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AbstractA compact analytical form is derived through an integration approach for the interaction between a sphere and a thin rod of finite and infinite lengths, with each object treated as a continuous medium of material points interacting by the Lennard-Jones 12-6 potential and the total interaction potential as a summation of the pairwise potential between material points on the two objects. Expressions for the resultant force and torque are obtained. Various asymptotic limits of the analytical sphere–rod potential are discussed. The integrated potential is applied to investigate the adhesion between a sphere and a thin rod. When the rod is sufficiently long and the sphere sufficiently large, the equilibrium separation between the two (defined as the distance from the center of the sphere to the axis of the rod) is found to be well approximated as$$a+0.787\sigma $$ $a+0.787\sigma$, whereais the radius of the sphere and$$\sigma $$ $\sigma$is the unit of length of the Lennard–Jones potential. Furthermore, the adhesion between the two is found to scale with$$\sqrt{a}$$ $\sqrt{a}$. Graphic abstract) 

Abstract BackgroundImaging, cognitive and fluid data have been widely studied to identify quantitative biomarkers that can help predict the status and progression of Alzheimer’s disease (AD). However, it is still an underexplored topic whether there exist subpopulations with different genetic profiles across which the biomarker‐based prediction models may vary. We propose to use the Chow test (Chow 1960 Econometrica 28(3)) to perform genetically stratified analyses for identifying SNP‐based subpopulations coupled with precision AD biomarkers with varying effects on future diagnosis in these subpopulations. The investigation of such SNPs and precision biomarkers may eventually pave the way for increased customization of AD care. MethodParticipants included 1,324 subjects from the ADNI cohort with both AD biomarker and genotyping data available (http://www.pi4cs.org/qt‐pad‐challenge). 30 significant (P < 1.5E‐278) AD SNPs were sourced from (Jansen 2019 NatGen). Chow tests were performed to determine whether each of baseline visit measures of 16 AD biomarkers predicted AD diagnosis at the three‐year visit with varying slopes when stratifying upon the allelic dosage of each of 30 chosen SNPs. Bonferroni correction (P < 1.04E‐4) was employed to correct for multiple comparisons. ResultMultiple SNP‐biomarker pairs showed significant genetically driven deviations in the regression coefficients when predicting diagnosis in three years using baseline biomarkers (Figure 1). Top SNP hits involved rs769449 (Chr 19,APOE) and rs7561528 (Chr 2,LOC105373605), and almost all 16 studied biomarkers demonstrated differential slopes in different genotype groups to predict diagnosis in three years. To examine the details of these top findings, the regression coefficients calculated for each of the five most significant biomarkers of both SNPs were bootstrapped and plotted in Figure 2. ConclusionGenetic analysis of AD candidate SNPs in conjunction with AD biomarker data via the Chow test identified several SNPs coupled with precision AD biomarkers with varying prognosis effects in the corresponding genotype groups. These findings provide valuable information to reveal disease heterogeneity and help facilitate precision medicine. 

Abstract Radiogenomics uses machine-learning (ML) to directly connect the morphologic and physiological appearance of tumors on clinical imaging with underlying genomic features. Despite extensive growth in the area of radiogenomics across many cancers, and its potential role in advancing clinical decision making, no published studies have directly addressed uncertainty in these model predictions. We developed a radiogenomics ML model to quantify uncertainty using transductive Gaussian Processes (GP) and a unique dataset of 95 image-localized biopsies with spatially matched MRI from 25 untreated Glioblastoma (GBM) patients. The model generated predictions for regional EGFR amplification status (a common and important target in GBM) to resolve the intratumoral genetic heterogeneity across each individual tumor—a key factor for future personalized therapeutic paradigms. The model used probability distributions for each sample prediction to quantify uncertainty, and used transductive learning to reduce the overall uncertainty. We compared predictive accuracy and uncertainty of the transductive learning GP model against a standard GP model using leave-one-patient-out cross validation. Additionally, we used a separate dataset containing 24 image-localized biopsies from 7 high-grade glioma patients to validate the model. Predictive uncertainty informed the likelihood of achieving an accurate sample prediction. When stratifying predictions based on uncertainty, we observed substantially higher performance in the group cohort (75% accuracy, n = 95) and amongst sample predictions with the lowest uncertainty (83% accuracy, n = 72) compared to predictions with higher uncertainty (48% accuracy, n = 23), due largely to data interpolation (rather than extrapolation). On the separate validation set, our model achieved 78% accuracy amongst the sample predictions with lowest uncertainty. We present a novel approach to quantify radiogenomics uncertainty to enhance model performance and clinical interpretability. This should help integrate more reliable radiogenomics models for improved medical decision-making.