Computer model challenges breast cancer treatment strategy

A Quasi Birth-and-Death model for tumor recurrence

A major cause of chemoresistance and recurrence in tumors is the presence of dormant tumor foci that survive chemotherapy and can eventually transition to active growth to regenerate the cancer. In this paper, we propose a Quasi Birth-and-Death (QBD) model for the dynamics of tumor growth and recurrence/remission of the cancer. Starting from a discrete-state master equation that describes the time-dependent transition probabilities between states with different numbers of dormant and active tumor foci, we develop a framework based on a continuum-limit approach to determine the time-dependent probability that an undetectable residual tumor will become large enough to be detectable. We derive an exact formula for the probability of recurrence at large times and show that it displays a phase transition as a function of the ratio of the death rate μ_A of an active tumor focus to its doubling rate λ. We also derive forward and backward Kolmogorov equations for the transition probability density in the continuum limit and, using a first-passage time formalism, we obtain a drift-diffusion equation for the mean recurrence time and solve it analytically to leading order for a large detectable tumor size N. We show that simulations of the discrete-state model agree with the analytical results, except for O(1/N) corrections. As an example of the use of our model in a clinical setting, we show that a range of model parameters can fit Kaplan-Meier recurrence-free survival data for ovarian cancer. Finally, we show in simulations that extending the duration of chemotherapy increases both the mean recurrence time and the asymptotic (large-time) probability of no recurrence. Our results should be useful in planning optimized chemotherapy dosing and duration for cancer treatment, especially in cancer types for which no targeted therapy is available.

Neurological deaths of American adults (55-74) and the over 75's by sex compared with 20 Western countries 1989-2010: Cause for concern

Background:

Have USA total neurological deaths (TNDs) of adults (55–74) and the over 75's risen more than in twenty Western Countries?

Methods:

World Health Organization TND data are compared with control mortalities cancer mortality rates (CMRs) and circulatory disease deaths (CDDs) between 1989–1991 and 2008–2010 and odds ratios (ORs) and confidence intervals calculated.

Results:

Neurological Deaths – Twenty country (TC) average 55–74 male rates per million (pm) rose 2% to 503 pm, USA increased by 82% to 627 pm. TC average females rose 1% to 390 pm, USA rising 48% to 560 pm. TC average over 75's male and female increased 117% and 143%; USA rising 368% and 663%, significantly more than 16 countries. Cancer mortality – Average 55–74 male and female fell 20% and 12%, USA down 36% and 18%. TC average over 75's male and female fell 13% and 15%, the USA 29% and 2%. Circulatory deaths – TC average 55–74 rates fell 60% and 46% the USA down 54% and 53%. Over 75's average down 46% and 39%, USA falling 40% and 33%. ORs for rose substantially in every country. TC average 75's ORs for CMR: TND male and females were 1:2.83 and 1:3.04 but the USA 1:5.18 and 1:6.50. The ORs for CDD: TND male and females TC average was 1:3.42 and 1:3.62 but the USA 1:6.13 and 1:9.89.

Conclusions:

Every country's neurological deaths rose relative to the controls, especially in the USA, which is a cause for concern and suggests possible environmental influences.

Seeding of epithelial cells into circulation during surgery for breast cancer: the fate of malignant and benign mobilized cells

Background

Surgery of malignant tumors has long been suspected to be the reason for enhancement of growth of metastases with fatal outcome. This often prevented surgeons from touching the tumor if not absolutely necessary. We have shown in lung cancer patients that surgery, itself, leads to mobilization of tumor cells into peripheral blood. Some of the mobilized cells finding an appropriate niche might grow to form early metastases. Monitoring of tumor cell release during and the fate of such cells after surgery for breast cancer may help to reveal how metastases develop after surgery.

Method

We used the MAINTRAC^® analysis, a new tool for online observation of circulating epithelial cells, to monitor the number of epithelial cells before, 30 min, 60 min, three and seven days after surgery and during subsequent variable follow up in breast cancer patients.

Results

Circulating epithelial cells were already present before surgery in all patients. During the first 30–60 min after surgery values did not change immediately. They started increasing during the following 3 to 4 days up to thousand fold in 85% of treated patients in spite of complete resection of the tumor with tumor free margins in all patients. There was a subsequent re-decrease, with cell numbers remaining above pre-surgery values in 58% of cases until onset of chemotherapy. In a few cases, where no further therapy or only hormone treatment was given due to low risk stage, cell numbers were monitored for up to three years. They remained elevated with no or a slow decrease over time. This was in contrast to the observation in a patient where surgery was performed for benign condition. She was monitored before surgery with no cells detectable. Epithelial cells increased up to more than 50 000 after surgery but followed by a complete reduction to below the threshold of detection.

Conclusion

Frequently before but regularly during surgery of breast cancer, epithelial cells are mobilized into circulation. Part of these cells, most probably normal or apoptotic cells, are cleared from the circulation as also shown to occur in benign conditions. After resection even if complete and of small tumors, cells can remain in the circulation over long times. Such cells may remain "dormant" but might settle and grow into metastases, if they find appropriate conditions, even after years.

Recent translational research: computational studies of breast cancer

The combination of mathematics – queen of sciences – and the general utility of computers has been used to make important inroads into insight-providing breast cancer research and clinical aids. These developments are in two broad areas. First, they provide useful prognostic guidelines for individual patients based on historic evidence. Second, by suggesting numeric tumor growth laws that are correlated to clinical parameters, they permit development of biologically relevant theories and comparison with patient data to help us understand complex biologic processes. These latter studies have produced many new ideas that are testable in clinical trials. In this review we discuss these developments from a clinical perspective, and ask whether and how they translate into useful tools for patient treatment.

Molecular biology of breast cancer metastasis. The use of mathematical models to determine relapse and to predict response to chemotherapy in breast cancer

Breast cancer mortality rates have shown only modest improvement despite the advent of effective chemotherapeutic agents which have been administered to a large percentage of women with breast cancer. In an effort to improve breast cancer treatment strategies, a variety of mathematical models have been developed that describe the natural history of breast cancer and the effects of treatment on the cancer. These models help researchers to develop, quantify, and test various treatment hypotheses quickly and efficiently. The present review discusses several of these models, with a focus on how they have been used to predict the initiation time of metastatic growth, the effect of operative therapy on the growth of metastases, and the optimal administration strategy for chemotherapy.

Evolving strategies for the management of non-palpable breast abnormalities

Increased public and professional awareness has resulted in more women obtaining mammograms. As a result, the surgeon is often called on to diagnose and treat occult breast lesions. The development of new diagnostic modalities has changed the way such breast lesions are approached. Management decisions are made in the context of new pressures applied by the growing managed care imperative and increased mediocolegal exposure. In this review, we establish guidelines for the management of non-palpable breast abnormalities that place the welfare of the patient first.