Dissecting the dynamics of serum prostate-specific antigen

Mechanistic modelling of prostate-specific antigen dynamics shows potential for personalized prediction of radiation therapy outcome

External beam radiation therapy is a widespread treatment for prostate cancer. The ensuing patient follow-up is based on the evolution of the prostate-specific antigen (PSA). Serum levels of PSA decay due to the radiation-induced death of tumour cells and cancer recurrence usually manifest as a rising PSA. The current definition of biochemical relapse requires that PSA reaches nadir and starts increasing, which delays the use of further treatments. Also, these methods do not account for the post-radiation tumour dynamics that may contain early information on cancer recurrence. Here, we develop three mechanistic models of post-radiation PSA evolution. Our models render superior fits of PSA data in a patient cohort and provide a biological justification for the most common empirical formulation of PSA dynamics. We also found three model-based prognostic variables: the proliferation rate of the survival fraction, the ratio of radiation-induced cell death rate to the survival proliferation rate, and the time to PSA nadir since treatment termination. We argue that these markers may enable the early identification of biochemical relapse, which would permit physicians to subsequently adapt patient monitoring to optimize the detection and treatment of cancer recurrence.

The Calculus of Serum PSA

OBJECTIVES

To review the mathematics of kinetic changes in serum prostate-specific antigen (PSA) and to use a compartmental model to derive a new kinetic measure, alpha.

METHODS

The calculus of kinetic measures of PSA changes with time is presented, and a compartmental model is then used to derive alpha of serum PSA. Alpha is then tested for prognostic importance in 119 men who underwent prostatectomy.

RESULTS

The percentage of tumor in the prostate is closely related to alpha and to tumor length in diagnostic needle biopsies, but not to tumor grade. The presence of adverse pathology in the prostatectomy specimens (positive margins or T3 stage) is significantly associated with alpha, but not to tumor length or grade.

CONCLUSIONS

The derived kinetic parameter, alpha, shows promise as a preoperative prognostic parameter, and may help sort patients into those with low vs high probability for adverse pathology features in the prostatectomy specimens.

Serum Prostate-Specific Antigen (PSA) Concentration, PSA Mass, and Obesity: A Mathematical Analysis

OBJECTIVES

To provide a mathematical background for understanding the phenomenon of analyte hemodilution using a kinetic analysis.

METHODS

The first assumption for this analysis is that change in concentration of any analyte, such as prostate-specific antigen (PSA), is due to the flux of the analyte from an organ into the blood minus its flux from the blood. What results is a relatively simple differential equation that emphasizes the importance of plasma volume, organ mass, and two rate constants.

RESULTS

The analyses demonstrate how serum PSA can be affected by plasma volume as well as body mass and how hemodilution due to obesity can be at least partly corrected for by expressing PSA in units of total mass or total mass density.

CONCLUSIONS

At a time when obesity is prevalent, expressing analytes in units of total mass may make them relate more closely to disease status and prognosis.

What explains the differences between centres in the European screening trial? A simulation study

BACKGROUND

The European Randomised study of Screening for Prostate Cancer (ERSPC) is a multicentre, randomised screening trial on men aged 55-69 years at baseline without known prostate cancer (PrCa) at randomisation to an intervention arm invited to screening or to a control arm. The ERSPC has shown a significant 21% reduction in PrCa mortality at 13 years of follow-up. The effect of screening appears to vary across centres, for which several explanations are possible. We set to assess if the apparent differences in PrCa mortality reduction between the centres can be explained by differences in screening protocols.

METHODS

We examined the centre differences by developing a simulation model and estimated how alternative screening protocols would have affected PrCa mortality.

RESULTS

Our results showed outcomes similar to those observed, when the results by centres were reproduced by simulating the screening regimens with PSA threshold of 3 versus 4ng/ml, or screening interval of two versus four years. The findings suggest that the differences are only marginally attributable to the different screening protocols.

CONCLUSION

The small screening impact in Finland was not explained by the differences in the screening protocols. A possible reason for it was the contamination of and the unexpectedly low PrCa mortality in the Finnish control arm.

Tissue-scale, personalized modeling and simulation of prostate cancer growth

Recently, mathematical modeling and simulation of diseases and their treatments have enabled the prediction of clinical outcomes and the design of optimal therapies on a personalized (i.e., patient-specific) basis. This new trend in medical research has been termed "predictive medicine." Prostate cancer (PCa) is a major health problem and an ideal candidate to explore tissue-scale, personalized modeling of cancer growth for two main reasons: First, it is a small organ, and, second, tumor growth can be estimated by measuring serum prostate-specific antigen (PSA, a PCa biomarker in blood), which may enable in vivo validation. In this paper, we present a simple continuous model that reproduces the growth patterns of PCa. We use the phase-field method to account for the transformation of healthy cells to cancer cells and use diffusion-reaction equations to compute nutrient consumption and PSA production. To accurately and efficiently compute tumor growth, our simulations leverage isogeometric analysis (IGA). Our model is shown to reproduce a known shape instability from a spheroidal pattern to fingered growth. Results of our computations indicate that such shift is a tumor response to escape starvation, hypoxia, and, eventually, necrosis. Thus, branching enables the tumor to minimize the distance from inner cells to external nutrients, contributing to cancer survival and further development. We have also used our model to perform tissue-scale, personalized simulation of a PCa patient, based on prostatic anatomy extracted from computed tomography images. This simulation shows tumor progression similar to that seen in clinical practice.

Identification of Most Aggressive Carcinoma Among Patients Diagnosed With Prostate Cancer Using Mathematical Modeling of Prostate-Specific Antigen Increases

BACKGROUND

Tools for differentiating aggressive and indolent prostate carcinoma (PCa) are needed. Mathematical modeling is a promising approach for longitudinal analysis of tumor marker kinetics.

PATIENTS AND METHODS

The prostate-specific antigen (PSA) increases from patients with PCa and those with benign prostatic hyperplasia (BPH) were retrospectively analyzed using a mathematical model. Using the NONMEM program, individual PSA kinetics were fit to the following equation: [d(PSA)/dt = (PROD.K × exp [RHO1 × t]) × (1 - BPH) + PROD.NK × exp (RHO2 × t) - KELIM × (PSA)], where RHO1 is the PSA production increase rate by PCa cells (PROD.K), RHO2 is the PSA production increase rate by non-PCa cells (PROD.NK), and KELIM is the PSA elimination rate. The comparative value of the modeled kinetic parameters, estimated for each patient, for predicting the D'Amico score and relapse-free survival (RFS) were tested using logistic regression analysis and multivariate survival tests.

RESULTS

The PSA kinetics from 62 patients with BPH and 149 patients with PCa before radical prostatectomy were successfully modeled. We identified statistically significant relationships between the PSA growth rate related to cancer cells (RHO1) and the probability of D'Amico high-risk group (less than the median RHO1 vs. at the median or greater: odds ratio, 2.15; 95% confidence interval [CI], 1.00-4.77; P = .05). RHO1 was also a significant prognostic factor for RFS on univariate analysis and against other reported prognostic factors using multivariate Cox tests. Three independent prognostic factors of RFS were found: RHO1 (hazard ratio [HR], 2.71; 95% CI, 1.25-5.84; P = .01), Gleason score (HR, 8.54; 95% CI, 4.19-17.40; P < .01), and positive surgical margins (HR, 2.04; 95% CI, 1.05-3.97; P = .03).

CONCLUSION

Using a few PSA time points analyzed with a mathematical model (easily manageable in routine practice), it could be possible to determine before surgery whether a patient has presented with aggressive PCa.

Prostate specific antigen kinetics following robotic stereotactic body radiotherapy for localized prostate cancer

BACKGROUND

Stereotactic body radiotherapy (SBRT) has emerged as an effective treatment for localized prostate cancer. However, prostate specific antigen (PSA) kinetics after prostate SBRT have not been well characterized. The purpose of this study was to analyze the trend in PSA decline following robotic SBRT from a prospective cohort of patients.

MATERIAL AND METHODS

In total 175 patients were treated definitively for localized prostate cancer to a dose of 35-36.25 Gy in 5 fractions using robotic SBRT in the absence of androgen deprivation therapy (ADT). PSA and testosterone were collected at regular intervals following treatment and patients were assessed for biochemical failure and benign PSA bounce. A PSA nadir threshold of 0.5 ng/ml was used as a predictor of long-term disease-free survival. Multivariate logistic regression was used to assess the effect of disease specific covariates on the likelihood of achieving a PSA nadir less than threshold. PSA kinetics were analyzed a multi-component exponential model accounting for benign and malignant sources of PSA.

RESULTS AND CONCLUSION

At a median follow-up of 3 years, 70% of patients achieved a PSA nadir below 0.5 ng/ml with a median PSA nadir of 0.3 ng/ml at a median time to nadir of 30 months. In our cohort, 36.2% experienced a benign PSA bounce. Absence of PSA bounce, initial PSA, and testosterone at the time of nadir proved to be significant predictors of achieving a PSA nadir below threshold. PSA kinetics after prostate SBRT were well described with a functional volume model with fitted half-lives of 4.4 and 14.8 months for malignant and benign sources of PSA, respectively. Patients treated with prostate SBRT experience an initial period of rapid PSA decline followed by a slow decline which will likely result in lower PSA nadirs after longer follow-up. The long-term disease specific impacts of these results remain to be determined.

A critical review of the analytical approaches for circulating tumor biomarker kinetics during treatment

Changes in serum tumor biomarkers may indicate treatment efficacy. Traditional tumor markers may soon be replaced by novel serum biomarkers, such as circulating tumor cells (CTCs) or circulating tumor nucleic acids. Given their promising predictive values, studies of their kinetics are warranted. Many methodologies meant to assess kinetics of traditional marker kinetics during anticancer treatment have been reported. Here, we review the methodologies, the advantages and the limitations of the analytical approaches reported in the literature. Strategies based on a single time point were first used (baseline value, normalization, nadir, threshold at a time t), followed by approaches based on two or more time points [half-life (HL), percentage decrease, time-to-events…]. Heterogeneities in methodologies and lack of consideration of inter- and intra-individual variability may account for the inconsistencies and the poor utility in routine. More recently, strategies based on a population kinetics approach and mathematical modeling have been reported. The identification of equations describing individual kinetic profiles of biomarkers may be an alternative strategy despite its complexity and higher number of necessary measurements. Validation studies are required. Efforts should be made to standardize biomarker kinetic analysis methodologies to ensure the optimized development of novel serum biomarkers and avoid the pitfalls of traditional markers.

Prostate-specific antigen growth rate constant after first-line cytotoxic chemotherapy in metastatic castration-resistant prostate cancer: a monoinstitutional experience

OBJECTIVE

Validation in clinical practice, after first-line chemotherapy (CT) of metastatic castration-resistant prostate cancer (PC), of prostate-specific antigen growth rate constant logarithm (PSA-G), calculated by a formula developed by Stein et al. in comparison with PSA decrease (PSA-D), calculated as recommended by PCWG2.

PATIENTS AND METHODS

This study is a retrospective monoinstitutional assessment of PSA-G and PSA-D after 12 weeks from the beginning of first-line cytotoxic CT in 49 patients with metastatic castration-resistant PC treated from 2006 to 2011, and whose pre-CT PSA and post-CT PSA determinations have been measured at specific time points. The 12-week PSA was measured at 80 to 91 days from the beginning of CT.

RESULTS

PSA-G exhibited a significant correlation with overall survival by Mann-Whitney U test and by linear regression, whereas PSA-D did only at the first test. After multivariate analysis, PSA-G was the only posttreatment measure to predict overall survival.

CONCLUSION

PSA-G appears a reliable surrogate end point after first-line cytotoxic CT outside of clinical trials. A cutoff value of PSA-G post-CT higher than-2.4 could be considered suggestive for moving to another treatment.

Prostate-specific antigen kinetics as a surrogate endpoint in clinical trials of metastatic castration-resistant prostate cancer: a review

Prostate cancer is the most common cancer in men. Overall survival is considered the best endpoint for clinical trials, but it is difficult to use in phase-2 studies. Although the reduction of PSA after cytotoxic chemotherapy has been identified as a valid surrogate for overall survival, it has not proven reliable for the evaluation of many biologics. Moreover, the PSA progression-free survival at 3 months was validated only for cytotoxic drugs, and the various measures of progression/delay have not been confirmed by large studies. Ultimately, outside of overall survival, no measure has been validated as a surrogate endpoint after treatment with targeted therapies and vaccine therapy. The PSA levels have a great variability and, theoretically, the use of measures of cell kinetics and PSA may be the most reliable approach to estimate the behavior of metastatic disease. Some measures of PSA kinetics have been well developed in the clinical castration-resistant prostate cancer, the PSA doubling time and the growth rate constant. The studies about the kinetics of PSA measures are reviewed and discussed. To date, studies that consider the measures of PSA kinetics as surrogate endpoints are still very few. However in the near future, the drug evaluation can not proceed separately, with distinct endpoints between cytotoxic and non-cytotoxic agents. Therefore, extensive analysis and validation of measures of kinetics derived from PSA, and candidates for a role for surrogate endpoint, will be needed in phase-3 studies, in order to test their effectiveness in different disease scenarios.