Toward an Ising Model of Cancer and Beyond

Theoretical and computational tools that can be used in the clinic to predict neoplastic progression and propose individualized optimal treatment strategies to control cancer growth is desired. To develop such a predictive model, one must account for the complex mechanisms involved in tumor growth. Here we review resarch work that we have done toward the development of an "Ising model" of cancer. The review begins with a description of a minimalist four-dimensional (three in space and one in time) cellular automaton (CA) model of cancer in which healthy cells transition between states (proliferative, hypoxic, and necrotic) according to simple local rules and their present states, which can viewed as a stripped-down Ising model of cancer. This model is applied to model the growth of glioblastoma multiforme, the most malignant of brain cancers. This is followed by a discussion of the extension of the model to study the effect on the tumor dynamics and geometry of a mutated subpopulation. A discussion of how tumor growth is affected by chemotherapeutic treatment is then described. How angiogenesis as well as the heterogeneous and confined environment in which a tumor grows is incorporated in the CA model is discussed. The characterization of the level of organization of the invasive network around a solid tumor using spanning trees is subsequently described. Then, we describe open problems and future promising avenues for future research, including the need to develop better molecular-based models that incorporate the true heterogeneous environment over wide range of length and time scales (via imaging data), cell motility, oncogenes, tumor suppressor genes and cell-cell communication. The need to bring to bear the powerful machinery of the theory of heterogeneous media to better understand the behavior of cancer in its microenvironment is presented.Comment: 55 pages, 21 figures and 3 tables. To appear in Physical Biology. Added reference

A Mechanistic Model of PCR for Accurate Quantification of Quantitative PCR Data

Background: Quantitative PCR (qPCR) is a workhorse laboratory technique for measuring the concentration of a target DNA sequence with high accuracy over a wide dynamic range. The gold standard method for estimating DNA concentrations via qPCR is quantification cycle (Cq) standard curve quantification, which requires the time- and labor-intensive construction of a Cq standard curve. In theory, the shape of a qPCR data curve can be used to directly quantify DNA concentration by fitting a model to data; however, current empirical model-based quantification methods are not as reliable as Cq standard curve quantification. Principal Findings: We have developed a two-parameter mass action kinetic model of PCR (MAK2) that can be fitted to qPCR data in order to quantify target concentration from a single qPCR assay. To compare the accuracy of MAK2-fitting to other qPCR quantification methods, we have applied quantification methods to qPCR dilution series data generated in three independent laboratories using different target sequences. Quantification accuracy was assessed by analyzing the reliability of concentration predictions for targets at known concentrations. Our results indicate that quantification by MAK2-fitting is as reliable as Cq standard curve quantification for a variety of DNA targets and a wide range of concentrations. Significance: We anticipate that MAK2 quantification will have a profound effect on the way qPCR experiments are designed and analyzed. In particular, MAK2 enables accurate quantification of portable qPCR assays with limited sampl

M2Net: Multi-modal Multi-channel Network for Overall Survival Time Prediction of Brain Tumor Patients

Early and accurate prediction of overall survival (OS) time can help to obtain better treatment planning for brain tumor patients. Although many OS time prediction methods have been developed and obtain promising results, there are still several issues. First, conventional prediction methods rely on radiomic features at the local lesion area of a magnetic resonance (MR) volume, which may not represent the full image or model complex tumor patterns. Second, different types of scanners (i.e., multi-modal data) are sensitive to different brain regions, which makes it challenging to effectively exploit the complementary information across multiple modalities and also preserve the modality-specific properties. Third, existing methods focus on prediction models, ignoring complex data-to-label relationships. To address the above issues, we propose an end-to-end OS time prediction model; namely, Multi-modal Multi-channel Network (M2Net). Specifically, we first project the 3D MR volume onto 2D images in different directions, which reduces computational costs, while preserving important information and enabling pre-trained models to be transferred from other tasks. Then, we use a modality-specific network to extract implicit and high-level features from different MR scans. A multi-modal shared network is built to fuse these features using a bilinear pooling model, exploiting their correlations to provide complementary information. Finally, we integrate the outputs from each modality-specific network and the multi-modal shared network to generate the final prediction result. Experimental results demonstrate the superiority of our M2Net model over other methods.Comment: Accepted by MICCAI'2

A Novel Three-Phase Model of Brain Tissue Microstructure

We propose a novel biologically constrained three-phase model of the brain microstructure. Designing a realistic model is tantamount to a packing problem, and for this reason, a number of techniques from the theory of random heterogeneous materials can be brought to bear on this problem. Our analysis strongly suggests that previously developed two-phase models in which cells are packed in the extracellular space are insufficient representations of the brain microstructure. These models either do not preserve realistic geometric and topological features of brain tissue or preserve these properties while overestimating the brain's effective diffusivity, an average measure of the underlying microstructure. In light of the highly connected nature of three-dimensional space, which limits the minimum diffusivity of biologically constrained two-phase models, we explore the previously proposed hypothesis that the extracellular matrix is an important factor that contributes to the diffusivity of brain tissue. Using accurate first-passage-time techniques, we support this hypothesis by showing that the incorporation of the extracellular matrix as the third phase of a biologically constrained model gives the reduction in the diffusion coefficient necessary for the three-phase model to be a valid representation of the brain microstructure

A new real-time PCR method to overcome significant quantitative inaccuracy due to slight amplification inhibition

<p>Abstract</p> <p>Background</p> <p>Real-time PCR analysis is a sensitive DNA quantification technique that has recently gained considerable attention in biotechnology, microbiology and molecular diagnostics. Although, the cycle-threshold (<it>Ct</it>) method is the present "gold standard", it is far from being a standard assay. Uniform reaction efficiency among samples is the most important assumption of this method. Nevertheless, some authors have reported that it may not be correct and a slight PCR efficiency decrease of about 4% could result in an error of up to 400% using the <it>Ct </it>method. This reaction efficiency decrease may be caused by inhibiting agents used during nucleic acid extraction or copurified from the biological sample.</p> <p>We propose a new method (<it>Cy</it>_<it>0</it>) that does not require the assumption of equal reaction efficiency between unknowns and standard curve.</p> <p>Results</p> <p>The <it>Cy</it>_{<it>0 </it>}method is based on the fit of Richards' equation to real-time PCR data by nonlinear regression in order to obtain the best fit estimators of reaction parameters. Subsequently, these parameters were used to calculate the <it>Cy</it>_{<it>0 </it>}value that minimizes the dependence of its value on PCR kinetic.</p> <p>The <it>Ct</it>, second derivative (<it>Cp</it>), sigmoidal curve fitting method (<it>SCF</it>) and <it>Cy</it>_{<it>0 </it>}methods were compared using two criteria: precision and accuracy. Our results demonstrated that, in optimal amplification conditions, these four methods are equally precise and accurate. However, when PCR efficiency was slightly decreased, diluting amplification mix quantity or adding a biological inhibitor such as IgG, the <it>SCF</it>, <it>Ct </it>and <it>Cp </it>methods were markedly impaired while the <it>Cy</it>_{<it>0 </it>}method gave significantly more accurate and precise results.</p> <p>Conclusion</p> <p>Our results demonstrate that <it>Cy</it>_{<it>0 </it>}represents a significant improvement over the standard methods for obtaining a reliable and precise nucleic acid quantification even in sub-optimal amplification conditions overcoming the underestimation caused by the presence of some PCR inhibitors.</p