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Research Paper

Periodic Nanomechanical Stimulation in a Biokinetics Model Identifying Anabolic and Catabolic Pathways Associated With Cartilage Matrix Homeostasis

[+] Author and Article Information
Asit K. Saha

Department of Mathematics and Computer Science and Center for Allaying Health Disparities Through Research and Education (CADRE), Central State University, Wilberforce, OH 45384asaha@centralstate.edu

Sean S. Kohles1

Department of Mechanical and Materials Engineering, Reparative Bioengineering Laboratory, Portland State University, Portland, OR 97201; Department of Surgery, Oregon Health and Science University, Portland, OR 97239kohles@cecs.pdx.edu

1

Corresponding author.

J. Nanotechnol. Eng. Med 1(4), 041001 (Oct 21, 2010) (7 pages) doi:10.1115/1.4002461 History: Received July 15, 2010; Revised August 16, 2010; Published October 21, 2010; Online October 21, 2010

Enhancing the available nanotechnology to describe physicochemical interactions during biokinetic regulation will strongly support cellular and molecular engineering efforts. In a recent mathematical model developed to extend the applicability of a statically loaded, single-cell biomechanical analysis, a biokinetic regulatory threshold was presented (Saha and Kohles, 2010, “A Distinct Catabolic to Anabolic Threshold Due to Single-Cell Static Nanomechanical Stimulation in a Cartilage Biokinetics Model,” J. Nanotechnol. Eng. Med., 1(3), p. 031005). Results described multiscale mechanobiology in terms of catabolic to anabolic pathways. In the present study, we expand the mathematical model to continue exploring the nanoscale biomolecular response within a controlled microenvironment. Here, we introduce a dynamic mechanical stimulus for regulating cartilage molecule synthesis. Model iterations indicate the identification of a biomathematical mechanism balancing the harmony between catabolic and anabolic states. Relative load limits were defined to distinguish between “healthy” and “injurious” biomolecule accumulations. The presented mathematical framework provides a specific algorithm from which to explore biokinetic regulation.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

The schematic network of growth factors and cytokines on a representative chondrocyte. Both growth factors and cytokines stimulate the chondrocyte positively, whereas the resulting effect acts on the ECM in two different pathways.

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Figure 2

ECM molecule accumulation when a periodic mechanical loading of 0.02 is applied at the 10,000th time step. The system is load-free from 0 to <10,000 time steps. Model parameters were derived from previous experiments (15).

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Figure 3

The phase-space dynamics of growth factors and cytokines (anabolic and catabolic actions) after an application of dynamic loading of 0.02 magnitude at the 10,000th time step. The limit cycle here moves clockwise and limits at an internal fixed point. This behavior can be construed as a “dump” oscillation.

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Figure 4

ECM molecule accumulation when an intermediate periodic mechanical loading level of 1.0 is applied at the 10,000th time step. Again, the system is free from loading up to the application of the mechanical stimulation.

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Figure 5

Phase-space dynamics of the growth factor and cytokine response (anabolic and catabolic balances) with a dynamic loading of 1.0 applied at the 10,000th time step. The limit cycle here also moves clockwise toward an internal fixed point. This also shows a dump oscillation although trending toward the steady state in a longer time frame. The system is moving toward a vanishingly small amplitude oscillation.

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Figure 6

ECM molecule accumulation when the highest healthy or maintenance mechanical load of 10.0 is applied at the 10,000th time step

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Figure 7

The steady state balance between anabolic and catabolic pathways with dynamic loading of 10.0 applied after the 10,000th time step. The limit cycle still moves clockwise with a clear “back and forth” oscillation.

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Figure 8

ECM molecule accumulation when an “optimal” or growth periodic mechanical load of 86.2 is applied at the 10,000th time step when initially free from any loading

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Figure 9

The steady state dynamics of anabolic and catabolic pathways with the dynamic load of 86.2 applied at the 10,000th time step. Again, the limit cycle here moves clockwise with a clear oscillation.

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Figure 10

An imbalanced or “catastrophic” response of the ECM molecule accumulations when a mechanical load greater than 86.2 was applied. Here, the steady state condition is never reached with dramatic ECM synthesis and loss exhibited.

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