Autologous Gradient Formation under Differential Interstitial Fluid Flow Environments
Abstract
:1. Introduction
2. Materials and Methods
2.1. Assumptions of the Model
2.2. Equations and Implementation of the Model
2.3. Conditions and Quantitative Values Used in the Model
3. Results
3.1. Effects of Transport Parameter Changes on Pericellular Gradients
3.2. Directionality of Flow Alters Gradient
3.3. Temporal Fluctuations in Velocity Yield Variable Gradients
3.4. Background Concentration Can Negate Bound CXCL12 Gradient
3.5. The Invading Cell Needs to Be a Certain Distance from Tumor Border for Gradient to Develop
3.6. Cell Type and Morphology Affects Gradient Formation
4. Discussion
5. Conclusions
Supplementary Materials
Author Contributions
Funding
Institutional Review Board Statement
Data Availability Statement
Conflicts of Interest
References
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Parameter | Variable | Value | Unit | Source |
---|---|---|---|---|
Density of fluid | ρ | 1 | g/mL | Anne Lui, Can J Anaesth, 1998 [39] |
Dynamic viscosity of fluid | µ | 0.7–1 | mPa·s | Bloomfield, Pediatr Neurosurg, 1998 [40] |
Temperature | T | 310.15 | K | Physiological temp |
Inlet velocity | v | 0.1–100 | µm/s | Munson JM, Can Man and Res, 2014 [7] |
Porosity | ε | 0.3 | Linninger A, IEEE Trans. on Biomed. Eng. 2007 [41] | |
Permeability | κ | 1.00 × 10−11 | cm2 | Munson JM, Cancer Research 2013 [18] |
Diffusion coefficient, chemokine | D_cxcl12 | 120 | µm2/s | Fleury M, Biophysics Journal, 2006 [34] |
Diffusion coefficient, protease | D_protease | 80 | µm2/s | Fleury M, Biophysics Journal, 2006 [34] |
Mass transfer coefficient, chemokine | k_cxcl12 | 2.80 × 10−5 | m/s | Calculated Value |
Mass transfer coefficient, protease | k_protease | 1.60 × 10−5 | m/s | Calculated Value |
Bulk concentration, chemokine | bulk_cxcl12 | 100 | nM | Estimated Value |
Bulk concentration, protease | bulk_protease | 1 | nM | Estimated Value |
Heparan sulfate concentration | HS | 2.60 × 10−3 | mM | Estimated Value |
Radius of sphere | r | 5.00 × 10−6 | M | Approximate Cell Diameter |
Chemokine binding rate | k_on | 9.30 × 104 | 1/(M·s) | Munson JM, Cancer Research 2013 [18] |
Chemokine unbinding rate | k_off | 1.16 × 10−5 | 1/s | Munson JM, Cancer Research 2013 [18] |
Chemokine release rate from protease | k_rel | 1.00 × 104 | 1/(M·s) | Estimated Value |
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Stine, C.A.; Munson, J.M. Autologous Gradient Formation under Differential Interstitial Fluid Flow Environments. Biophysica 2022, 2, 16-33. https://doi.org/10.3390/biophysica2010003
Stine CA, Munson JM. Autologous Gradient Formation under Differential Interstitial Fluid Flow Environments. Biophysica. 2022; 2(1):16-33. https://doi.org/10.3390/biophysica2010003
Chicago/Turabian StyleStine, Caleb A., and Jennifer M. Munson. 2022. "Autologous Gradient Formation under Differential Interstitial Fluid Flow Environments" Biophysica 2, no. 1: 16-33. https://doi.org/10.3390/biophysica2010003
APA StyleStine, C. A., & Munson, J. M. (2022). Autologous Gradient Formation under Differential Interstitial Fluid Flow Environments. Biophysica, 2(1), 16-33. https://doi.org/10.3390/biophysica2010003