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Determination of nonlinear genetic architecture using compressed sensing.

ABSTRACT: BACKGROUND:One of the fundamental problems of modern genomics is to extract the genetic architecture of a complex trait from a data set of individual genotypes and trait values. Establishing this important connection between genotype and phenotype is complicated by the large number of candidate genes, the potentially large number of causal loci, and the likely presence of some nonlinear interactions between different genes. Compressed Sensing methods obtain solutions to under-constrained systems of linear equations. These methods can be applied to the problem of determining the best model relating genotype to phenotype, and generally deliver better performance than simply regressing the phenotype against each genetic variant, one at a time. We introduce a Compressed Sensing method that can reconstruct nonlinear genetic models (i.e., including epistasis, or gene-gene interactions) from phenotype-genotype (GWAS) data. Our method uses L1-penalized regression applied to nonlinear functions of the sensing matrix. RESULTS:The computational and data resource requirements for our method are similar to those necessary for reconstruction of linear genetic models (or identification of gene-trait associations), assuming a condition of generalized sparsity, which limits the total number of gene-gene interactions. An example of a sparse nonlinear model is one in which a typical locus interacts with several or even many others, but only a small subset of all possible interactions exist. It seems plausible that most genetic architectures fall in this category. We give theoretical arguments suggesting that the method is nearly optimal in performance, and demonstrate its effectiveness on broad classes of nonlinear genetic models using simulated human genomes and the small amount of currently available real data. A phase transition (i.e., dramatic and qualitative change) in the behavior of the algorithm indicates when sufficient data is available for its successful application. CONCLUSION:Our results indicate that predictive models for many complex traits, including a variety of human disease susceptibilities (e.g., with additive heritability h (2)?0.5), can be extracted from data sets comprised of n ??100s individuals, where s is the number of distinct causal variants influencing the trait. For example, given a trait controlled by ?10 k loci, roughly a million individuals would be sufficient for application of the method.

SUBMITTER: Ho CM

PROVIDER: S-EPMC4570224 | biostudies-literature | 2015

REPOSITORIES: biostudies-literature

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Determination of nonlinear genetic architecture using compressed sensing.

Ho Chiu Man CM Hsu Stephen D H SD

GigaScience 20150914

<h4>Background</h4>One of the fundamental problems of modern genomics is to extract the genetic architecture of a complex trait from a data set of individual genotypes and trait values. Establishing this important connection between genotype and phenotype is complicated by the large number of candidate genes, the potentially large number of causal loci, and the likely presence of some nonlinear interactions between different genes. Compressed Sensing methods obtain solutions to under-constrained ...[more]

PMID: 26380078

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Project description:Electron paramagnetic resonance (EPR) imaging has evolved as a promising tool to provide non-invasive assessment of tissue oxygenation levels. Due to the extremely short T2 relaxation time of electrons, single point imaging (SPI) is used in EPRI, limiting achievable spatial and temporal resolution. This presents a problem when attempting to measure changes in hypoxic state. In order to capture oxygen variation in hypoxic tissues and localize cycling hypoxia regions, an accelerated EPRI imaging method with minimal loss of information is needed.We present an image acceleration technique, partial Fourier compressed sensing (PFCS), that combines compressed sensing (CS) and partial Fourier reconstruction. PFCS augments the original CS equation using conjugate symmetry information for missing measurements. To further improve image quality in order to reconstruct low-resolution EPRI images, a projection onto convex sets (POCS)-based phase map and a spherical-sampling mask are used in the reconstruction process. The PFCS technique was used in phantoms and in vivo SCC7 tumor mice to evaluate image quality and accuracy in estimating O2 concentration.In both phantom and in vivo experiments, PFCS demonstrated the ability to reconstruct images more accurately with at least a 4-fold acceleration compared to traditional CS. Meanwhile, PFCS is able to better preserve the distinct spatial pattern in a phantom with a spatial resolution of 0.6mm. On phantoms containing Oxo63 solution with different oxygen concentrations, PFCS reconstructed linewidth maps that were discriminative of different O2 concentrations. Moreover, PFCS reconstruction of partially sampled data provided a better discrimination of hypoxic and oxygenated regions in a leg tumor compared to traditional CS reconstructed images.EPR images with an acceleration factor of four are feasible using PFCS with reasonable assessment of tissue oxygenation. The technique can greatly enhance EPR applications and improve our understanding cycling hypoxia. Moreover this technique can be easily extended to various MRI applications.

Project description:BackgroundEndogenous contrast T1? cardiovascular magnetic resonance (CMR) can detect scar or infiltrative fibrosis in patients with ischemic or non-ischemic cardiomyopathy. Existing 2D T1? techniques have limited spatial coverage or require multiple breath-holds. The purpose of this project was to develop an accelerated, free-breathing 3D T1? mapping sequence with whole left ventricle coverage using a multicoil, compressed sensing (CS) reconstruction technique for rapid reconstruction of undersampled k-space data.MethodsWe developed a cardiac- and respiratory-gated, free-breathing 3D T1? sequence and acquired data using a variable-density k-space sampling pattern (A?=?3). The effect of the transient magnetization trajectory, incomplete recovery of magnetization between T1?-preparations (heart rate dependence), and k-space sampling pattern on T1? relaxation time error and edge blurring was analyzed using Bloch simulations for normal and chronically infarcted myocardium. Sequence accuracy and repeatability was evaluated using MnCl2 phantoms with different T1? relaxation times and compared to 2D measurements. We further assessed accuracy and repeatability in healthy subjects and compared these results to 2D breath-held measurements.ResultsThe error in T1? due to incomplete recovery of magnetization between T1?-preparations was T1?healthy =?6.1% and T1?infarct =?10.8% at 60?bpm and T1?healthy =?13.2% and T1?infarct =?19.6% at 90?bpm. At a heart rate of 60?bpm, error from the combined effects of readout-dependent magnetization transients, k-space undersampling and reordering was T1?healthy =?12.6% and T1?infarct =?5.8%. CS reconstructions had improved edge sharpness (blur metric?=?0.15) compared to inverse Fourier transform reconstructions (blur metric?=?0.48). There was strong agreement between the mean T1? estimated from the 2D and accelerated 3D data (R2 =?0.99; P <?0.05) acquired on the MnCl2 phantoms. The mean R1? estimated from the accelerated 3D sequence was highly correlated with MnCl2 concentration (R2 =?0.99; P?<?0.05). 3D T1? acquisitions were successful in all human subjects. There was no significant bias between undersampled 3D T1? and breath-held 2D T1? (mean bias?=?0.87) and the measurements had good repeatability (COV2D =?6.4% and COV3D =?7.1%).ConclusionsThis is the first report of an accelerated, free-breathing 3D T1? mapping of the left ventricle. This technique may improve non-contrast myocardial tissue characterization in patients with heart disease in a scan time appropriate for patients.

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Determination of nonlinear genetic architecture using compressed sensing.

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Determination of nonlinear genetic architecture using compressed sensing.

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