Optimal Finite Cancer Treatment Duration by Using Mixed Vaccine Therapy and Chemotherapy: State Dependent Riccati Equation Control

The main objective of this paper is to propose an optimal finite duration treatment method for cancer. A mathematical model is proposed to show the interactions between healthy and cancerous cells in the human body. To extend the existing models, the effect of vaccine therapy and chemotherapy are also added to the model. The equilibrium points and the related local stability are derived and discussed. It is shown that the dynamics of the cancer model must be changed and modified for finite treatment duration. Therefore, the vaccine therapy is used to change the parameters of the system and the chemotherapy is applied for pushing the system to the domain of attraction of the healthy state. For optimal chemotherapy, an optimal control is used based on state dependent Riccati equation (SDRE). It is shown that, in spite of eliminating the treatment, the system approaches the healthy state conditions. The results show that the development of optimal vaccine-chemotherapy protocols for removing tumor cells would be an appropriate strategy in cancer treatment. Also, the present study states that a proper treatment method not only reduces the population of the cancer cells but also changes the dynamics of the cancer.

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FINITE DURATION TREATMENT OF CANCER BY USING VACCINE THERAPY AND OPTIMAL CHEMOTHERAPY: STATE-DEPENDENT RICCATI EQUATION CONTROL AND EXTENDED KALMAN FILTER

Journal of Biological System ◽

10.1142/s0218339015500011 ◽

2015 ◽

Vol 23 (01) ◽

pp. 1-29 ◽

Cited By ~ 5

Author(s):

MOSTAFA NAZARI ◽

ALI GHAFFARI ◽

FARHAD ARAB

Keyword(s):

Kalman Filter ◽

Riccati Equation ◽

Extended Kalman Filter ◽

Control Method ◽

Domain Of Attraction ◽

Treatment Method ◽

Drug Dosage ◽

Vaccine Therapy ◽

Finite Duration ◽

State Dependent

The main purpose of this paper is to propose an optimal finite duration treatment method for preventing tumor growth. The obtained results show that changing the dynamics of the cancer model is essential for a finite duration treatment. Therefore, vaccine therapy is used for changing the parameters of the system and chemotherapy is applied for pushing the system to the domain of attraction of the healthy state. The state-dependent Riccati equation (SDRE)-based optimal control method is used for optimal chemotherapy. In this method, the special conditions of the patients could be considered by choosing suitable weighting matrices in the cost function and restricting the drug dosage. Also, there are infinite ways to choose these state-dependent matrices. In this paper, these interesting features of this method are used for each patient. Since measuring the states of the system is impossible at each time for states feedback; an extended Kalman filter (EKF) is designed as an observer in the nonlinear system. So, the SDRE method is employed just by measuring the population of normal cells. Numerical simulations show the flexibility and effectiveness of this treatment method.

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The effect of finite duration inputs on the dynamics of a system: Proposing a new approach for cancer treatment

International Journal of Biomathematics ◽

10.1142/s1793524515500369 ◽

2015 ◽

Vol 08 (03) ◽

pp. 1550036 ◽

Cited By ~ 4

Author(s):

Mostafa Nazari ◽

Ali Ghaffari

Keyword(s):

Dynamic Systems ◽

Domain Of Attraction ◽

Treatment Method ◽

Free System ◽

New Approach ◽

Finite Duration ◽

State Dependent ◽

Healthy State ◽

System Approaches ◽

Limited Duration

In this paper, a principal question regarding the effect of inputs on the characteristics of dynamic systems is discussed. Whether an input implemented only for a limited duration, can change the characteristics of a dynamic system such that the behavior of the free system, after eliminating the input, differs from that before acting the input? In this paper, it is shown that a limited time acted input is not able to change the dynamical properties of a system after its elimination. Regarding the proposed approach, a novel finite duration treatment method is developed for a tumor-immune system. The vaccine therapy is used to change the parameters of the system and the chemotherapy is applied for pushing the system to the domain of attraction of the healthy state. For optimal chemotherapy, an optimal control is used based on state-dependent Riccati equation (SDRE). It is shown that, in spite of eliminating the treatment (therapeutic inputs), the system approaches to healthy state conditions. The present analysis suggests that a proper treatment method must change the dynamics of the cancer instead of only reducing the population of cancer cells.

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State Dependent Riccati Equation controlled drug delivery for mixed therapy of cancer treatment**This work was supported by the Scientific and Technological Research Council of Turkey (TUBITAK) under the Project no. 112M209.

IFAC-PapersOnLine ◽

10.1016/j.ifacol.2015.11.098 ◽

2015 ◽

Vol 48 (25) ◽

pp. 265-270 ◽

Cited By ~ 2

Author(s):

Naser Babaei ◽

Metin U. Salamci ◽

Tayfun Çimen

Keyword(s):

Drug Delivery ◽

Cancer Treatment ◽

Riccati Equation ◽

Research Council ◽

Controlled Drug Delivery ◽

Technological Research ◽

State Dependent ◽

Technological Research Council

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State Dependent Riccati Equation Based Model Reference Adaptive Stabilization of Nonlinear Systems with Application to Cancer Treatment

IFAC Proceedings Volumes ◽

10.3182/20140824-6-za-1003.02282 ◽

2014 ◽

Vol 47 (3) ◽

pp. 1296-1301 ◽

Cited By ~ 12

Author(s):

Naser Babaei ◽

Metin U. Salamci

Keyword(s):

Nonlinear Systems ◽

Cancer Treatment ◽

Riccati Equation ◽

Adaptive Stabilization ◽

Model Reference ◽

State Dependent ◽

Model Reference Adaptive

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Suboptimal mixed vaccine and chemotherapy in finite duration cancer treatment: state-dependent Riccati equation control

Journal of the Brazilian Society of Mechanical Sciences and Engineering ◽

10.1007/s40430-014-0172-9 ◽

2014 ◽

Vol 37 (1) ◽

pp. 45-56 ◽

Cited By ~ 7

Author(s):

A. Ghaffari ◽

M. Nazari ◽

F. Arab

Keyword(s):

Cancer Treatment ◽

Riccati Equation ◽

Finite Duration ◽

State Dependent

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Optimal chemotherapy in cancer treatment: state dependent Riccati equation control and extended Kalman filter

Optimal Control Applications and Methods ◽

10.1002/oca.2039 ◽

2012 ◽

Vol 34 (5) ◽

pp. 562-577 ◽

Cited By ~ 35

Author(s):

Yazdan Batmani ◽

Hamid Khaloozadeh

Keyword(s):

Kalman Filter ◽

Cancer Treatment ◽

Riccati Equation ◽

Extended Kalman Filter ◽

State Dependent

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Innovatory role of nanomaterials as bio-tools for treatment of cancer

Reviews in Inorganic Chemistry ◽

10.1515/revic-2020-0015 ◽

2020 ◽

Vol 0 (0) ◽

Author(s):

Khuram Shahzad Ahmad ◽

Muntaha Talat ◽

Shaan Bibi Jaffri ◽

Neelofer Shaheen

Keyword(s):

Cancer Treatment ◽

Cancer Therapeutics ◽

Physicochemical Characteristics ◽

Global Scale ◽

Current Review ◽

Anti Cancer ◽

Different Types ◽

Cancerous Cells

AbstractConventional treatment modes like chemotherapy, thermal and radiations aimed at cancerous cells eradication are marked by destruction pointing the employment of nanomaterials as sustainable and auspicious materials for saving human lives. Cancer has been deemed as the second leading cause of death on a global scale. Nanomaterials employment in cancer treatment is based on the utilization of their inherent physicochemical characteristics in addition to their modification for using as nano-carriers and nano-vehicles eluted with anti-cancer drugs. Current work has reviewed the significant role of different types of nanomaterials in cancer therapeutics and diagnostics in a systematic way. Compilation of review has been done by analyzing voluminous investigations employing ERIC, MEDLINE, NHS Evidence and Web of Science databases. Search engines used were Google scholar, Jstore and PubMed. Current review is suggestive of the remarkable performance of nanomaterials making them candidates for cancer treatment for substitution of destructive treatment modes through investigation of their physicochemical characteristics, utilization outputs and long term impacts in patients.

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Recent Progress in Mitochondria-Targeting-Based Nanotechnology for Cancer Treatment

Nanoscale ◽

10.1039/d1nr01068a ◽

2021 ◽

Author(s):

Jingbo Qin ◽

Ningqiang Gong ◽

Zhihuan Liao ◽

Shouwen Zhang ◽

Peter S. Timashev ◽

...

Keyword(s):

Cancer Treatment ◽

Targeted Delivery ◽

Recent Progress ◽

Proliferation And Apoptosis ◽

Cancerous Cells ◽

Mitochondria Targeting

Mitochondria play critical roles in the regulation of the proliferation and apoptosis of cancerous cells. Nanosystems for targeted delivery of cargos to mitochondria for cancer treatment have attracted increasing attention...

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