygen extraction fraction, thus indicating that observed changes in BOLD imaging are more likely to be attributed to changes in oxygenation than to capillary alignment.

Calcium waves in a grid of clustered channels with synchronous IP3 binding and unbinding.

Calcium signals in cells occur at multiple spatial scales and variable temporal duration. However, a physical explanation for transitions between long-lasting global oscillations and localized short-term elevations (puffs) of cytoplasmic Ca2+ is still lacking. Here we introduce a phenomenological, coarse-grained model for the calcium variable, which is represented by ordinary differential equations. Due to its small number of parameters, and its simplicity, this model allows us to numerically study the interplay of multi-scale calcium concentrations with stochastic ion channel gating dynamics even in larger systems. We apply this model to a single cluster of inositol trisphosphate (IP 3) receptor channels and find further evidence for the results presented in earlier work: a single cluster may be capable of producing different calcium release types, where long-lasting events are accompanied by unbinding of IP 3 from the receptor (Rückl et al., PLoS Comput. Biol. 11, e1003965 (2015)). Finally, we show the practicability of the model in a grid of 64 clusters which is computationally intractable with previous high-resolution models. Here long-lasting events can lead to synchronized oscillations and waves, while short events stay localized. The frequency of calcium releases as well as their coherence can thereby be regulated by the amplitude of IP 3 stimulation. Finally the model allows for a new explanation of oscillating [IP 3], which is not based on metabolic production and degradation of IP 3.