How Cancer Cells Resist Drugs and How the Timing of Medical Treatment Affects Them?

An interactive exploration of cancer cells development with medical intervention

By: Yukai Yan, Zhennan Zhou, Yu Xin, Feiyou Guo


There is an everlasting war between humans and cancers. In human history, we have won many battles against cancers and saved millions of lives using various treatments. However, under the promising clinical solutions is the one of the major limitations to cancer treatment: drug resistance .

Drug resistance is largely hidden under microscopes and abstract mathematical models, and are dependent on many factors, including the time of medical intervention, types of cancers, and the mutation rate. Disease and sickness are scary and unsettling in real life. We attempt to unravel and present how tumor develops the drug resistance with and without medical intervention through visualized and interactive charts. We hope they can help people deepen their understanding of cancers and give them more confidence when facing and fighting with such disease.


Tumors are dynamic ecosystems where each cell undergoes constant cycles of cell division, death, and mutation. Each of the cancer cells grows and divides at an abnormally rapid rate during its lifetime (largely due to the expression of an enzyme named telomerase).

When it divides, there is a slim chance where it makes mistakes copying its DNAs (mutation), and there lies a small possibility that such mistake can make the cell acquire resistance to a specific type of drug. Even though the chances seem rare for a single cancer cell to obtain such mutation, it is likely to happen at some point given there are billions and trillions of cancer cells in a tumor that are diving endlessly. Once it happens, almost all of the descendants of the drug-resistant cancer cell will inherit with the ability.

One Drug Scenario

Let's consider a cancer treatment involving only one type of drug, drug-I . In this case, we are only interested in two types of cancer cells: one that is resistant to the drug used in the treatment, and one that is not . For simplicity, we assume the birth and death rates remain constant between the normal and resistant (mutated) cancer cells. We also assume mutations only happens in one direction, i.e., the descendants of drug-resistant cells can never be normal cells.

The visualization on the right demonstrates the cell mutation states from being susceptible to being resistant to one drug intervention.

Below, the graph shows the growth of the tumor in 52 weeks (about one year). If tumor starts with 100 million cancer cells , in which 3% are resistant to drug-I . Without the the intervention of any treatment, the tumor will end up with about 8.5 trillion cancer cells , in which 26% are drug resistant . However, if we move the yellow stick, which represents the starting time of the treatment, to week 9 on the graph, the tumor will end up about 78% smaller in size. The only downside is that there are now 75% drug-resistant cancer cells in the tumor, which will make the following treatment particularly hard if we still use drug-I .

Susceptible to drug-I

Resistant to one drug-I

Slide the slider above to simulate what the tumor looks like at a given time.

There are two conclusions that can be drawn. First, the earlier the intervention of the treatment, the better we can keep the growth of the tumor under control (but not cure it!) . Second, the introduction of the drug doesn't really flatten the yellow curve , which means the drug-resistant cancer cells are still growing exponentially. This is because there are two "sources" of the drug-resistant cells: mutating from the normal cancer cells and dividing from the existing drug-resistant cells. Using one drug can dramatically reduce the resistant cells derivated from the former by effectively killing normal cancer cells, but not the latter.

Two Drug Scenario

Now, let's take a look what will happen if we treat the patient with two different types of drugs instead, which is often the case in the real world. Let's refer the two drugs as drug-I and drug-II for simplicity. The situation is a little more complicated now since we need to focus on four types of cancer cells: the normal cancer cells that are susceptible to both drugs, cells resistant to drug1 , cells resistant to drug2 , and cells resistant to both drugs .

In this model, we assume the birth, death, and mutation rates remain constant among all different types of cancer cells and all mutations are not bidirectional. In addition, We also assume the two drugs are equally effective at killing susceptible cancer cells, and they are from distinct families such that a normal cell have to develop mono-drug resistance before evolving bi-drug resistance. Hence, there are only three "sources" of the bi-drug resistant cells: mutating from the drug-I resistant cancer cells, mutating from the drug-II resistant cancer cells, and dividing from the existing bi-drug resistant cells directly.

The graph below displays the growth of the tumor in 52 weeks (about one year). If the tumor starts with about 100 million cancer cells , in which 3% are drug-I resistant , 3% are drug-II resistant , and 1% are resistant to both drugs . Without the use of any treatment during the 52 weeks, the tumor will grow 100 times in size , where 20% are resistant to drug-I, 20% to drug-II, and 6% to both.

However, if the the drugs were introduced earlier in the therapy, things will be a lot different. For example, if drug-I is administrated in week 9 (move yellow stick to week 9), and drug-II is administrated on week 13 (move orange stick to week 21), we will see the tumor will end up with only about 600 million cancer cells, , which is 95% smaller than not using any drug in the 52 weeks. Comparing to one-drug scenario, we can see this is already a great improvement. At the end of week 52, there are 50% cancer cells resistant to both drugs .

Susceptible to both drugs

Resistant to drug-I only

Resistant to drug-II only

Resistant to both drugs

Slide the slider above to simulate what the tumor looks like at a given time.

While the conclusions from one-drug scenario still hold, we also found that using a combination of drugs is much more effective than the simple drug. However, it does not mean that the patient should take as many different medicines as possible to control or eliminate the tumor. In real life, we also have to consider the side effects of drugs and the patient's own health condition. Moreover, we can see that there are still about 50% cancer cells susceptible to at least one of the drugs at the end of week 52, so the two-drug treatment are still relatively effectively even after being used for about a year.


Drug resistance strongly limits the success of chemotherapy. It can be a severe problem once cancer becomes resistant to all possible drugs, leaving the patient with no therapeutic alternatives. However, the introduction of drug therapy is still effective in controlling the population of cancer cells. As demonstrated in the visualization, the earlier the intervention of the treatment, the better we can keep the growth of the tumor under control. Although it will not change the trend of exponential growth, limiting the number of cancer cells can significantly improve a person's lifespan, giving more time to other therapies such as radiation therapy, Hyperthermia, and Hormone Therapy.


To be minded that the data we used are generated from a simplified model in order to show the underlying mechanism more clear. The real world examples are often much more complicated and less predicable, so please listen to your doctor if any of the information above isn't consistent with your doctor's advice.