TY  - JOUR
AU  - Farias, Matheus dos Santos
PY  - 2026
DA  - 2026/09/20
TI  - From the Formalism of the Delayed Mackey-Glass Equation and Its Application to Leukemia Growth
JO  - Journal of Numerical Simulations in Physics and Mathematics
T2  - Journal of Numerical Simulations in Physics and Mathematics
JF  - Journal of Numerical Simulations in Physics and Mathematics
VL  - 2
IS  - 2
SP  - 130
EP  - 140
DO  - 10.62762/JNSPM.2026.604346
UR  - https://www.icck.org/article/abs/JNSPM.2026.604346
KW  - Mackey-Glass equation
KW  - leukemia growth
KW  - delay differential equations
KW  - mathematical oncology
KW  - radiotherapy
KW  - numerical simulation
AB  - This study develops a mathematically explicit and computationally reproducible framework based on the delayed Mackey--Glass equation for leukemia-related population dynamics. The classical model is formulated from a population balance law, delayed maturation, and saturating nonlinear feedback, and is then extended by a stage-dependent treatment-control term. Parameters that are not identifiable from the available clinical information are taken from established mathematical and hematopoietic literature, while the treatment-control coefficients are constrained phenomenologically by the modeled burden states. A brief systematic literature search was used to characterize previous Mackey--Glass applications in hematopoiesis and leukemia and to define the methodological gap addressed here. A published case of acute myeloid leukemia-associated myeloid sarcoma treated with radiotherapy and azacitidine provides the clinical treatment schedule and volumetric constraint. The model output is mapped explicitly to a three-dimensional point-cloud representation through a deterministic population-to-point transformation, while the observed reduction from 560~cm$^3$ to 157~cm$^3$ after 19.8~Gy provides an independent constraint for a population-to-volume mapping. Sensitivity to the delay and Hill exponent is examined, and the delay-adapted fourth-order Runge--Kutta implementation is compared with an independent adaptive method-of-steps reference. The resulting framework integrates formal derivation, structured literature evidence, treatment modeling, numerical verification, and clinically anchored visualization without presenting the point cloud as a patient-specific radiological reconstruction.
SN  - 3068-9082
PB  - Institute of Central Computation and Knowledge
LA  - English
ER  - 

@article{Farias2026From,
  author = {Matheus dos Santos Farias},
  title = {From the Formalism of the Delayed Mackey-Glass Equation and Its Application to Leukemia Growth},
  journal = {Journal of Numerical Simulations in Physics and Mathematics},
  year = {2026},
  volume = {2},
  number = {2},
  pages = {130-140},
  doi = {10.62762/JNSPM.2026.604346},
  url = {https://www.icck.org/article/abs/JNSPM.2026.604346},
  abstract = {This study develops a mathematically explicit and computationally reproducible framework based on the delayed Mackey--Glass equation for leukemia-related population dynamics. The classical model is formulated from a population balance law, delayed maturation, and saturating nonlinear feedback, and is then extended by a stage-dependent treatment-control term. Parameters that are not identifiable from the available clinical information are taken from established mathematical and hematopoietic literature, while the treatment-control coefficients are constrained phenomenologically by the modeled burden states. A brief systematic literature search was used to characterize previous Mackey--Glass applications in hematopoiesis and leukemia and to define the methodological gap addressed here. A published case of acute myeloid leukemia-associated myeloid sarcoma treated with radiotherapy and azacitidine provides the clinical treatment schedule and volumetric constraint. The model output is mapped explicitly to a three-dimensional point-cloud representation through a deterministic population-to-point transformation, while the observed reduction from 560~cm\$^3\$ to 157~cm\$^3\$ after 19.8~Gy provides an independent constraint for a population-to-volume mapping. Sensitivity to the delay and Hill exponent is examined, and the delay-adapted fourth-order Runge--Kutta implementation is compared with an independent adaptive method-of-steps reference. The resulting framework integrates formal derivation, structured literature evidence, treatment modeling, numerical verification, and clinically anchored visualization without presenting the point cloud as a patient-specific radiological reconstruction.},
  keywords = {Mackey-Glass equation, leukemia growth, delay differential equations, mathematical oncology, radiotherapy, numerical simulation},
  issn = {3068-9082},
  publisher = {Institute of Central Computation and Knowledge}
}