TY - JOUR
T1 - Inverse problem approaches for mutation laws in heterogeneous tumours with local and nonlocal dynamics
AU - Alwuthaynani, Maher
AU - Eftimie, Raluca
AU - Trucu, Dumitru
N1 - Funding Information:
The first author would like to thank Saudi Arabian Cultural Bureau in the United Kingdom (UKSACB) on behalf of Taif University and the University College of Al-Khurmah in Saudi Arabia for supporting and sponsoring his PhD studies at the University of Dundee.
Publisher Copyright:
© 2022 the Author(s), licensee AIMS Press.
PY - 2022/2/10
Y1 - 2022/2/10
N2 - Cancer cell mutations occur when cells undergo multiple cell divisions, and these mutations can be spontaneous or environmentally-induced. The mechanisms that promote and sustain these mutations are still not fully understood. This study deals with the identification (or reconstruction) of the usually unknown cancer cell mutation law, which lead to the transformation of a primary tumour cell population into a secondary, more aggressive cell population. We focus on local and nonlocal mathematical models for cell dynamics and movement, and identify these mutation laws from macroscopic tumour snapshot data collected at some later stage in the tumour evolution. In a local cancer invasion model, we first reconstruct the mutation law when we assume that the mutations depend only on the surrounding cancer cells (i.e., the ECM plays no role in mutations). Second, we assume that the mutations depend on the ECM only, and we reconstruct the mutation law in this case. Third, we reconstruct the mutation when we assume that there is no prior knowledge about the mutations. Finally, for the nonlocal cancer invasion model, we reconstruct the mutation law that depends on the cancer cells and on the ECM. For these numerical reconstructions, our approximations are based on the finite di erence method combined with the finite elements method. As the inverse problem is ill-posed, we use the Tikhonov regularisation technique in order to regularise the solution. Stability of the solution is examined by adding additive noise into the measurements.
AB - Cancer cell mutations occur when cells undergo multiple cell divisions, and these mutations can be spontaneous or environmentally-induced. The mechanisms that promote and sustain these mutations are still not fully understood. This study deals with the identification (or reconstruction) of the usually unknown cancer cell mutation law, which lead to the transformation of a primary tumour cell population into a secondary, more aggressive cell population. We focus on local and nonlocal mathematical models for cell dynamics and movement, and identify these mutation laws from macroscopic tumour snapshot data collected at some later stage in the tumour evolution. In a local cancer invasion model, we first reconstruct the mutation law when we assume that the mutations depend only on the surrounding cancer cells (i.e., the ECM plays no role in mutations). Second, we assume that the mutations depend on the ECM only, and we reconstruct the mutation law in this case. Third, we reconstruct the mutation when we assume that there is no prior knowledge about the mutations. Finally, for the nonlocal cancer invasion model, we reconstruct the mutation law that depends on the cancer cells and on the ECM. For these numerical reconstructions, our approximations are based on the finite di erence method combined with the finite elements method. As the inverse problem is ill-posed, we use the Tikhonov regularisation technique in order to regularise the solution. Stability of the solution is examined by adding additive noise into the measurements.
KW - Inverse problems
KW - Mutation Identification
KW - Tikhonov Regularisation
KW - Tumour Growth
KW - Mutation identification
KW - Tikhonov regularisation
KW - Tumour growth
UR - http://www.scopus.com/inward/record.url?scp=85124807205&partnerID=8YFLogxK
U2 - 10.3934/mbe.2022171
DO - 10.3934/mbe.2022171
M3 - Article
C2 - 35341271
AN - SCOPUS:85124807205
VL - 19
SP - 3720
EP - 3747
JO - Mathematical Biosciences and Engineering
JF - Mathematical Biosciences and Engineering
SN - 1547-1063
IS - 4
ER -