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Research Papers

Computational Modeling of Developing Cartilage Using Experimentally Derived Geometries and Compressive Moduli

[+] Author and Article Information
Roy J. Lycke

Weldon School of Biomedical Engineering,
Purdue University,
206 South Martin Jischke Drive,
West Lafayette, IN 47907
e-mail: rlycke@purdue.edu

Michael K. Walls

Weldon School of Biomedical Engineering,
Purdue University,
206 South Martin Jischke Drive,
West Lafayette, IN 47907
e-mail: mkwalls@purdue.edu

Sarah Calve

Weldon School of Biomedical Engineering,
Purdue University,
206 South Martin Jischke Drive,
West Lafayette, IN 47907
e-mail: scalve@purdue.edu

1Corresponding author.

Manuscript received May 29, 2018; final manuscript received March 6, 2019; published online May 6, 2019. Assoc. Editor: Paul Barbone.

J Biomech Eng 141(8), 081002 (May 06, 2019) (8 pages) Paper No: BIO-18-1256; doi: 10.1115/1.4043208 History: Received May 29, 2018; Revised March 06, 2019

During chondrogenesis, tissue organization changes dramatically. We previously showed that the compressive moduli of chondrocytes increase concomitantly with extracellular matrix (ECM) stiffness, suggesting cells were remodeling to adapt to the surrounding environment. Due to the difficulty in analyzing the mechanical response of cells in situ, we sought to create an in silico model that would enable us to investigate why cell and ECM stiffness increased in tandem. The goal of this study was to establish a methodology to segment, quantify, and generate mechanical models of developing cartilage to explore how variations in geometry and material properties affect strain distributions. Multicellular geometries from embryonic day E16.5 and postnatal day P3 murine cartilage were imaged in three-dimensional (3D) using confocal microscopy. Image stacks were processed using matlab to create geometries for finite element analysis using ANSYS. The geometries based on confocal images and isolated, single cell models were compressed 5% and the equivalent von Mises strain of cells and ECM were compared. Our simulations indicated that cells had similar strains at both time points, suggesting that the stiffness and organization of cartilage changes during development to maintain a constant strain profile within cells. In contrast, the ECM at P3 took on more strain than at E16.5. The isolated, single-cell geometries underestimated both cell and ECM strain and were not able to capture the similarity in cell strain at both time points. We expect this experimental and computational pipeline will facilitate studies investigating other model systems to implement physiologically derived geometries.

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Figures

Grahic Jump Location
Fig. 1

Model system and experimental workflow: (a) relative scale of E16.5 embryo and P3 pup. Bars = 5 mm, (b) immunohistochemical staining for perlecan (red) and type VI collagen (green) reveal a dramatic change in ECM organization from E16.5 to P3. Confocal image stacks to build geometries were acquired starting at the articular surface (*). Nuclei stained with 4′,6-diamidino-2-phenylindole (blue). Bars = 25 μm, and (c) workflow showing the processing of a P3 femur from harvest to analysis in ANSYS. (See color figure online.)

Grahic Jump Location
Fig. 2

Single-cell simulations underestimate cell strain. Geometries based off E16.5 cartilage were compressed 5% in the –z direction and modeled using compressive moduli from Ref. [11]. Materials were mixed to determine the effect of different cell/ECM stiffness ratios on calculated strain. Strain in isolated cells (ϕE16.5 cell = 0.25) was similar to strain in all cells. However, analysis of all cells versus core cells (i.e., any cells at least 1 μm away from a boundary) indicated that inclusion of strain from boundary cells significantly reduced the strain for all cell/ECM combinations (***p < 0.001, ****p <0.0001; Tukey's post hoc test). When boundary cells were removed from the simulation, strain was also significantly greater than all cells (p < 0.0001) and core cells (p < 0.001). Two-way ANOVA revealed the effect of cell/ECM combination (p < 0.001) and geometry (p < 0.0001) on strain were significant. Error bars = standard deviation. N = 3 biological replicates, where each biological replicate is an average of 3 ROIs.

Grahic Jump Location
Fig. 3

Effect of spacing on cell strain. The in-line conformation had a larger influence on strain than side-by-side and generated values that more closely approximated the core cell strain determined using the true geometries. Variation in cell strain increased as spacing decreased. The amount of ECM between outer cell edges and the boundary of the simulation was keptconstant as distance between cells varied, and the volume fraction of the cells was constant for the two orientations for agiven cell spacing. Simulations used the E16.5 WT/WT materialcombination. Geometries were compressed 5% in the –z direction (arrow) and the cell or ECM strain was averaged across intracellular nodes of both cells. Error bars = standard deviation. See color figures online.

Grahic Jump Location
Fig. 4

Strain in core cells from E16.5 and P3 geometries showed similar trends when material properties were altered. (a) Cell strain in the isolated geometries indicated that strain increased approximately 8% in cells from E16.5 to P3; however, the strain remained relatively constant when the core cells of the true geometry were analyzed. Two-way ANOVA revealed the effect of cell/ECM combination (p < 0.01) and age (p < 0.05) were significant on strain. (b) Both isolated and true geometries showed an increase in ECM strain between E16.5 and P3. There was little variation of ECM strain due to age or material in the isolated geometries. ECM strain at P3 was significantly higher than at E16.5 for all cell/ECM combinations (****p < 0.0001; Tukey's post hoc test). Two-way ANOVA indicated the effect of cell/ECM combination (p < 0.01) and age (p < 0.0001) was significant on strain. Geometries were compressed 5% and the cell or ECM strain was averaged. Error bars = standard deviation. N = 3 biological replicates, where each biological replicate is an average of 3 ROIs.

Grahic Jump Location
Fig. 5

Age-specific geometry affects strain more than cell/ECM material properties. There was no significant difference between strains when E16.5 geometries were simulated with E16.5 or P3 material properties, and vice versa. Two-way ANOVA indicated that age/geometry combination had no effect on cell strain, whereas cell/ECM combination did (p < 0.01). For ECM, both age/geometry (p < 0.0001) and cell/ECM combination (p < 0.01) had an effect. For each cell/ECM combination, simulations that used the P3 geometry had significantly higher strains than those that used E16.5 geometries (bars, p < 0.0001; Tukey's post hoc test); however, there was no difference when the same geometry was used and materials were varied. Geometries were compressed 5% and the core cell or ECM strain was averaged. Error bars = standard deviation. N = 3 biological replicates, where each biological replicate is an average of 3 ROIs.

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