Blasting neuroblastoma using optimal control of chemotherapy

Collins, Charles T.; Fister, K. Renee; Key, Bethany; Williams, Molly

doi:10.3934/mbe.2009.6.451

Cited by 9 publications

(5 citation statements)

References 24 publications

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“…Second, optimising traditional chemotherapy is a cost-effective way to improve neuroblastoma treatment as the therapeutic agents have already been approved, but the one-size-fits-all rapid COJEC regimen is still the standard. The most relevant studies were published over a decade ago [ 54 , 55 ]. In both studies, only topotecan was considered, and they focused on myelosuppression and cell cycle–specific mechanisms, not evolutionary dynamics and drug resistance mechanisms.…”

Section: Discussionmentioning

confidence: 99%

Mathematical Model of Clonal Evolution Proposes a Personalised Multi-Modal Therapy for High-Risk Neuroblastoma

Italia

Wertheim

Taschner‐Mandl

et al. 2023

Cancers

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Neuroblastoma is the most common extra-cranial solid tumour in children. Despite multi-modal therapy, over half of the high-risk patients will succumb. One contributing factor is the one-size-fits-all nature of multi-modal therapy. For example, during the first step (induction chemotherapy), the standard regimen (rapid COJEC) administers fixed doses of chemotherapeutic agents in eight two-week cycles. Perhaps because of differences in resistance, this standard regimen results in highly heterogeneous outcomes in different tumours. In this study, we formulated a mathematical model comprising ordinary differential equations. The equations describe the clonal evolution within a neuroblastoma tumour being treated with vincristine and cyclophosphamide, which are used in the rapid COJEC regimen, including genetically conferred and phenotypic drug resistance. The equations also describe the agents’ pharmacokinetics. We devised an optimisation algorithm to find the best chemotherapy schedules for tumours with different pre-treatment clonal compositions. The optimised chemotherapy schedules exploit the cytotoxic difference between the two drugs and intra-tumoural clonal competition to shrink the tumours as much as possible during induction chemotherapy and before surgical removal. They indicate that induction chemotherapy can be improved by finding and using personalised schedules. More broadly, we propose that the overall multi-modal therapy can be enhanced by employing targeted therapies against the mutations and oncogenic pathways enriched and activated by the chemotherapeutic agents. To translate the proposed personalised multi-modal therapy into clinical use, patient-specific model calibration and treatment optimisation are necessary. This entails a decision support system informed by emerging medical technologies such as multi-region sequencing and liquid biopsies. The results and tools presented in this paper could be the foundation of this decision support system.

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Section: Discussionmentioning

confidence: 99%

Mathematical Model of Clonal Evolution Proposes a Personalised Multi-Modal Therapy for High-Risk Neuroblastoma

Italia

Wertheim

Taschner‐Mandl

et al. 2023

Cancers

View full text Add to dashboard Cite

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“…We utilize concepts from optimal control techniques that have been applied to other epidemiological models relating to such diseases as cholera and cancer, to name a few (Fister and Panetta [2000], Ledzewicz et al. [2004], Collins et al. [2009], Neilan et al.…”

Section: Optimal Controlmentioning

confidence: 99%

“…The solutions to the state equations can be shown to exist and are bounded using a result from Lukes [1982]. Additionally, one can see a detailed existence proof in Collins et al [2009]. The objective functional is convex on the compact closed set and the state equations are linear functions of the control.…”

Section: Optimal Controlmentioning

confidence: 99%

Optimal Control Applied to Rift Valley Fever

Adongo¹,

Fister²,

Gaff³

et al. 2013

Natural Resource Modeling

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Abstract. Rift Valley Fever (RVF) virus is a mosquito-born pathogen that infects livestock but it also has the capability to infect humans through direct or indirect contact with blood or organs of infected animals and by bites from infected mosquitos. The economic and social cost of the disease to rural populations can lead to a cascade of negative effects on the sustainability of animal and human populations. Vaccines exist to protect against this disease. Through a compartment model depicting the interactions leading to the spread of RVF in Aedes and Culex mosquitos and a livestock population, an optimal control problem is developed to minimize the number of vaccinated livestock at the final time while minimizing the negative effects of the infected Aedes and Culex mosquitos and the cost of the vaccination process. The unique optimal vaccination strategy is produced for given high transmission parameters and numerical results portray that vaccination depends on the level of effectiveness of the protocol.

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“…As current treatment dosages are largely determined by the weight or surface area of the subject, there is almost no way of predicting the efficacy or any adverse effects while the drug is being administered. Mathematical models and controls have been applied towards developing strategies which would determine when and how much of a drug to inject to produce a prolonged and effective therapeutic result [2], [3], [4]. However, the combination of mathematical models with real-time clinical data could assist in providing better quality control in dosing.…”

Section: Introductionmentioning

confidence: 99%

LQR tracking of a delay differential equation model for the study of nanoparticle dosing strategies for cancer therapy

Adhikari

Bracey

Evans

et al. 2013

2013 American Control Conference

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Currently, the most commonly used treatments for cancerous tumors (chemotherapy, radiation, etc.) have almost no method of monitoring the administration of the treatment for adverse effects in real time. Without any real time feedback or control, treatment becomes a "guess and check" method with no way of predicting the effects of the drugs based on the actual bioavailability to the patient's body. One particular drug may be effective for one patient, yet provide no benefit to another. Doctors and scientists do no routinely attempt to quantifiably explain this discrepancy.In this work, mathematical modeling and analysis techniques are joined together with experimentation to gain further insight into the challenges of nanoparticle delivery to tumor sites. There exists a commonly accepted model of drug clearance in the pharmacokinetics community, and it is demonstrated here that this model provides an accurate reflection of reality, as observed in experiment for delivery of gold-coated nanorods. This model is then utilized in a state space feedback control framework to regulate the nanoparticle concentration in the bloodstream. An equal time delay is also introduced in both the state and control input for the purpose of studying alternate dosing strategies. This study will aid in the prediction of the effects of the drugs in a patient's body, thus leading to better models for drug regimen and administration.

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Blasting neuroblastoma using optimal control of chemotherapy

Cited by 9 publications

References 24 publications

Mathematical Model of Clonal Evolution Proposes a Personalised Multi-Modal Therapy for High-Risk Neuroblastoma

Mathematical Model of Clonal Evolution Proposes a Personalised Multi-Modal Therapy for High-Risk Neuroblastoma

Optimal Control Applied to Rift Valley Fever

LQR tracking of a delay differential equation model for the study of nanoparticle dosing strategies for cancer therapy

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