Session B06: Theoretical, Computational, and Statistical Modeling in Medicine

A statistical ensemble approach to understanding adaptive immunity: using sequence data to quantify the extraordinary diversity, in both sequence and protective specifictiy, of the T- and B-cells cells that make up an individual human's immune system.

Individual T cells of the adaptive immune system recognize specific pathogens via a certain protein expressed on the surface of the cell. The gene for this protein undergoes random editing each time a new immune cell is created. As a result, any individual’s immune system is an ensemble of distinct T cell types (in fact about 10^9 in number) created by a stochastic process. I will explain how high-throughput DNA sequencing has made it possible to develop a precise quantitative understanding of this stochastic process. I will then explain some consequences of this understanding: a) that the stochastic gene editing process is nearly universal across the human species, b) that the diversity of the process is so large that the overlap between T cell repertoires of two individuals is small, c) that the one-shot generation probabilities of specific T cell types range over nearly twenty orders of magnitude, and, as a corollary, d) that certain specific T cell types will be found in all individuals, while others have negligible sharing likelihood. I will then discuss how these developments bring into sharp focus the central biophysical question of adaptive immunity, namely: what is the diversity of pathogenic molecules that a single T cell can recognize, and is the diversity of the T cells present in one individual large enough so that the entire space of pathogenic molecules can be recognized? Implications of these developments for cancer immunotherapy will be briefly discussed. References for this talk are:
1. Statistical inference of the generation probability of T-cell receptors from sequence repertoires, with A.Murugan, T.Mora, and A.Walczak, Proc. Natl. Acad. Sci. USA, 109 (2012) 16161-16166.
2. OLGA: fast computation of generation probability of B- and T-cell receptor amino-acid sequences and motifs, with Y.Elhanati, Z.Sethna, T.Mora, and A.M.Walczak, Bioinformatics, 35 (2019) 2974-2981.   

Evaluation of nuclear reaction cross sections via proton induced reactions for the production of 72As: a potential entrant for theranostic pairs

Theranostic applications of radiopharmaceuticals have revolutionized present era specially, dealing with cancer diseases. Increase in the uses of radionuclides in nuclear medicine has resulted in the demands of optimized new radionuclides to be produced focussing on the economy, simplicity and maximum yield. Some arsenic radionuclides have wide range of positron-emission, half-lives ranging from an hour to weeks and have potential to be used for nuclear medicine. Present work will elucidate all over the production of ⁷²As on Germanium (Ge) and Selenium (Se). The experimental results obtained by several nuclear reactions were compared with the results of nuclear model calculations using the codes ALICE-IPPE, EMPIRE 3.2 and TALYS 1.9. The thick target yields (TTY) of ⁷²As were calculated from the recommended excitation functions. Analysis of radio-impurities was also discussed. A comparison of the various radio-impurities showed that to produce ⁷²As, ⁷²Ge(p, n)⁷²As and ⁷⁶Se(p, x)⁷²As reactions in different energy ranges. We have identified the nuclear process which gives high yield with minimum impurities to make it as a potential candidate for theranostic applications and in particular in Positron Emission Tomography (PET).   

Improving blood vessel tortuosity measurements via highly sampled numerical integration of the Frenet-Serret equations

Measures of vascular tortuosity, how curved and twisted a vessel is, are associated with a variety of vascular diseases. Consequently, accurate measurements of vessel tortuosity are greatly needed yet have proven problematic. Some researchers do not measure it at all, and others' results have been mismeasured, null, or contradictory. We present a new method that ensures accurate measurement of vessel tortuosity from medical image data that relies on numerical integration of the Frenet-Serret equations. By reconstructing vessel coordinates from tortuosity measurements, our approach identifies a minimally-sufficient sampling rate based on vessel radius. This work further identifies a key failing in current practices of filtering asymptotic measurements, and also highlights inconsistencies bewteen existing tortuosity metrics. We demonstrate the utility of our method on published data for a range of healthy human vessels including: cerebral and coronary vascular networks and individual carotid, abdominal, renal and illiac arteries. Preliminary application to disease data will also be discussed.   

Diffeomorphic morphometry of the tibio-femoral joint for quantitative assessment of osteoarthritis

We present an application of the framework of Large Diffeomorphic Deformation Metric Mapping (LDDMM) for statistical analysis of moprhological variants of knee anatomy associated with osteoarthritis (OA).
The LDDMM models the morphological variability by associating each population member – here, a tibial surface – with a diffeomorphic transformation that maps the shape of that member to a common template (mean shape). Compared to conventional Active Shape Models, LDDM has the significant advantage in that it does not require a priori point correspondences between the surfaces in the population. We also investigated an extension of LDDMM (functional shapes, fshapes) that jointly considers the variations in shape and variations in a function on the shape (signal) – here, the signal was a map of tibio-femoral joint space width.
The diffeomorphic modeling was applied to 34 CT scans of normal and OA subjects. To validate that the resulting model captures the morphology of OA, we measured the acuracy of a Suport Vector Machine (SVM) classifier using either only the shape features or the joint shape+signal features. We achieved correct classification (OA vs. normal) in 91% of subjects using shape features and in 85% of subjects using shape+signal.   

Probabilistic approach to treatment planning in radiation therapy

Radiation therapy (RT) is a common treatment for cancer. Current RT planning uses binary tumor definitions and accounts for uncertainties by simply expanding target volume by margins. This approach has several limitations and oversimplifies complex processes that are not linear in nature.
Here, we present a probabilistic approach to RT planning. First, mapping of tumor occupancy probability density functions was performed by sampling existing segmentation methods. Voxel-based microscopic tumor infiltration likelihood was simulated using CT imaging-derived anatomical constraints and clinically measured ranges of cellular infiltration. Desired voxel-level ranges of RT dose were prescribed based on this infiltration likelihood and its uncertainty. Realistic dose plans were created using an in-house treatment planning software modified to use minimax robust optimization over a range of uncertainty realizations. Finally, traditional and probabilistic dose plans were compared, and their performance quantified.
Using this approach, traditional expansion by margins was replaced with non-binary tumor maps and robust optimization, which more realistically represent treatment planning and delivery.   

Evolutionary dynamics of cancer on complex stress landscapes

Understanding the evolutionary dynamics of cancer progression requires explicit consideration of both spatial and environmental heterogeneities. We have recently developed a purely diffusion-based cancer-on-chip microfluidic platform, enabling the quantitative study of various cell types on chemotherapeutic gradients on long time scales. In a co-culture of bone-metastatic prostate cancer cells (PC3-EPI) with bone marrow stromal cells (HS5), we found a marked transition in population dominance across a docetaxel gradient. To interpret these results, we employ evolutionary game theory (EGT) as a predictive framework for cancer-stroma dynamics. We generate a spatial interacting-agent EGT model comprised of interconnected habitats in various network topologies. Informed by our experimental findings, we explore distinct strategies utilized by populations under stress by considering system parameters as a function of both space and time as well as by modulating migrational probabilities. This model will be adapted to probe interactions between drug-resistant cancer subpopulations, stromal cells, and immune cells, providing clinical implications for therapeutic approaches.   

Doppler Spectroscopy of Intracellular Dynamics During Chemotherapy in Tumor Biopsies

Biodynamic imaging is a high-content optical imaging technology based on Doppler spectroscopy and digital holography that uses dynamic speckle as high-content image contrast to probe living tissue. Biomarkers from the living tissues were extracted using fluctuation spectroscopy from intracellular Doppler light scattering in response to the molecular mechanisms of action of therapeutic drugs that modify a range of intracellular motions. Biodynamic imaging measurements of canine B-cell cancer tissues with unknown outcomes were performed and the drug-response spectrograms were compared to results from tissues of 22 pre-clinical trial dogs with known outcomes. A machine learning classifier was constructed based on feature vector correlations and linear separability in high dimensional feature space. The prediction of resistance or sensitivity to chemotherapy for unknown patient clinical outcomes was demonstrated. These results point to the potential for biodynamic profiling to contribute to personalized medicine by aiding the selection of chemotherapy for cancer patients.   

Quantifying Similarity in Histopathology Images Using Pathology-specific Deep-learned Features

Interpretation of histopathology slides is often labor intensive and operator dependent. This work aims to support the pathologists by matching unknown slides with reference slides of similar characteristics (normal, benign, type of carcinoma, etc) from an annotated collection. We expand on prior efforts in this area by developing a set of pathology-specific deep-learned features for the similarity matching. The features were extracted from digitized breast histopathology slides using a convolutional autoencoder (CAE). For training, random patches of 256x256 pixel ROIs (tiles) were extracted from each slide and augmented with random affine transformations and perturbations in HSV color space to consider variability in orientation, magnification, staining and lighting conditions. Batch sizes of 128 were used in training for 2000 epochs. To assess the ability to detect similar images using the deep-learned features, we compared feature vectors of neighboring tiles of the same slide using a separate validation slide set. For inference, input tiles extracted from unknown slides are featurized with the encoder and a kNN search is performed on feature vectors derived from an annotated reference collection, returning similar tiles and corresponding slides for the pathologist.   

Mathematical Models for Living Forms in Medical Physics Submodel 1: The Information Processing from Teeth to Nerves

This talk continues the presentations at APS March Meeting 2019 and APS April Meeting 2019. In this part of the project the first submodel is presented; The information processing from teeth to the nerves.
Information processing is modeled via p-waves passing through the tooth layers enamel and dentin. Odontoblasts located in the liquid in the tubules of the tooth dentin layer perform finally the transformation into electrical information (an electrical signal) that passes along nerves.   

Potential Efficacy of the Monte Carlo Dose Calculations of 6MV Flattening Filter-Free Photon Beam of M6™ Cyberknife® System

Retrospective MapCheck measurements of 50 patient’s treatment plans have suggested that MapCheck could be effectively employed in routine patient specific quality assurance in M6 Cyberknife with beams delivered at different treatment angles. However, for smaller MLCs segments (< 8 mm) a correction of (-4 %) was used to match the planned dose with MapCheck. To generalize this correction, a Monte Carlo (MC) simulation is required for such types of treatment plans. In doing so, MC simulations were performed for the M6 Cyberknife using the EGSnrc program. A total of 2-5 and 10-20 millions of incident particles histories in BEAMnrc and DOSXYZnrc, respectively were simulated. Preliminary results showed dose uncertainties ≤ 3% for all the standard fields (7.6 x 7.7 mm² to 100 x 100 mm²). During the simulation, an incident electron beam of 7 MeV with a FWHM of 2.2 mm was used to match with the stated nominal energy by comparing the simulation and corresponding measurement results. Good agreements for the dose profiles (≤ 2%) and dose outputs (≤ 3%) were found between the simulations and measurements at 800 mm Source to Axis Distance (SAD).   

Thermal transport simulation in healthy and arthritic fingers

Infrared thermography can distinguish rheumatoid arthritic (RA) joints from healthy joints by measuring elevated skin surface temperature caused by the inflammation present in RA joints. However, infrared thermography is more sensitive for the assessment of small joints.
Thermal transport simulations of healthy and arthritic fingers were implemented by solving the bio-heat diffusion equation within joint models using finite elements method (FEM). FEM models were based on high resolution MR images. Arthritic joint models were simulated by increasing the metabolic heat generation of healthy joint models. Simulated thermographic images were compared to real images.
Our simulations confirmed that elevated internal joint temperature results in elevated surface temperature. Internal and surface temperature depended on internal heat generation, heat dissipation due to perfusion, joint geometry, and finger surface cooling. Patterns of finger surface temperature from simulation were similar to that in thermographic images.
Thermal transport simulations relate thermographic images of the finger, finger geometry, internal temperature distribution and internal heat sources or sinks. Understanding these relations facilitate better RA diagnostics with infrared thermography.   

A fast and effective denoising solution using deep learning for real time X-ray Acoustic Computed Tomography

The X-ray acoustic (XA) computed tomography has recently been proposed as a method for real-time 3D in-vivo patient dosimetry for radiation therapy. The XA effect follows the same principles as the photoacoustic effect: acoustic waves are induced due to the absorption of heat energy by the tissue from a pulsed photon beam. XA signals are small in amplitude and suffer from interference from RF noise generated by the Linear Accelerator electronics. For a real time dose reconstruction, a fast and effective denoising solution is required to increase the signal to noise in the measured XA signals. Here, we present a method to denoise the XA signals using deep learning neural networks. A Convolutional Neural Network (CNN) that operates on the spectral domain of XA signals is used. Given a noisy XA spectrogram, the CNN predicts clean XA signals. An advanced numerical model for time domain propagation of XA waves (kWave) is used to generate the training data for the CNN. Theoretical and experimental clean and noisy XA signals are obtained by megavoltage energy X-rays with long pulse width (4 us) generated from a clinical linear accelerator.   

Modeling polymer precursors for preparation of molecularly imprinted polymers for drug delivery and sensing

Molecularly imprinted polymers (MIPs) are synthetic receptors and are promising alternatives to natural receptors (e.g. antibodies) for a range of applications requiring specific and selective molecular recognition (e.g. sensing, drug delivery, sample clean and separation, etc.). In the absence of a rational approach to the design of MIPs, monomer selection is often made on the basis of previous experience or chemical intuition which can be time intensive and very expensive. Here, we present an example of a careful computational analysis of selected monomers with the main purpose to screen out the least suitable and identify the most appropriate ones. The modeling is based on the statistical mechanical theory of molecular liquids in terms of the Reference Interaction Site Model (RISM). With this instrument, we are be able to yield one- and three-dimensional distribution functions of interaction sites constituting the molecules and predict the solution structure and thermodynamics of its species on the nanometer scale. The recommendations for synthesis and subsequent experimental verification of selected monomers are based on visual examination of the solvent nanomorphology and quantitative analysis of their thermodynamic properties, both predicted by modeling.