Probabilistic analysis of spatial viscoelastic cues in 3D cell culture using magnetic microrheometry

Breast tumors are typically surrounded by extracellular matrix (ECM), which is heterogeneous, not just structurally but also mechanically. Conventional rheometry is inadequate for describing cell-size-level spatial differences in ECM mechanics that are evident at micrometer scales. Optical tweezers and passive microrheometry provide a microscale resolution for the purpose but are incapable of measuring ECM viscoelasticity (the liquid-like viscous and solid-like elastic characteristics) at stiffness levels as found in breast tumor biopsies. Magnetic microrheometry records data on varying microscale viscoelasticity within 3D ECM-mimicking materials up to the biopsy-relevant stiffness. However, the measurement probe-based microrheometry data has limitations in spatial resolution. Here, we present a probabilistic modeling method—providing analysis of sparse, probe-based spatial information on microscale viscoelasticity in ECM obtained from magnetic microrheometry—in two parts. First, we validate the method's applicability for analysis of a controlled stiffness difference, based on two collagen type 1 concentrations in one sample, showing a detectable stiffness gradient in the interface of the changing concentrations. Second, we used the method to quantify and visualize differences in viscoelasticity within 3D cell cultures containing breast-cancer-associated fibroblasts, and collagen type 1 (both typically present in the tumor ECM). The fibroblasts’ presence stiffens the collagen material, which aligns with previous research. Importantly, we provide probabilistic quantification of related spatial heterogeneity differences in viscoelasticity recorded by magnetic microrheometry, for the first time. The fibroblasts culturing leads to an initially higher spatial heterogeneity in the collagen stiffness. In summary, this method reports on enhanced spatial mapping of viscoelasticity in breast cancer 3D cultures, with the future potential for matching of spatial viscoelasticity distribution in the 3D cultures with the one in biopsies.