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Research Papers

[+] Author and Article Information
Sylvana García-Rodríguez

Department of Mechanical Engineering,  University of Wisconsin—Madison, 1513 University Avenue, Madison, WI 53706-1572garcia1@wisc.edu

Everett L. Smith

Department of Population Health Sciences,  University of Wisconsin—Madison, 1300 University Avenue, Room 1097, Madison, WI 53706 elsmith1@facstaff.wisc.edu

Heidi-Lynn Ploeg

Department of Mechanical Engineering,  University of Wisconsin—Madison, 1513 University Avenue, Madison, WI 53706-1572ploeg@engr.wisc.edu

J. Med. Devices 2(1), 011006 (Mar 11, 2008) (6 pages) doi:10.1115/1.2889059 History: Received June 27, 2007; Revised February 05, 2008; Published March 11, 2008

## Abstract

Trabecular bone tissue is a three-dimensional structure that is difficult to duplicate with in vitro cell cultures or animal models. In an attempt to better understand the underlying mechanisms of tissue response to load, a system to load isolated bone preparations was developed. This ex vivo bone culture and loading system, given the name of ZETOS, compressively loads trabecular bone ($10mm$ diameter, $5.0mm$ height) to evaluate its morphological and physiological responses while keeping cells viable. Compliance of the system may change with time, thus requiring recalibration. The purpose of this research was to develop and validate a recalibration protocol for the ZETOS system. Ten reference bodies (RBs) were designed and machined out of aluminum 7075-T6, with a structural rigidity range representative of trabecular bone ($0.628–28.3N∕μm$, or apparent elastic modulus of $40MPa–1.80GPa$). Finite element analysis (FEA) was used to calculate the rigidity of each RB and was validated with physical testing in a universal testing machine. Results from FEA were then used to calibrate the system and relate force, piezoelectric actuator expansion, and specimen compressive deformation through a surface generated by spline interpolation, thus creating a calibration table. Calibration of ZETOS was verified by testing the RBs as well as three custom-made, metal springs and comparing measured rigidity to that calculated by FEA. Mean percent difference of FEA results with respect to those from physical testing was 3.28%. The mean percent difference of RB rigidity found with ZETOS with respect to rigidity found with FEA was 1.12% and for the metal springs, the mean percent difference was 1.74%. The calibration procedure for the ZETOS bone loading system has been successfully applied and verified. The use of RBs and FEA allows users to easily and periodically evaluate and recalibrate the system. Accuracy in studies of human bone mechanotransduction in a controlled environment can therefore be achieved. The recalibration procedure is relevant for other ZETOS users and may serve as the basis for calibration of other testing systems for small specimens of compliant materials.

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## Figures

Figure 1

(a) Schematic showing the ZETOS loading unit. The load cell, PZA, and bone chamber are arranged in series within the system. (b) A closer look at the bone chamber, where the trabecular bone sample is placed between two sapphire cylinders. The loading end of the PZA is comprised of a convex sapphire surface to account for nonparallel surfaces most likely present in the cylindrical bone sample.

Figure 6

Interpolated surface based on ZETOS force, expansion, and FEA compression of ten RBs

Figure 2

(a) Schematic of a section view of a reference body (RB) and the stainless steel rod (not to scale). As the piston undergoes compressive load, the diaphragm deflects causing the downward displacement of the rod. (b) Geometry of a RB in three-dimensional representation, sectioned through the middle (rod not shown).

Figure 3

Experimental setup for calibration of the strain gage by measuring the PZA expansion. Voltage is applied to the PZA causing its expansion. The lack of load allows the measurement of rod displacement obtained with the fiber optic sensor to directly represent PZA expansion without system compliance effects.

Figure 4

Diagram (side view) of experimental setup used in the universal testing machine. The fixture has a c-shaped geometry (when viewed from the top) with the concavity on the front, allowing the microscope lens to be located near the rod tip for recording of digital images. Note also that the RB rests on a steel base, a solid block with a hole for the rod, to mimic the ZETOS system. This base is also included in the FEA. The diagram also shows the ball bearing element between the RB and the compression platen.

Figure 5

Schematic showing the cross section of a cylindrical metallic spring specimen between two sapphire cylinders

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