Some optimal control problems in cancer chemotherapy with a toxicity limit

Cancer cells accumulate genetic changes at an abnormally rapid rate due to the defects in the DNA repair mechanisms. From an evolutionary perspective, such genetic instability is advantageous for cancer development. Mutant cell lines accumulate a series of beneficial mutations that contribute to their progression into cancer.
Some of the advantages that cancer cells have on normal cells include - enhanced ability to divide without terminally differentiating, induce new blood vessel formation,...

Cancer therapies are various modes of treatment, such as surgery, radiation therapy, and chemotherapy that are administered to cancer patients.
However, cancer treatments can pose several challenges, as therapies used to kill cancer cells are generally also toxic to normal cells. Moreover, cancer cells mutate rapidly and can develop resistance to chemical agents or radiation therapy. Besides, all types of cancer cells may not respond to the same therapy. Some cancer cells respond to one...

The targeted cancer therapies, also known as “molecular targeted therapies,” take advantage of the molecular and genetic differences between the cancer cells and the normal cells. It needs a thorough understanding of the cancer cells to develop drugs that can target specific molecular aspects that drive the growth, progression, and spread of cancer cells without affecting the growth and survival of other normal cells in the body.
There are several types of targeted therapies against specific...

Cancer is the second leading cause of death in the United States. A cancer cell is genetically unstable and hence can mutate faster. They can also modify their microenvironment and escape immune surveillance. The difficulties in treating cancer are further compounded by the emergence of rapid resistance to anticancer drugs. The most common ways to attain resistance in cancer cells include alteration in drug transport and metabolism, modification of drug target, elevated DNA damage response, or...

Combining two or more treatment methods increases the life span of cancer patients while reducing damage to vital organs or tissue from the overuse of a single treatment. Combination therapy also targets different cancer-inducing pathways, thus reducing the chances of developing resistance to treatment.
The combination of the drug acetazolamide and sulforaphane is a good example of combination therapy to treat cancer. The cells in the interior of a large tumor often die due to the hypoxic and...

Drug toxicities can be stratified into pharmacological, pathological, or genotoxic based on their mechanisms. The incidence and severity of these toxicities generally increase with the drug's concentration in the body and exposure time.Pharmacological toxicity is evident when the therapeutic effects of drugs overshoot into adverse reactions in a predictable, dose-dependent manner. Central nervous system (CNS) depression from barbiturates is a classic example, with effects escalating from...