Magnetic resonance elastography in nonlinear viscoelastic materials under load

Characterisation of soft tissue mechanical properties is a topic of increasing interest in translational and clinical research. Magnetic resonance elastography (MRE) has been used in this context to assess the mechanical properties of tissues in vivo noninvasively. Typically, these analyses rely on linear viscoelastic wave equations to assess material properties from measured wave dynamics. However, deformations that occur in some tissues (e.g. liver during respiration, heart during the cardiac cycle, or external compression during a breast exam) can yield loading bias, complicating the interpretation of tissue stiffness from MRE measurements. In this paper, it is shown how combined knowledge of a material’s rheology and loading state can be used to eliminate loading bias and enable interpretation of intrinsic (unloaded) stiffness properties. Equations are derived utilising perturbation theory and Cauchy’s equations of motion to demonstrate the impact of loading state on periodic steady-state wave behaviour in nonlinear viscoelastic materials. These equations demonstrate how loading bias yields apparent material stiffening, softening and anisotropy. MRE sensitivity to deformation is demonstrated in an experimental phantom, showing a loading bias of up to twofold. From an unbiased stiffness of \(4910.4 \pm 635.8\) Pa in unloaded state, the biased stiffness increases to 9767.5 \(\pm \,\)1949.9 Pa under a load of \(\approx \) 34% uniaxial compression. Integrating knowledge of phantom loading and rheology into a novel MRE reconstruction, it is shown that it is possible to characterise intrinsic material characteristics, eliminating the loading bias from MRE data. The framework introduced and demonstrated in phantoms illustrates a pathway that can be translated and applied to MRE in complex deforming tissues. This would contribute to a better assessment of material properties in soft tissues employing elastography.

     

Hotspots of species loss do not vary across future climate scenarios in a drought‐prone river basin

Climate change is expected to alter the distributions of species around the world, but estimates of species’ outcomes vary widely among competing climate scenarios. Where should conservation resources be directed to maximize expected conservation benefits given future climate uncertainty? Here, we explore this question by quantifying variation in fish species’ distributions across future climate scenarios in the Red River basin south‐central United States. We modeled historical and future stream fish distributions using a suite of environmental covariates derived from high‐resolution hydrologic and climatic modeling of the basin. We quantified variation in outcomes for individual species across climate scenarios and across space, and identified hotspots of species loss by summing changes in probability of occurrence across species. Under all climate scenarios, we find that the distribution of most fish species in the Red River Basin will contract by 2050. However, the variability across climate scenarios was more than 10 times higher for some species than for others. Despite this uncertainty in outcomes for individual species, hotspots of species loss tended to occur in the same portions of the basin across all climate scenarios. We also find that the most common species are projected to experience the greatest range contractions, underscoring the need for directing conservation resources toward both common and rare species. Our results suggest that while it may be difficult to predict which species will be most impacted by climate change, it may nevertheless be possible to identify spatial priorities for climate mitigation actions that are robust to future climate uncertainty. These findings are likely to be generalizable to other ecosystems around the world where future climate conditions follow prevailing historical patterns of key environmental covariates.