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The structural origins of brittle star arm kinematics: An integrated tomographic, additive manufacturing, and parametric modeling-based approach

Journal Publications
Lara Tomholt, Larry J. Friesen, Daniel Berdichevsky, Matheus C. Fernandes, Christoph Pierre, Robert J. Wood, James C. Weaver
Journal of Structural Biology, Volume 211, Issue 1, 107481, July 2020
Publication year: 2020


Brittle stars are known for the high flexibility of their arms, a characteristic required for locomotion, food grasping, and for holding onto a great diversity of substrates. Their high agility is facilitated by the numerous discrete skeletal elements (ossicles) running through the center of each arm and embedded in the skin. While much has been learned regarding the structural diversity of these ossicles, which are important characters for taxonomic purposes, their impact on the arms’ range of motion, by contrast, is poorly understood. In the present study, we set out to investigate how ossicle morphology and skeletal organization affect the flexibility of brittle star arms. Here, we present the results of an in-depth analysis of three brittle star species (Ophioplocus esmarki, Ophiopteris papillosa, and Ophiothrix spiculata), chosen for their different ranges of motion, as well as spine size and orientation. Using an integrated approach that combines behavioral studies with parametric modeling, additive manufacturing, micro-computed tomography, scanning electron microscopy, and finite element simulations, we present a high-throughput workflow that provides a fundamental understanding of 3D structurekinematic relationships in brittle star skeletal systems.

A geometrically adaptable heart valve replacement

Journal Publications
Sophie C. Hofferberth, Mossab Y. Saeed, Lara Tomholt, Matheus C. Fernandes, Christopher J. Payne, Karl Price, Gerald R. Marx, Jesse J. Esch, David W. Brown, Jonathan Brown, Peter E. Hammer, Richard W. Bianco, James C. Weaver, Elazer R. Edelman, Pedro J. del Nido
Science Translational Medicine, Volume 12, Issue 531, eaay4006, February 2020
Publication year: 2020


Congenital heart valve disease has life-threatening consequences that warrant early valve replacement; however, the development of a growth-accommodating prosthetic valve has remained elusive. Thousands of children continue to face multiple high-risk open-heart operations to replace valves that they have outgrown. Here, we demonstrate a biomimetic prosthetic valve that is geometrically adaptable to accommodate somatic growth and structural asymmetries within the heart. Inspired by the human venous valve, whose geometry is optimized to preserve functionality across a wide range of constantly varying volume loads and diameters, our balloon-expandable synthetic bileaflet valve analog exhibits similar adaptability to dimensional and shape changes. Benchtop and acute in vivo experiments validated design functionality, and in vivo survival studies in growing sheep demonstrated that mechanical valve expansion accommodated growth. As illustrated in this work, dynamic size adaptability with preservation of unidirectional flow in prosthetic valves thus offers a paradigm shift in the treatment of heart valve disease.

Harnessing Geometric Frustration to Form Band Gaps in Acoustic Networks

Journal Publications
Pai Wang, Yue Zheng, Matheus C. Fernandes, Yushen Sun, Kai Xu, Sijie Sun, Sung Hoon Kang, Vincent Tournat, Katia Bertoldi
Physical Review Letters, Volume 118, Issue 8, EID 084302, February 2017
Publication year: 2017


We demonstrate both numerically and experimentally that geometric frustration in two-dimensional periodic acoustic networks consisting of arrays of narrow air channels can be harnessed to form  band gaps (ranges of frequency in which the waves cannot propagate in any direction through the system). While resonant standing wave modes and interferences are ubiquitous in all the analyzed network geometries, we show that they give rise to band gaps only in the geometrically frustrated ones (i.e. those comprising of triangles and pentagons). Our results not only reveal a new mechanism based on geometric frustration to suppress the propagation of pressure waves in specific frequency ranges, but also opens avenues for the design of a new generation of smart systems that control and manipulate sound and vibrations.

Effects of Ice Deformation on Röthlisberger Channels and Implications for Transitions in Subglacial Hydrology

Journal Publications
Colin R. Meyer, Matheus C. Fernandes, Timothy T. Creyts, James R. Rice
Journal of Glaciology, Volume 62, Issue 234, Pages 750-762, May 2016
Publication year: 2016


Along the base of glaciers and ice sheets, the sliding of ice over till depends critically on water drainage. In locations where drainage occurs through Röthlisberger channels, the effective pressure along the base of the ice increases and can lead to a strengthening of the bed, which reduces glacier sliding. The formation of Röthlisberger channels depends on two competing effects: (1) melting from turbulent dissipation opens the channel walls and (2) creep flow driven by the weight of the overlying ice closes the channels radially inward. Variation in downstream ice velocity along the channel axis, referred to as an antiplane shear strain rate, decreases the effective viscosity. This softening of the ice increases creep closure velocities. In this way, even a modest addition of antiplane shear can double the size of the Röthlisberger channels for a fixed water pressure or allow channels of a fixed radius to operate at lower effective pressure, potentially decreasing the strength of the surrounding bed. Furthermore, we show that Röthlisberger channels can be deformed away from a circular cross section under applied antiplane shear. These results can have broad impacts on sliding velocities and potentially affect the total ice flux out of glaciers and ice streams.

Time Scale for Rapid Drainage of a Surficial Lake into the Greenland Ice Sheet

Journal Publications
James R. Rice, Victor C. Tsai, Matheus C. Fernandes, John D. Platt
Journal of Applied Mechanics, Volume 82, Issue 7, Pages 1-8, July 2015
Publication year: 2015


A 2008 report by Das et al. documented the rapid drainage during summer 2006 of a supraglacial lake, of approximately , into the Greenland ice sheet over a time scale moderately longer than 1 hr. The lake had been instrumented to record the time-dependent fall of water level and the uplift of the ice nearby. Liquid water, denser than ice, was presumed to have descended through the sheet along a crevasse system and spread along the bed as a hydraulic facture. The event led two of the present authors to initiate modeling studies on such natural hydraulic fractures. Building on results of those studies, we attempt to better explain the time evolution of such a drainage event. We find that the estimated time has a strong dependence on how much a pre-existing crack/crevasse system, acting as a feeder channel to the bed, has opened by slow creep prior to the time at which a basal hydraulic fracture nucleates. We quantify the process and identify appropriate parameter ranges, particularly of the average temperature of the ice beneath the lake (important for the slow creep opening of the crevasse). We show that average ice temperatures 5–7 below melting allow such rapid drainage on a time scale which agrees well with the 2006 observations.