Mathematical modeling demonstrates efficacy of combinational drug therapy for breast cancer treatment

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A recent Scientific Reports study used a mathematical model to assess the efficacy of a new combinational therapy of AZD9496 and palbociclib for breast cancer (BC) treatment.

Study: A new treatment for breast cancer using a combination of two drugs: AZD9496 and palbociclib. Image Credit: Gorodenkoff /


If BC is detected at an early stage, the cure rate can be up to about 90%. In BC, a malignant tumor develops either in the epithelial cells that line the system involved with the production or transport of milk to the nipple. 

If the tumor originates from cells that produce milk, it is referred to as a lobular tumor. Comparatively, tumors that develop from duct cells that transport milk to the nipple are known as tubular tumors.

As compared to a lobular tumor, a tubular tumor is more prevalent. Although this tumor is mostly found in women, men may also develop lobular tumors at a rate of 1:100.

BC comprises several groups of tumors with varying risk factors. Therefore, after BC diagnosis, it is important to understand the underlying risk factors, which could include multiple gene expression, estrogen receptor expression, sensitivity to anti-cancer treatments, or Her2 protein expression to support clinical decision-making processes.

Cancers are associated with abnormal changes in genetic materials of the cell that cause rapid and uncontrolled growth of disease cells. Abnormal genetic expression causes metabolic disorders and evasion of the host defense mechanism, which is responsible for the detection and elimination of damaged cells.

As compared to healthy cells, damaged cells undergo rapid growth, which leads to the development of a mass that spreads throughout the lymphatic system to regional lymph nodes. In some cases, cancer cells can metastasize, during which they are deposited to other organs, such as the liver and bones, through the bloodstream.

A recent study revealed that drug treatments for metastatic BC can reduce chemotherapy needs by about 50%. Different types of therapeutics are available for metastatic BC treatment, including target-oriented biological drugs and certain immunotherapies. 

A mathematical model for BC has been developed that considers multiple parameters to evaluate how different immune cells of the host interact with tumor cells and drug treatment. Several studies have indicated that mathematical models can provide insights about the size of the tumor as a function of time. One of the key advantages of using mathematical models in cancer research is that they reduce the need to perform experiments using animals or humans.

About the study

The current study examined the efficacy of new combinational drug therapy of AZD9496 and palbociclib for BC treatment. AZD9496 is an oral estrogen receptor inhibitor that inhibits the growth of ER- and ESR1-positive breast tumors in preclinical models, whereas palbociclib is a selective inhibitor of cyclin-dependent kinase 4 (CDK4) and CDK6.

Two semi-analytical methods, including the homotopy analysis method (HAM) and the method of integral invariant manifold (MIM) were combined to assess a non-linear ordinary differential equation (ODE) system. HAM uses the topology concept to generate convergent series solutions for nonlinear systems, whereas MIM enables the simplification of reaction mechanisms using dynamic systems.

Study findings

AZD9496 was administered at a predetermined dose of 300 mg. One AZD9496 dose was provided for two weeks, followed by a gap of fourteen days. This treatment regimen was followed for four cycles.

Although the palbociclib dose changed randomly, the time interval for its administration remained constant. The maximum and minimum doses of palbociclib used in this study were 125 mg and 20 mg, respectively. 

Following treatment, a reduction in the number of cancer cells was observed from the initial condition to zero in 72 days. At this point, the initial proposed dose of AZD9496 administration was changed in which the new protocol/dose involved the administration of 300 mg of AZD9496 daily for two weeks with a break for fourteen days, followed by 135 mg of AZD9496 for two weeks with a fourteen-day gap, followed by 250 mg of AZD9496 for 14 days with a two weeks break, and subsequently 50 mg of AZD9496 for two weeks.

In the case of palbociclib, the drug dose changed cyclically with a constant time interval for its administration. Initially, 125 mg of palbociclib was administered, which was reduced to 100 mg and then 60 mg, with a subsequent increase of 125 mg, followed by 110 mg. At the end of treatment, 40 mg of palbociclib was used.

For the combination treatment, AZD9496 and palbociclib doses and time intervals remained constant. To this end, 250 mg of AZD9496 was administered for 14 days with a two-week gap.

In addition, a constant dose of 125 mg palbociclib was maintained at constant intervals. The combination treatments lead to a reduction of cancer cells from their initial condition to zero in 32 days of treatment. 


Based on a mathematical approach, researchers predict that the combination therapy of AZD9496 and palbociclib for BC treatment can lead to a rapid reduction in BC cells.

Journal reference:
  • Nave, O., Shor, Y., Bar, R., et al. (2024). A new treatment for breast cancer using a combination of two drugs: AZD9496 and palbociclib. Scientific Reports 14(1); 1-16. doi:10.1038/s41598-023-48305-z

Article Revisions

  • Jan 19 2024 - Spelling mistake in title Mathetatical to Mathematical
Dr. Priyom Bose

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Dr. Priyom Bose

Priyom holds a Ph.D. in Plant Biology and Biotechnology from the University of Madras, India. She is an active researcher and an experienced science writer. Priyom has also co-authored several original research articles that have been published in reputed peer-reviewed journals. She is also an avid reader and an amateur photographer.


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