Mathematical characterization of population dynamics in breast cancer cells treated with doxorubicin

The development of chemoresistance remains a significant cause of treatment failure in breast cancer. We posit that a mathematical understanding of chemoresistance could assist in developing successful treatment strategies. Towards that end, we have developed a model that describes the cytotoxic effects of the standard chemotherapeutic drug doxorubicin on the MCF-7 breast cancer cell line. We assume that treatment with doxorubicin induces a compartmentalization of the breast cancer cell population into surviving cells, which continue proliferating after treatment, and irreversibly damaged cells, which gradually transition from proliferating to treatment-induced death. The model is fit to experimental data including variations in drug concentration, inter-treatment interval, and number of doses. Our model recapitulates tumor cell dynamics in all these scenarios (as quantified by the concordance correlation coefficient, CCC > 0.95). In particular, superior tumor control is observed with higher doxorubicin concentrations, shorter inter-treatment intervals, and a higher number of doses (p < 0.05). Longer inter-treatment intervals require adapting the model parameterization after each doxorubicin dose, suggesting the promotion of chemoresistance. Additionally, we propose promising empirical formulas to describe the variation of model parameters as functions of doxorubicin concentration (CCC > 0.78). Thus, we conclude that our mathematical model could deepen our understanding of the cytotoxic effects of doxorubicin and could be used to explore practical drug regimens achieving optimal tumor control.

Quantification of long-term doxorubicin response dynamics in breast cancer cell lines to direct treatment schedules

While acquired chemoresistance is recognized as a key challenge to treating many types of cancer, the dynamics with which drug sensitivity changes after exposure are poorly characterized. Most chemotherapeutic regimens call for repeated dosing at regular intervals, and if drug sensitivity changes on a similar time scale then the treatment interval could be optimized to improve treatment performance. Theoretical work suggests that such optimal schedules exist, but experimental confirmation has been obstructed by the difficulty of deconvolving the simultaneous processes of death, adaptation, and regrowth taking place in cancer cell populations. Here we present a method of optimizing drug schedules in vitro through iterative application of experimentally calibrated models, and demonstrate its ability to characterize dynamic changes in sensitivity to the chemotherapeutic doxorubicin in three breast cancer cell lines subjected to treatment schedules varying in concentration, interval between pulse treatments, and number of sequential pulse treatments. Cell populations are monitored longitudinally through automated imaging for 600–800 hours, and this data is used to calibrate a family of cancer growth models, each consisting of a system of ordinary differential equations, derived from the bi-exponential model which characterizes resistant and sensitive subpopulations. We identify a model incorporating both a period of growth arrest in surviving cells and a delay in the death of chemosensitive cells which outperforms the original bi-exponential growth model in Akaike Information Criterion based model selection, and use the calibrated model to quantify the performance of each drug schedule. We find that the inter-treatment interval is a key variable in determining the performance of sequential dosing schedules and identify an optimal retreatment time for each cell line which extends regrowth time by 40%-239%, demonstrating that the time scale of changes in chemosensitivity following doxorubicin exposure allows optimization of drug scheduling by varying this inter-treatment interval.

Acquired chemoresistance is a common cause of treatment failure in cancer. The scheduling of a multi-dose course of chemotherapeutic treatment may influence the dynamics of acquired chemoresistance, and drug schedule optimization may increase the duration of effectiveness of a particular chemotherapeutic agent for a particular patient. Here we present a method for experimentally optimizing an in vitro drug schedule through iterative rounds of experimentation and computational analysis, and demonstrate the method’s ability to improve the performance of doxorubicin treatment in three breast carcinoma cell lines. Specifically, we find that the interval between drug exposures can be optimized while holding drug concentration and number of treatments constant, suggesting that this may be a key variable to explore in future drug schedule optimization efforts. We further use this method’s model calibration and selection process to extract information about the underlying biology of the doxorubicin response, and find that the incorporation of delays on both cell death and regrowth are necessary for accurate parameterization of cell growth data.

Integrating transcriptomics and bulk time course data into a mathematical framework to describe and predict therapeutic resistance in cancer

A significant challenge in the field of biomedicine is the development of methods to integrate the multitude of dispersed data sets into comprehensive frameworks to be used to generate optimal clinical decisions. Recent technological advances in single cell analysis allow for high-dimensional molecular characterization of cells and populations, but to date, few mathematical models have attempted to integrate measurements from the single cell scale with other types of longitudinal data. Here, we present a framework that actionizes static outputs from a machine learning model and leverages these as measurements of state variables in a dynamic model of treatment response. We apply this framework to breast cancer cells to integrate single cell transcriptomic data with longitudinal bulk cell population (bulk time course) data. We demonstrate that the explicit inclusion of the phenotypic composition estimate, derived from single cell RNA-sequencing data (scRNA-seq), improves accuracy in the prediction of new treatments with a concordance correlation coefficient (CCC) of 0.92 compared to a prediction accuracy of CCC = 0.64 when fitting on longitudinal bulk cell population data alone. To our knowledge, this is the first work that explicitly integrates single cell clonally-resolved transcriptome datasets with bulk time-course data to jointly calibrate a mathematical model of drug resistance dynamics. We anticipate this approach to be a first step that demonstrates the feasibility of incorporating multiple data types into mathematical models to develop optimized treatment regimens from data.

A multi-state model of chemoresistance to characterize phenotypic dynamics in breast cancer

The development of resistance to chemotherapy is a major cause of treatment failure in breast cancer. While mathematical models describing the dynamics of resistant cancer cell subpopulations have been proposed, experimental validation has been difficult due to the complex nature of resistance that limits the ability of a single phenotypic marker to sufficiently identify the drug resistant subpopulations. We address this problem with a coupled experimental/modeling approach to reveal the composition of drug resistant subpopulations changing in time following drug exposure. We calibrate time-resolved drug sensitivity assays to three mathematical models to interrogate the models' ability to capture drug response dynamics. The Akaike information criterion was employed to evaluate the three models, and it identified a multi-state model incorporating the role of population heterogeneity and cellular plasticity as the optimal model. To validate the model's ability to identify subpopulation composition, we mixed different proportions of wild-type MCF-7 and MCF-7/ADR resistant cells and evaluated the corresponding model output. Our blinded two-state model was able to estimate the proportions of cell types with an R-squared value of 0.857. To the best of our knowledge, this is the first work to combine experimental time-resolved drug sensitivity data with a mathematical model of resistance development.

Orbital dermoid cysts located within the lateral rectus muscle

BACKGROUND

Two patients, a 13-year-old girl and a 31-year-old man, had an orbital dermoid tumor located in the lateral rectus muscle. This unusual location of dermoid tumors has not been reported previously.

METHODS

Computed tomography and magnetic resonance imaging showed a cystic mass within the belly of the lateral rectus in each patient. Surgical excision through a lateral orbitotomy showed a well-circumscribed mass surrounded by lateral rectus fibers. No periorbital attachment was noted.

RESULTS

Results of histopathologic evaluations showed a dermoid cyst. Postoperatively, the diplopia and proptosis resolved. In one patient, an unusual subconjunctival deposition of fat droplets was seen.

CONCLUSION

The findings in patients demonstrate an unusual presentation of dermoid cysts and make an addition to the differential diagnosis of enlarged extraocular muscles.

The silent sinus syndrome. A cause of spontaneous enophthalmos

PURPOSE

Spontaneous enophthalmos and hypoglobus, in the absence of other symptoms and unrelated to trauma or surgery, may be alarming to both physician and patient. The authors describe the clinicopathologic features of a benign syndrome ("silent sinus syndrome") with this constellation of features and discuss the possible pathophysiology.

METHODS

A multicenter retrospective search for similar clinical cases was performed. All clinical records, computed tomographs, and pathology reports for each case were reviewed at one center. A literature search for similar cases also was conducted.

RESULTS

Nineteen cases of a new syndrome are presented. This syndrome affects individuals at approximately the fourth decade of life (average age, 36 years; range, 29-46 years); is characterized by bone resorption and remodeling of the orbital floor due to otherwise asymptomatic maxillary sinus disease; is associated with ipsilateral maxillary sinus hypoplasia; and is not fully explained by any previously described, classic cystic lesion of the maxillary antrum.

CONCLUSION

Enophthalmos and hypoglobus unassociated with prior trauma, surgery, or other symptoms may represent "silent sinus syndrome," which is ipsilateral maxillary sinus hypoplasia and orbital floor resorption.

Orbital multiple myeloma mimicking acquired angio-oedema

Images

Medial canthoplasty with microplate fixation

Six patients with malpositioned or surgically excised medial canthal tendons underwent repair with titanium microplate, and two patients underwent repair with titanium miniplate fixation. The T-shaped rigid fixation plates were chosen for medial canthal reconstruction to allow for stabilization of the plate along the anterior lacrimal crest and extension of the plate over the posterior lacrimal crest. The medial canthal tissue was reattached to the titanium plate with 3.0 polypropylene (Prolene) suture. This technique appears to be safer, faster, and, in many cases, more effective than traditional techniques for reconstruction of the medial canthus after tendon avulsion or loss from excision of cutaneous carcinoma.

Clinical characteristics associated with orbital invasion of cutaneous basal cell and squamous cell tumors of the eyelid

Over a six-year period, between 1984 and 1990, 622 patients with basal cell and squamous cell carcinoma of the eyelids were examined at our institution. Thirteen patients had orbital invasion at initial examination. The average age of patients at orbital invasion was 75.8 years. Ten patients were men, eight of whom had basal cell carcinoma and two of whom had squamous cell carcinoma. Most patients had an orbital mass and incomitant strabismus at initial examination. Invasive basal cell carcinoma developed in 11 patients, and squamous cell carcinoma developed in two patients. Ten patients were treated for cutaneous carcinoma at the site of invasion before examination at our institution. The average duration between onset of a cutaneous lesion and our examination for orbital invasion was 9.8 years for basal cell carcinoma and one year for squamous cell carcinoma. Radiologic and histopathologic features were reviewed. The clinical characteristics of these patients were reviewed and orbital exenteration was recommended to all 13 patients. Nine patients underwent exenteration and four refused the operation.

Relation of extent of extracranial carotid artery atherosclerosis as measured by B-mode ultrasound to the extent of coronary atherosclerosis

The extent of carotid artery atherosclerosis as measured by B-mode ultrasound has been shown to be strongly and independently correlated with the presence or absence of coronary atherosclerotic disease (CAD), but no studies to date have used carotid B-mode ultrasound to compare the extent of atherosclerotic disease in the two arterial circulations. We used data from a registry of patients undergoing cardiac catheterization and B-mode ultrasound of the carotid arteries to compare the extent of CAD (number of major coronary vessels with 50% or greater stenosis as judged by a consensus interpretation) with the extent of extracranial carotid atherosclerosis. Four hundred thirty-four patients (234 men, 200 women) greater than 40 years of age were stratified by gender and then divided into quartiles on the basis of a B-mode score that was derived by summing arterial wall thickness at nine sites in the left and nine sites in the right carotid arteries. Evaluation of extent of CAD for the four B-mode quartiles showed that men in the lowest B-mode quartile were over six times more likely to have normal coronary arteries than three- to four-vessel CAD, while men in the highest B-mode quartile were over 10 times more likely to have three- to four-vessel CAD than normal coronary arteries. The findings were similar for women but not as dramatic. Gender-specific discriminant function models using traditional risk factors alone or in combination with B-mode score were developed to predict the extent of CAD.(ABSTRACT TRUNCATED AT 250 WORDS)

Intraocular tissue plasminogen activator in a rabbit model of traumatic hyphema

Tissue plasminogen activator was used to evaluate the clearance of traumatic hyphema in a rabbit model. A neodymium-YAG laser was used to disrupt iris vessels, creating a traumatic hyphema. Tissue plasminogen activator (1800 IU/0.1 mL) was injected into the anterior chamber 24 hours after creation of the hyphema. Two control groups (one receiving balanced salt solution and one receiving no treatment) were used for comparison. A multivariate analysis of covariance indicated that the greatest difference in hyphema clearance between the groups occurred at days 3, 4, and 5. Five days after tissue plasminogen activator treatment, the mean size of the clot remaining in the anterior chamber was 27% of that of the original hyphema. In control eyes, almost 60% of the original clot remained at day 5. Treatment of animals with tissue plasminogen activator doses of 5000 IU and 10,000 IU produced a substantial increase in repeated bleeding episodes in our rabbit model. We concluded that although the use of tissue plasminogen activator in our rabbit model of traumatic hyphema significantly improved clearance of blood from the anterior chamber, the remaining clot was of such size that the clinical benefit was questionable.