Andrew M. Stein

An algorithm for extracting the network geometry of three-dimensional collagen gels

The geometric structure of a biopolymer network impacts its mechanical and biological properties. In this paper, we develop an algorithm for extracting the network architecture of three‐dimensional (3d) fluorescently labeled collagen gels, building on the initial work of Wu et al., (2003) . Using artificially generated images, the network extraction algorithm is then validated for its ability to reconstruct the correct bulk properties of the network, including fiber length, persistence length, cross‐link density, and shear modulus.

The micromechanics of three-dimensional collagen-I gels

We study the micromechanics of collagen-I gel with the goal of bridging the gap between theory and experiment in the study of biopolymer networks. Three-dimensional images of fluorescently labeled collagen are obtained by confocal microscopy, and the network geometry is extracted using a 3D network skeletonization algorithm. Each fiber is modeled as an elastic beam that resists stretching and bending, and each crosslink is modeled as torsional spring. The stress–strain curves of networks at three different densities are compared with rheology measurements. The model shows good agreement with experiment, confirming that strain stiffening of collagen can be explained entirely by geometric realignment of the network, as opposed to entropic stiffening of individual fibers. The model also suggests that at small strains, crosslink deformation is the main contributer to network stiffness, whereas at large strains, fiber stretching dominates. As this modeling effort uses networks with realistic geometries, this analysis can ultimately serve as a tool for understanding how the mechanics of fibers and crosslinks at the microscopic level produce the macroscopic properties of the network.

Lithium inhibits invasion of glioma cells; possible involvement of glycogen synthase kinase-3

Therapies targeting glioma cells that diffusely infiltrate normal brain are highly sought after. Our aim was to identify novel approaches to this problem using glioma spheroid migration assays. Lithium, a currently approved drug for the treatment of bipolar illnesses, has not been previously examined in the context of glioma migration. We found that lithium treatment potently blocked glioma cell migration in spheroid, wound-healing, and brain slice assays. The effects observed were dose dependent and reversible, and worked using every glioma cell line tested. In addition, there was little effect on cell viability at lithium concentrations that inhibit migration, showing that this is a specific effect. Lithium treatment was associated with a marked change in cell morphology, with cells retracting the long extensions at their leading edge. Examination of known targets of lithium showed that inositol monophosphatase inhibition had no effect on glioma migration, whereas inhibition of glycogen synthase kinase-3 (GSK-3) did. This suggested that the effects of lithium on glioma cell migration could possibly be mediated through GSK-3. Specific pharmacologic GSK-3 inhibitors and siRNA knockdown of GSK-3alpha or GSK-3beta isoforms both reduced cell motility. These data outline previously unidentified pathways and inhibitors that may be useful for the development of novel anti-invasive therapeutics for the treatment of brain tumors.

BCR-ABL transcript dynamics support the hypothesis that leukemic stem cells are reduced during imatinib treatment

Purpose: Imatinib induces a durable response in most patients with Philadelphia chromosome–positive chronic myeloid leukemia, but it is currently unclear whether imatinib reduces the leukemic stem cell (LSC) burden, which may be an important step toward enabling safe discontinuation of therapy. In this article, we use mathematical models of BCR–ABL levels to make inferences on the dynamics of LSCs. Experimental Design: Patients with at least 1 BCR–ABL transcript measurement on imatinib were included (N = 477). Maximum likelihood methods were used to test 3 potential hypotheses of the dynamics of BCR–ABL transcripts on imatinib therapy: (i) monoexponential, in which there is little, if any, decline in BCR–ABL transcripts; (ii) biexponential, in which patients have a rapid initial decrease in BCR–ABL transcripts followed by a more gradual response; and (iii) triexponential, in which patients first exhibit a biphasic decline but then have a third phase when BCR–ABL transcripts increase rapidly. Results: We found that most patients treated with imatinib exhibit a biphasic decrease in BCR–ABL transcript levels, with a rapid decrease during the first few months of treatment, followed by a more gradual decrease that often continues over many years. Conclusions: We show that the only hypothesis consistent with current data on progenitor cell turnover and with the long-term, gradual decrease in the BCR–ABL levels seen in most patients is that these patients exhibit a continual, gradual reduction of the LSCs. This observation may explain the ability to discontinue imatinib therapy without relapse in some cases. Clin Cancer Res; 17(21); 6812–21. ©2011 AACR.

Survival Prediction in Everolimus-treated Patients with Metastatic Renal Cell Carcinoma Incorporating Tumor Burden Response in the RECORD-1 Trial

BACKGROUND The phase 3 RECORD-1 study demonstrated clinical benefit of everolimus over placebo (median progression-free survival: 4.9 mo compared with 1.9 mo, p<0.001) in treatment-resistant patients with metastatic renal cell carcinoma (mRCC). However, the Response Evaluation Criteria in Solid Tumors (RECIST) objective response rate was low. OBJECTIVE To explore the potential role of tumor burden response to everolimus in predicting patient survival. DESIGN, SETTING, AND PARTICIPANTS RECORD-1 patients with at least two tumor assessments (baseline and weeks 2-14) were included (n=246). OUTCOME MEASUREMENTS AND STATISTICAL ANALYSIS A multivariate Cox proportional hazard model was used to assess the impact of various prognostic factors on overall survival (OS). Components of RECIST progression were explored using univariate Cox regression. RESULTS AND LIMITATIONS The baseline sum of longest tumor diameters (SLD) and progression at weeks 2-14 were prognostic factors of OS by multivariate analysis. Univariate analysis at weeks 2-14 demonstrated that growth of nontarget lesions and appearance of new lesions were predictive of OS (p<0.001). This retrospective analysis used data from one arm of one trial; patients in the placebo arm were excluded because of confounding effects when they crossed over to everolimus. CONCLUSIONS This analysis identified baseline SLD as a predictive factor of OS, and the appearance of a new lesion or progression of a nontarget lesion at first assessment after baseline also affects OS in patients with mRCC treated with everolimus.

Dynamic tumor modeling of the dose–response relationship for everolimus in metastatic renal cell carcinoma using data from the phase 3 RECORD-1 trial

BackgroundThe phase 3 RECORD-1 trial (NCT00410124) established the efficacy and safety of everolimus in patients with metastatic renal cell carcinoma (mRCC) who progress on sunitinib or sorafenib. In RECORD-1, patients received 10 mg everolimus daily, with dose reduction to 5 mg daily allowed for toxicity. We have developed a model of tumor growth dynamics utilizing serial measurements of the sum of the longest tumor diameters (SLD) from individual RECORD-1 patients to define the dose–response relationship of everolimus.ResultsThe model predicts that after 1 year of continuous dosing, the change in SLD of target lesions will be +142.1% ± 98.3%, +22.4% ± 17.2%, and –15.7% ± 11.5% in the average patient treated with placebo, 5 mg everolimus, and 10 mg everolimus, respectively. This nonlinear, mixed-effects modeling approach can be used to describe the dynamics of each individual patient, as well as the overall population. This allows evaluation of how an actual dosing history and individual covariates impact on the observed drug effect, and offers the possibility of predicting clinical observations as a function of time.ConclusionsIn this pharmacodynamic model of tumor response, everolimus more effectively shrinks target lesions in mRCC when dosed 10 mg daily versus 5 mg daily, although a 5-mg dose still shows an antitumor effect. These data support earlier studies that established 10 mg daily as the preferred clinical dose of everolimus, and improve our understanding of the everolimus dose–response relationship.

A model for glioma growth This paper was submitted as an invited paper resulting from “Understanding Complex Systems” conference held at University of Illinois-Urbana Champaign, May 2005

Glioblastoma Multiforme (GBM) is the most invasive form of primary brain tumor. We propose a mathematical model that describes such tumor growth and allows us to describe two different mechanisms of cell invasion: diffusion (random motion) and chemotaxis (directed motion along the gradient of the chemoattractant concentration). The results are in a quantitative agreement with recent in vitro experiments. It was observed in experiments that the outer invasive zone grows faster than the inner proliferative region. We argue that this feature indicates transient behavior, and that the growth velocities tend to the same constant value for larger times. A longer-time experiment is needed to verify this hypothesis and to choose between the two basic mechanisms for tumor growth.

Estimating the cell density and invasive radius of three-dimensional glioblastoma tumor spheroids grown in vitro.

To gain insight into brain tumor invasion, experiments are conducted on multicellular tumor spheroids grown in collagen gel. Typically, a radius of invasion is reported, which is obtained by human measurement. We present a simple, heuristic algorithm for automated invasive radii estimation (AIRE) that uses local fluctuations of the image intensity. We then derive an analytical expression relating the image graininess to the cell density for a model imaging system. The result agrees with the experiment up to a multiplicative constant and thus describes a novel method for estimating the cell density from bright-field images.

Benchmarking QSP Models Against Simple Models: A Path to Improved Comprehension and Predictive Performance

Quantitative Systems Pharmacology (QSP) models provide a means of integrating knowledge into a quantitative framework and, ideally, this integration leads to a better understanding of biology and better predictions of new experiments and clinical trials. In practice, these goals may be compromised by model complexity and uncertainty. To address these problems, we recommend that the predictive performance of QSP models be assessed through comparison with simpler models developed specifically for this purpose.

Practical Unidentifiability Of Receptor Density In Target Mediated Drug Disposition Models Can Lead To Over-Interpretation Of Drug Concentration Data

For monoclonal antibodies, mathematical models of target mediated drug disposition (TMDD) are often fit to data in order to estimate key physiological parameters of the system. These parameter estimates can then be used to support drug development by assisting with the assessment of whether the target is druggable and what the first in human dose should be. The TMDD model is almost always over-parameterized given the available data, resulting in the practical unidentifiability of some of the model parameters, including the target receptor density. In particular, when only PK data is available, the receptor density is almost always practically unidentifiable. However, because practical identifiability is not regularly assessed, incorrect interpretation of model fits to the data can be made. This issue is illustrated using two case studies from the literature.