Modeling of Optimal Targeted Therapies Using Drug-Loaded Magnetic Nanoparticles for Liver Cancer

Mellal, Lyes; Folio, David; Belharet, Karim; Ferreira, Antoine

doi:10.1109/tnb.2016.2535380

Cited by 14 publications

(13 citation statements)

References 32 publications

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“…The short aggregate transversal stabilization time calculated is compatible with these higher velocities. Theoretical models exist to predict how many aggregates will be needed for one‐lobe embolization, but in vivo MRN experiments are needed to give an accurate estimate on the time required for one‐lobe embolization. Third, the efficacy of magnetic microbeads as an embolizing agent cannot be evaluated by the current study and, although it is expected to be equivalent to that of beads used for DEB‐TACE, only in vivo MRN experiments will allow to answer this question.…”

Section: Discussionmentioning

confidence: 99%

Selective embolization with magnetized microbeads using magnetic resonance navigation in a controlled‐flow liver model

Michaud

Plantefève

et al. 2018

Medical Physics

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Purpose The purpose of this study was to demonstrate the feasibility of using a custom gradient sequence on an unmodified 3T magnetic resonance imaging (MRI) scanner to perform magnetic resonance navigation (MRN) by investigating the blood flow control method in vivo, reproducing the obtained rheology in a phantom mimicking porcine hepatic arterial anatomy, injecting magnetized microbead aggregates through an implantable catheter, and steering the aggregates across arterial bifurcations for selective tumor embolization. Materials and Methods In the first phase, arterial hepatic velocity was measured using cine phase‐contrast imaging in seven pigs under free‐flow conditions and controlled‐flow conditions, whereby a balloon catheter is used to occlude arterial flow and saline is injected at different rates. Three of the seven pigs previously underwent selective lobe embolization to simulate a chemoembolization procedure. In the second phase, the measured in vivo controlled‐flow velocities were approximately reproduced in a Y‐shaped vascular bifurcation phantom by injecting saline at an average rate of 0.6 mL/s with a pulsatile component. Aggregates of 200‐μm magnetized particles were steered toward the right or left hepatic branch using a 20‐mT/m MRN gradient. The phantom was oriented at 0°, 45°, and 90° with respect to the B0 magnetic field. The steering differences between left–right gradient and baseline were calculated using Fisher's exact test. A theoretical model of the trajectory of the aggregate within the main phantom branch taking into account gravity, magnetic force, and hydrodynamic drag was also designed, solved, and validated against the experimental results to characterize the physical limitations of the method. Results At an injection rate of 0.5 mL/s, the average flow velocity decreased from 20 ± 15 to 8.4 ± 5.0 cm/s after occlusion in nonembolized pigs and from 13.6 ± 2.0 to 5.4 ± 3.0 cm/s in previously embolized pigs. The pulsatility index measured to be 1.7 ± 1.8 and 1.1 ± 0.1 for nonembolized and embolized pigs, respectively, decreased to 0.6 ± 0.4 and 0.7 ± 0.3 after occlusion. For MRN performed at each orientation, the left–right distribution of aggregates was 55%, 25%, and 75% on baseline and 100%, 100%, and 100% (P < 0.001, P = 0.003, P = 0.003) after the application of MRN, respectively. According to the theoretical model, the aggregate reaches a stable transverse position located toward the direction of the gradient at a distance equal to 5.8% of the radius away from the centerline within 0.11 s, at which point the aggregate will have transited through a longitudinal distance of 1.0 mm from its release position. Conclusion In this study, we showed that the use of a balloon catheter reduces arterial hepatic flow magnitude and variation with the aim to reduce steering failures caused by fast blood flow rates and low magnetic steering forces. A mathematical model confirmed that the reduced flow rate is low enough to maximize steering ratio. After reproducing the flow rate in a vascular bifur...

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Section: Discussionmentioning

confidence: 99%

Selective embolization with magnetized microbeads using magnetic resonance navigation in a controlled‐flow liver model

Michaud

Plantefève

et al. 2018

Medical Physics

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“…15 and 16). 40,41 Logistic and Gompertz model structures were applied under this assumption. A model structure displayed by Eq.…”

Section: Empirical Model Structures Describing Therapeutic Effectmentioning

confidence: 99%

“…16. Although as far as we know there is no clinical study that utilized this model framework, it has been used to perform simulations to optimize the delivery of therapeutic agents for enhancing targeted therapies for liver cancer 41 and to investigate the optimization of antiangiogenic treatment. 42 Immune system.…”

Section: Empirical Model Structures Describing Therapeutic Effectmentioning

confidence: 99%

“…39 In addition, the effect of angiogenesis inhibition treatment can also be incorporated by introducing a first-order drug exposure dependent decline term (Eq. 22) on the dynamics of tumor vascular support, 40,41 when the vascular support was assumed to determine the carrying capacity of tumor (Eqs. 15 and 16).…”

Section: Tumor Dynamics and Resistance Evolution Modelsmentioning

confidence: 99%

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A Review of Mathematical Models for Tumor Dynamics and Treatment Resistance Evolution of Solid Tumors

Yin

Moes

Hasselt

et al. 2019

CPT Pharmacom & Syst Pharma

129

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Increasing knowledge of intertumor heterogeneity, intratumor heterogeneity, and cancer evolution has improved the understanding of anticancer treatment resistance. A better characterization of cancer evolution and subsequent use of this knowledge for personalized treatment would increase the chance to overcome cancer treatment resistance. Model‐based approaches may help achieve this goal. In this review, we comprehensively summarized mathematical models of tumor dynamics for solid tumors and of drug resistance evolution. Models displayed by ordinary differential equations, algebraic equations, and partial differential equations for characterizing tumor burden dynamics are introduced and discussed. As for tumor resistance evolution, stochastic and deterministic models are introduced and discussed. The results may facilitate a novel model‐based analysis on anticancer treatment response and the occurrence of resistance, which incorporates both tumor dynamics and resistance evolution. The opportunities of a model‐based approach as discussed in this review can be of great benefit for future optimizing and personalizing anticancer treatment.

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“…Unfortunately, the results of various experimental and clinical studies (see [36] and the references cited therein) have not produced clear guidelines on how to proceed with combined therapies, in part due to the multitude of drugs presently available and patient-specific interactions of multiple drugs. Hence, mathematicians and physicians have turn towards the framework of optimal control to infer protocols, dosages and timings that maximise tumour reduction and minimise harmful side-effects [27,30,31,37,39]. To contribute to this effort, we study an optimal control problem with the model (1.1) as the state system, and as controls we work with the boundary nutrient supply w 1 = σ B , the cytotoxic coefficient w 2 = m(t) and the antiangiogentic coefficient w 3 = s(t).…”

Section: Introductionmentioning

confidence: 99%

Sparse optimal control of a phase field tumour model with mechanical effects

Garcke,

Lam,

Signori

2020

Preprint

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In this paper, we study an optimal control problem for a macroscopic mechanical tumour model based on the phase field approach. The model couples a Cahn-Hilliard type equation to a system of linear elasticity and a reaction-diffusion equation for a nutrient concentration. By taking advantage of previous analytical well-posedness results established by the authors, we seek optimal controls in the form of a boundary nutrient supply, as well as concentrations of cytotoxic and antiangiogenic drugs that minimise a cost functional involving mechanical stresses. Special attention is given to sparsity effects, where with the inclusion of convex non-differentiable regularisation terms to the cost functional, we can infer from the first-order optimality conditions that the optimal drug concentrations can vanish on certain time intervals.

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Modeling of Optimal Targeted Therapies Using Drug-Loaded Magnetic Nanoparticles for Liver Cancer

Cited by 14 publications

References 32 publications

Selective embolization with magnetized microbeads using magnetic resonance navigation in a controlled‐flow liver model

Selective embolization with magnetized microbeads using magnetic resonance navigation in a controlled‐flow liver model

A Review of Mathematical Models for Tumor Dynamics and Treatment Resistance Evolution of Solid Tumors

Sparse optimal control of a phase field tumour model with mechanical effects

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