Mellal, Lyès and Folio, David and Belharet, Karim and Ferreira, Antoine


To enhance locoregional therapies for liver cancer treatment, we propose in this study a mathematical model to optimize the transcatheter arterial delivery of therapeutical agents. To maximize the effect of the treatment and minimize adverse effects on the patient, different mathematical models of the tumor growth are considered in this study to find the optimal number of the therapeutic drug-loaded magnetic nanoparticles to be administered. Three types of therapy models are considered, e.g. angiogenesis inhibition therapy, chemotherapy and radiotherapy. We use state-dependent Riccati equations (SDRE) as an optimal control methodology framework to the Hahnfeldt's tumor growth formulation. Based on this, design optimal rules are derived for each therapy to reduce the growth of a tumor through the administration of appropriate dose of anti-angiogenic, radio- and chemo-therapeutic agents. Simulation results demonstrate the validity of the proposed optimal delivery approach, leading to reduced intervention time, low drug administration rates and optimal targeted delivery.


  • cancer
  • drug delivery systems
  • liver
  • magnetic particles
  • nanomedicine
  • nanoparticles
  • radiation therapy
  • tumours
  • hahnfeldt tumor growth formulation
  • angiogenesis inhibition therapy
  • chemotherapy
  • liver cancer treatment
  • locoregional therapies
  • mathematical model
  • radiotherapy
  • state-dependent riccati equations
  • therapeutic drug-loaded magnetic nanoparticles
  • therapeutical agents
  • transcatheter arterial delivery
  • tumor growth model
  • cancer
  • drugs
  • liver
  • magnetic resonance imaging
  • mathematical model
  • tumors
  • locoregional therapies
  • magnetic resonance navigation
  • optimal drug delivery
  • optimal tumor control
  • tumor growth model


  title = {Modeling of Optimal Targeted Therapies using Drug-Loaded Magnetic Nanoparticles for the Liver Cancer},
  author = {Mellal, Lyès and Folio, David and Belharet, Karim and Ferreira, Antoine},
  journal = {IEEE Transactions on Nano-Bioscience},
  year = {2016},
  month = apr,
  number = {3},
  pages = {265--274},
  volume = {15},
  doi = {10.1109/TNB.2016.2535380},
  hal = {01305959},
  issn = {1536-1241},
  keywords = {cancer,drug delivery systems,liver,magnetic particles,nanomedicine,nanoparticles,radiation therapy,tumours,Hahnfeldt tumor growth formulation,angiogenesis inhibition therapy,chemotherapy,liver cancer treatment,locoregional therapies,mathematical model,radiotherapy,state-dependent Riccati equations,therapeutic drug-loaded magnetic nanoparticles,therapeutical agents,transcatheter arterial delivery,tumor growth model,Cancer,Drugs,Liver,Magnetic resonance imaging,Mathematical model,Tumors,Locoregional therapies,magnetic resonance navigation,optimal drug delivery,optimal tumor control,tumor growth model}