Spherical indentation load-relaxation of soft biological tissues
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Anthony G. Lau Department of Biomedical Engineering, University of Virginia, Charlottesville, Virginia 22908
Michelle L. Oyena) and Richard W. Kentb) Center for Applied Biomechanics, Department of Mechanical and Aerospace Engineering, University of Virginia, Charlottesville, Virginia 22904 (Received 21 December 2005; accepted 9 March 2006)
Elastic-viscoelastic correspondence was used to generate displacement–time solutions for spherical indentation testing of soft biological materials with time-dependent mechanical behavior. Boltzmann hereditary integral operators were used to determine solutions for indentation load-relaxation following a constant displacement rate ramp. A “ramp correction factor” approach was used for routine analysis of experimental load-relaxation data. Experimental load-relaxation tests were performed on rubber, as well as kidney tissue and costal cartilage, two hydrated soft biological tissues with vastly different mechanical responses. The experimental data were fit to the spherical indentation ramp-relaxation solutions to obtain values of short- and long-time shear modulus and of material time constants. The method is used to demonstrate linearly viscoelastic responses in rubber, level-independent indentation results for costal cartilage, and age-independent indentation results for kidney parenchymal tissue.
I. INTRODUCTION
Motor vehicle crashes are the leading cause of blunt abdominal trauma in children.1 Serious abdominal injuries, such as kidney lacerations, are particularly significant as children transition from child seats to adult seatbelts.2 Injuries to the thoracic cage are relatively rare in children, but the mechanical properties of its constituents are important because the chest is the primary structure coupling the child to the vehicle, and thus its interaction with the restraint system dictates the trajectory of the head during a crash. This paper focuses on the mechanical properties of two pediatric tissues that are not well understood but are important for accurately modeling the pediatric crash victim: the kidney parenchyma and the costal cartilage. The kidney and costal cartilage are biological materials that serve different physiologic functions. The kidney, located on the posterior abdominal wall, is a vital a)
This author was an editor of this focus issue during the review and decision stage. For the JMR policy on review and publication of manuscripts authored by editors, please refer to http:// www.mrs.org/publications/jmr/policy.html. b) Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/JMR.2006.0243 J. Mater. Res., Vol. 21, No. 8, Aug 2006
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urinary organ responsible for separating toxins and waste materials from the blood while preserving body hydration. Although its primary function is not mechanical, the integrity of the kidney must be maintained for it to fulfill its function. Thus, researchers have studied the mechanical behavior of adult kidney tissue in compression,3,
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