Iron Transport across Brain Barriers: Model and Numerical Parameter Estimation
Abstract
:1. Introduction
1.1. Biological Background
1.2. Previous Mathematical Models
1.3. Aim of the Work
2. Methods
2.1. Mathematical Model
(1) | |
(2) | |
(3) |
2.2. Parameters Estimation
3. Results
3.1. Estimation of One Parameter
3.2. Estimation of Two Parameters
3.3. Estimation of Three Parameters
4. Discussion
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Parameter | Description | Normal Value | High Rate Value |
---|---|---|---|
E | Iron intake into the blood from food (mg/L) | 0.22 | 0.22 |
k | Iron consumption from blood and excretion mechanisms | 0.23 | 0.23 |
Kinetic constant rate for iron entering from blood to CSF across BCSFB | 0.0002 | 0.001 | |
Kinetic constant rate for iron returning from CSF and brain to blood | 0.05 | 0.08 | |
Kinetic constant rate for iron passing from CSF to ISF | 0.8 | 0.8 | |
Kinetic constant rate for iron passing from ISF to CSF | 1 | 1 | |
Kinetic constant rate for iron entering from blood to brain (consequently ISF), across BBB | 0.002 | 0.005 | |
Kinetic constant rate for iron returning from the brain to blood | 1 × 10−6 | 5 × 10−6 |
N° of Estimated Parameters | Noise | Parameter | Estimation for PC | Estimation for HRC | ||
---|---|---|---|---|---|---|
1 | 0 | 0.0500 | 4.2689 × 10−15 | 0.0800 | 3.8223 × 10−15 | |
1.0000 | 1.1465 × 10−15 | 1.0000 | 7.0460 × 10−13 | |||
0.8000 | 2.3891 × 10−11 | 0.8000 | 8.4539 × 10−15 | |||
0.0020 | 0.6540 | 0.0050 | 0.9318 | |||
0.001 | 0.0501 | 5.8056 × 10−6 | 0.0799 | 1.9159 × 10−6 | ||
1.0014 | 1.2567 × 10−6 | 1.0041 | 2.8066 × 10−5 | |||
0.7926 | 3.5431 × 10−5 | 0.7977 | 1.0568 × 10−5 | |||
0.0020 | 0.5723 | 0.0050 | 0.4659 | |||
0.01 | 0.0491 | 4.9117 × 10−4 | 0.0818 | 0.0011 | ||
0.9356 | 0.0023 | 0.9647 | 0.0019 | |||
0.7457 | 0.0024 | 0.7780 | 0.0010 | |||
0.0020 | 0.4909 | 0.0050 | 0.9318 | |||
2 | 0 | 0.0500 | 3.3379 × 10−14 | 0.0800 | 7.9000 × 10−15 | |
1.0000 | 1.0000 | |||||
0.0500 | 3.4623 × 10−15 | 0.0800 | 1.2001 × 10−4 | |||
0.8000 | 0.8000 | |||||
0.8000 | 0.0079 | 0.5998 | 0.0013 | |||
1.0000 | 0.7692 | |||||
0.0930 | 0.0542 | 0.0800 | 0.0428 | |||
0.0037 | 0.0050 | |||||
1.0000 | 0.3967 | 0.9909 | 0.5573 | |||
0.0020 | 0.0050 | |||||
0.001 | 0.0503 | 3.5199 × 10−5 | 0.0800 | 1.2536 × 10−5 | ||
0.9900 | 1.0007 | |||||
0.0499 | 5.0687 × 10−6 | 0.0798 | 1.0124 × 10−5 | |||
0.7968 | 0.7967 | |||||
0.0865 | 0.0324 | 0.6639 | 0.2220 | |||
0.1594 | 0.8440 | |||||
0.0503 | 0.2401 | 0.0861 | 0.1399 | |||
0.0020 | 0.0054 | |||||
1.0223 | 0.1548 | 0.9963 | 0.5516 | |||
0.0020 | 0.0050 | |||||
0.01 | 0.0530 | 0.0052 | 0.0824 | 0.0044 | ||
0.9310 | 0.9339 | |||||
0.0505 | 0.0232 | 0.0791 | 0.1628 | |||
0.7411 | 0.7824 | |||||
0.0036 | 1.0892 × 10−4 | 0.0767 | 5.0163 × 10−4 | |||
0.0610 | 0.1621 | |||||
0.1105 | 0.1275 | 0.0850 | 0.0238 | |||
0.0043 | 0.0053 | |||||
0.8054 | 0.2116 | 0.9838 | 0.4631 | |||
0.0019 | 0.0049 | |||||
3 | 0 | 1.4080 | 6.4164 × 10−4 | 1.5710 | 0.0920 | |
2.6049 | 2.7064 | |||||
0.0620 | 0.1121 | |||||
0.0500 | 0.1364 | 0.0800 | 0.0157 | |||
1.2887 | 0.9199 | |||||
1.0443 | 0.7302 | |||||
0.001 | 0.8329 | 41.6743 | 0.6466 | 0.1379 | ||
1.9264 | 1.6499 | |||||
0.0366 | 0.0459 | |||||
0.0500 | 4.5772 × 10−5 | 0.0799 | 0.4450 | |||
1.3334 | 0.3549 | |||||
1.0806 | 0.2391 | |||||
0.01 | 1.9090 | 9.6464 | 1.0405 | 0.0699 | ||
3.1090 | 2.0884 | |||||
0.0844 | 0.0743 | |||||
0.0486 | 0.0030 | 0.0809 | 0.5067 | |||
0.1231 | 2.2613 | |||||
0.0451 | 1.9322 |
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Ficiarà, E.; Stura, I.; Guiot, C. Iron Transport across Brain Barriers: Model and Numerical Parameter Estimation. Mathematics 2022, 10, 4461. https://doi.org/10.3390/math10234461
Ficiarà E, Stura I, Guiot C. Iron Transport across Brain Barriers: Model and Numerical Parameter Estimation. Mathematics. 2022; 10(23):4461. https://doi.org/10.3390/math10234461
Chicago/Turabian StyleFiciarà, Eleonora, Ilaria Stura, and Caterina Guiot. 2022. "Iron Transport across Brain Barriers: Model and Numerical Parameter Estimation" Mathematics 10, no. 23: 4461. https://doi.org/10.3390/math10234461
APA StyleFiciarà, E., Stura, I., & Guiot, C. (2022). Iron Transport across Brain Barriers: Model and Numerical Parameter Estimation. Mathematics, 10(23), 4461. https://doi.org/10.3390/math10234461