Mathematical Modeling of Metastatic Cancer Migration through a Remodeling Extracellular Matrix
Abstract
:1. Introduction
2. Methods
2.1. Cancer Cells
2.2. Extracellular Matrix Collagen Fibers
2.3. Enzyme MMP
2.4. Enzyme LOX
2.5. Nondimensionalization and Parameter Values
2.6. Initial and Boundary Conditions
2.7. Numerical Methods and Code Repository
3. Results and Discussion
3.1. Case I: LOX Is Absent
3.2. Case II: LOX Is Present But Not Coupled to the Haptotactic Migration of Cancer Cells
3.3. Case III: LOX Is Present and Is Coupled to the Haptotactic Migration of Cancer Cells
3.4. Sensitivity Analysis
4. Conclusions
Author Contributions
Acknowledgments
Conflicts of Interest
References
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Term | Description | Value | Unit | Sources |
---|---|---|---|---|
L | Reference length | 1 | cm | [33] |
Reference time | 32 | hours | [55,56,57,58] | |
Reference number of cancer cells per volume | cells/cm | [33] | ||
Reference value for | M | [61] | ||
, | Reference value for m, l | M | [47] | |
Diffusion coefficient of cancer cells | cms | [59] | ||
Diffusion coefficient of MMP | cms | [60] | ||
D | Reference chemical diffusion coefficient | cms | [59] | |
Haptotaxis coefficient toward f | cm M s | [32] |
Term | Description | Value | Sources |
---|---|---|---|
Diffusion coefficient of cell | 0.001 | Calculated [59] | |
Rate expression for tumor proliferation | Assumed | ||
Haptotaxis toward f | Calculated [59,61] | ||
Haptotaxis toward | Assumed | ||
Space fraction per unit | 1 | By definition from [40] | |
Space fraction per unit | 1 | By definition from [40] | |
Space fraction per unit | 1 | By definition from [40] | |
Rate constant for MMP cleavage of f | 10 | Estimated from [33] | |
Rate constant for production of f | 0.15 | Estimated from [47] | |
Rate constant for LOX remodeling of f | 18 | Assumed | |
Diffusion of MMP | Calculated [33,59,60] | ||
Rate constant for decay of MMP | Estimated from [33,62] | ||
Rate constant for secretion of MMP by cells | Estimated from [33] | ||
Diffusion coefficient of LOX | Assumed | ||
Rate constant for decay of LOX | Assumed | ||
Rate constant for secretion of LOX by cells | Assumed |
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Nguyen Edalgo, Y.T.; Ford Versypt, A.N. Mathematical Modeling of Metastatic Cancer Migration through a Remodeling Extracellular Matrix. Processes 2018, 6, 58. https://doi.org/10.3390/pr6050058
Nguyen Edalgo YT, Ford Versypt AN. Mathematical Modeling of Metastatic Cancer Migration through a Remodeling Extracellular Matrix. Processes. 2018; 6(5):58. https://doi.org/10.3390/pr6050058
Chicago/Turabian StyleNguyen Edalgo, Yen T., and Ashlee N. Ford Versypt. 2018. "Mathematical Modeling of Metastatic Cancer Migration through a Remodeling Extracellular Matrix" Processes 6, no. 5: 58. https://doi.org/10.3390/pr6050058
APA StyleNguyen Edalgo, Y. T., & Ford Versypt, A. N. (2018). Mathematical Modeling of Metastatic Cancer Migration through a Remodeling Extracellular Matrix. Processes, 6(5), 58. https://doi.org/10.3390/pr6050058