(318b) Bifurcation Pattern Formation in Biological Tissues: A New Discovery of Interfacial Instability with Applications in Healthcare

Pattern formation driven by interfacial instabilities are commonly found in chemical and physical processes. They are studied, at length, in the contexts of Enhanced Oil Recovery (EOR) and geophysics with viscous fingering (VF) and hydraulic fracturing (HF) being the classical examples. In physiological systems, however, pattern formation is seldom reported, and much of the work is limited to studying the problem of pulmonary airway reopening [1]. Here, we report a new observation of pattern formations at biological tissue interfaces. Our findings show that injecting fluid to an interfacial space between flexible tissue layers leads to formation of intriguing patterns with complex and highly branched features. This discovery uncovers a new class of flow instability problems in biological systems that has not been previously identified in literature.

To understand the underlying mechanism, different liquid formulations were injected into tissues in the rat in vivo. Solutions of various viscosities, colloids and suspensions containing solid particles of different size and electrostatic charge were prepared and tested. Moreover, experiments with varied flow rates and injection volumes were conducted to examine the effect of flow conditions on the pattern characteristics. Using advanced imaging techniques such as optical coherence tomography (OCT) and confocal scanning laser photography, en face and cross-sectional images of the tissues were captured to generate a 3D reconstruction of the pattern and extract quantitative data (pattern wavelength, spread radius, tip-splitting angle, blister resolution, etc.).

Our results suggest that fluid propagates in the interfacial space via two mechanisms: 1) radial spread by hydraulic fracturing with unstable front dynamics, and 2) blister formation by transverse deflection of delaminated tissue layers. Fracturing instability produces distinct patterns characterized by highly bifurcated and “stringy” fingers that are unlike typical VF and HF patterns. In principle, this instability can arise from coupled interactions of competing forces in the tissue including fracture mechanics governing the propagation of crack front, viscous forces dictating the dynamics of the injected fluid and viscoelastic forces controlling the vertical deflection of the delaminated tissue. Furthermore, our results indicate that the bifurcation pattern characteristics were independent of the injected colloid’s particle size and surface charge. More notable, however, was the observation that injecting solutions or suspensions of larger particle size only led to blister inflation and did not produce bifurcation patterns at any flow conditions.

From a healthcare standpoint, these findings have significant implications for developing novel therapies by injecting deep into tissues across large areas without the possibly damaging effects of complete tissue delamination or blister formation. While interfacial instabilities are disadvantageous in many other cases [2], bifurcation pattern formation may be advantageous in this case as it can translate to greater radial distribution of injected materials, and thus higher treatment efficacy. In addition to potential medical applications, we believe that these results uncover new fundamental science of bifurcating patterns formed by delaminating flow at the interface of two soft tissues not previously reported, where multiple physics of blister mechanics, viscoelastic mechanics, fluid mechanics and fracture mechanics intersect.

Acknowledgements: the authors thank Dr. Anne Juel, Dr. Martin Z. Bazant and Dr. Mohammad Mirzadeh for valuable technical discussions. This work is supported by the National Institutes of Health Grants R01EY028450, R01EY021592, P30EY006360, R01EY028859, T32EY07092.

References:

[1] Pihler-Puzović, D., Anne Juel, and Matthias Heil. "The interaction between viscous fingering and wrinkling in elastic-walled Hele-Shaw cells." Physics of Fluids 26.2 (2014): 022102.

[2] Mirzadeh, Mohammad, and Martin Z. Bazant. "Electrokinetic control of viscous fingering." Physical review letters 119.17 (2017): 174501.