Thermosensitive Liposome-Mediated Drug Delivery in Chemotherapy: Mathematical Modelling for Spatio–temporal Drug Distribution and Model-Based Optimisation
Abstract
:1. Introduction
2. Methods
2.1. Systemic Drug Transport: Pharmacokinetics of TSLs and Anticancer Drug
2.2. Drug Transport in the Tumour Compartment
2.2.1. Transport in Tumour Plasma
2.2.2. Transport in the Tumour Interstitium
2.3. Parameterisation and Initialisation
2.4. Numerical Methods
2.5. Optimisation
3. Results and Discussion
3.1. Simulation Results for the Baseline Scenario
3.2. Comparison of DOX and TOP
3.3. Effects of Drug Release Rates
3.4. Effects of Hyperthermia (HT) Duration
3.5. Optimisation Results
4. Conclusions and Future Perspectives
Author Contributions
Funding
Conflicts of Interest
References
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Symbol | Description | Value | Reference |
---|---|---|---|
Rate constant of TSLs clearance | 9.417 × 10−6 (1/s) | [9] | |
Rate constant of drug clearance | 1.1 × 10−3 (1/s) | [6] | |
Transfer constant from systemic plasma to tissue | 1.6 × 10−3 (1/s) | [6] | |
Transfer constant from tissue to systemic plasma | 4.68 × 10−5 (1/s) | [6] | |
Release rate constant from iTSLs at body temperature | 3 × 10−4 (1/s) | [16] | |
Release rate constant from iTSLs during HT (at 42 °C) | 0.114 (1/s) | [16] | |
Michaelis constant for transmembrane transport | 2.19 × 10−4 (µg/mm3) | [19] | |
Michaelis constant for transmembrane transport | 1.37 (ng/105 cells) | [19] | |
Maximum rate for transmembrane transport | 0.28 (ng/(105 cells·min)) | [19] | |
Rate for passive intracellular uptake | 6.33 × 10−4 (1/s) | Fit to [6] | |
Volume of systemic plasma | 3.04 (L) | [9] | |
Volume of body tissue | 64.47 (L) | [9] | |
Volume of tumour tissue | 8.82 × 10−2 (L) | Estimated based on a spherical tumour with a radius of 2.7 cm | |
Volume fraction of tumour plasma | 0.07452 | [9] | |
Volume fraction of tumour EES | 0.454 | [9] | |
Volume fraction of intracellular space | 0.454 | [9] | |
Blood perfusion rate | 0.018 (1/s) | [9] | |
Haematocrit for tumour microvasculature | 0.19 | [9] | |
Permeability surface area product for drugs | 2.53 × 10−3 (1/s) (TOP) 7 × 10−3 (1/s) (DOX) | Estimated based on molecular size [9] | |
Permeability surface area product for TSL | 4.76 × 10−6 (1/s) (TOP) 2.38 × 10−5 (1/s) (DOX) | Estimated using the , and of DOX and TOP respectively | |
Diffusive permeability for drugs | 3.61 × 10−7 (m/s) (TOP) 1 × 10−6 (m/s) (DOX) | Estimated based on molecular size [19] | |
Diffusive permeability for TSLs and iTSLs | 3.4 × 10−9 (m/s) | [19] | |
Diffusion coefficient | 4.123 × 10−10 (m2/s) (TOP) 1.578 × 10−10 (m2/s) (DOX) | Estimated based on molecular size [12] | |
Diffusion coefficient for TSLs and iTSLs | 9 × 10−12 (m2/s) | [20] | |
Tumour capillary radius | 10 () | [12] | |
Tumour cord radius | 120 () | [12] | |
Volume of single tumour cell | 1 × 10−6 (mm3/cell) | [19] | |
Total dose | 49 (mg) | Calculated at a dose of 0.7 mg/kg in a 70 kg human |
Weighting Factor, w1, for the Systemic Plasma Conc. | Weighting Factor, w2, for the Intracellular Conc. | kr37 (10−4 s−1) | kr42 (s−1) | Hyperthermia Duration (s) | Systemic Plasma Concentration (μg/mL) | Intracellular Concentration (ng/105 cells) |
---|---|---|---|---|---|---|
0 | 1 | 0.3 | 1.14 | 3600 | 0.26 | 0.56 |
0.25 | 0.75 | 0.3 | 1.1 | 3600 | 0.25 | 0.56 |
0.5 | 0.5 | 0.3 | 0.7 | 3600 | 0.24 | 0.55 |
0.75 | 0.25 | 0.3 | 0.13 | 3600 | 0.21 | 0.48 |
1 | 0 | 0.3 | 0.0114 | 3600 | 0.18 | 0.19 |
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Huang, Y.; Gu, B.; Liu, C.; Stebbing, J.; Gedroyc, W.; Thanou, M.; Xu, X.Y. Thermosensitive Liposome-Mediated Drug Delivery in Chemotherapy: Mathematical Modelling for Spatio–temporal Drug Distribution and Model-Based Optimisation. Pharmaceutics 2019, 11, 637. https://doi.org/10.3390/pharmaceutics11120637
Huang Y, Gu B, Liu C, Stebbing J, Gedroyc W, Thanou M, Xu XY. Thermosensitive Liposome-Mediated Drug Delivery in Chemotherapy: Mathematical Modelling for Spatio–temporal Drug Distribution and Model-Based Optimisation. Pharmaceutics. 2019; 11(12):637. https://doi.org/10.3390/pharmaceutics11120637
Chicago/Turabian StyleHuang, Yu, Boram Gu, Cong Liu, Justin Stebbing, Wladyslaw Gedroyc, Maya Thanou, and Xiao Yun Xu. 2019. "Thermosensitive Liposome-Mediated Drug Delivery in Chemotherapy: Mathematical Modelling for Spatio–temporal Drug Distribution and Model-Based Optimisation" Pharmaceutics 11, no. 12: 637. https://doi.org/10.3390/pharmaceutics11120637
APA StyleHuang, Y., Gu, B., Liu, C., Stebbing, J., Gedroyc, W., Thanou, M., & Xu, X. Y. (2019). Thermosensitive Liposome-Mediated Drug Delivery in Chemotherapy: Mathematical Modelling for Spatio–temporal Drug Distribution and Model-Based Optimisation. Pharmaceutics, 11(12), 637. https://doi.org/10.3390/pharmaceutics11120637