Neuroimaging with PET is unique in its capability to measure in vivo the occupancy of a drug. The occupancy is typically obtained by conducting PET measurements before and after administration of the ...drug. For radioligands for which no reference region exists, however, the only established procedure to estimate the occupancy from these data is via linear regression analysis, forming the basis for the so-called Lassen plot. There are several reasons why simple linear regression analysis is not ideal for analyzing these data, including regression attenuation and correlated errors.
Here, we propose the use of Likelihood Estimation of Occupancy (LEO) in such a situation. Similar to the Lassen plot, LEO uses the total distribution volume estimates at baseline and at block condition as input, but estimates the non-displaceable distribution volume (VND) and fractional occupancy (Δ) via direct maximum likelihood estimation (MLE).
This study outlines the rationale for using MLE to estimate Δ and VND from PET data, and evaluates its performance in relation to the Lassen Plot via two separate simulation experiments. Finally, LEO and Lassen plot are applied to a PET dataset acquired with 11CWAY-100635.
LEO can exploit the covariance structure of the data to improve the accuracy and precision of the estimates of Δ and VND. Theoretically, the covariance matrix can be extracted from a test-retest dataset for the radioligand at hand. Several procedures to estimate the covariance matrix were considered as part of the simulation experiments, and the effect of the test-retest sample size was also assessed.
The results are conclusive in that MLE can be used to estimate Δ and VND from PET data, avoiding the limitations associated with linear regression. The performance of LEO was, naturally, dependent on the procedure used to estimate the covariance matrix, and the test-retest sample size. Given a test-retest sample size of at least 5, but preferably 10 individuals, LEO provides higher accuracy and precision than Lassen plot in the estimation of Δ and VND. We conclude that LEO is valuable in drug occupancy studies.
•We present a new method to estimate drug occupancy from brain PET studies.•The method is evaluated using two simulation experiments and a real dataset.•The performance of the new method is compared to that of a wellestablished Method.•Results are conclusive in that the new method is preferable over existing methods.•We share the code to other researchers conducting drug occupancy studies.
Spline-based approaches to non-parametric and semiparametric regression, as well as to regression of scalar outcomes on functional predictors, entail choosing a parameter controlling the extent to ...which roughness of the fitted function is penalized. We demonstrate that the equations determining two popular methods for smoothing parameter selection, generalized cross-validation and restricted maximum likelihood, share a similar form that allows us to prove several results which are common to both, and to derive a condition under which they yield identical values. These ideas are illustrated by application of functional principal component regression, a method for regressing scalars on functions, to two chemometric data sets.
The N-methyl-D-aspartate receptor antagonist ketamine can improve major depressive disorder (MDD) within hours. To evaluate the putative role of glutamatergic and GABAergic systems in ketamine's ...antidepressant action, medial prefrontal cortical (mPFC) levels of glutamate+glutamine (Glx) and γ-aminobutyric acid (GABA) were measured before, during, and after ketamine administration using proton magnetic resonance spectroscopy. Ketamine (0.5 mg kg(-1) intravenously) was administered to 11 depressed patients with MDD. Glx and GABA mPFC responses were measured as ratios relative to unsuppressed voxel tissue water (W) successfully in 8/11 patients. Ten of 11 patients remitted (50% reduction in 24-item Hamilton Depression Rating Scale and total score ⩽10) within 230 min of commencing ketamine. mPFC Glx/W and GABA/W peaked at 37.8%±7.5% and 38.0%±9.1% above baseline in ~26 min. Mean areas under the curve for Glx/W (P=0.025) and GABA/W (P=0.005) increased and correlated (r=0.796; P=0.018). Clinical improvement correlated with 90-min norketamine concentration (df=6, r=-0.78, P=0.023), but no other measures.
•SiMBA is a pharmacokinetic modelling approach for Positron Emission Tomography data.•It is a multivariate hierarchical implementation of the two-tissue compartment model.•This approach exploits ...similarities between individuals, regions and parameters.•SiMBA improves quantitative accuracy, but also precision of statistical inferences.
Positron emission tomography (PET) is an in vivo imaging method essential for studying the neurochemical pathophysiology of psychiatric and neurological disease. However, its high cost and exposure of participants to radiation make it unfeasible to employ large sample sizes. The major shortcoming of PET imaging is therefore its lack of power for studying clinically-relevant research questions. Here, we introduce a new method for performing PET quantification and analysis called SiMBA, which helps to alleviate these issues by improving the efficiency of PET analysis by exploiting similarities between both individuals and regions within individuals. In simulated 11CWAY100635 data, SiMBA greatly improves both statistical power and the consistency of effect size estimation without affecting the false positive rate. This approach makes use of hierarchical, multifactor, multivariate Bayesian modelling to effectively borrow strength across the whole dataset to improve stability and robustness to measurement error. In so doing, parameter identifiability and estimation are improved, without sacrificing model interpretability. This comes at the cost of increased computational overhead, however this is practically negligible relative to the time taken to collect PET data. This method has the potential to make it possible to test clinically-relevant hypotheses which could never be studied before given the practical constraints. Furthermore, because this method does not require any additional information over and above that required for traditional analysis, it makes it possible to re-examine data which has already previously been collected at great expense. In the absence of dramatic advancements in PET image data quality, radiotracer development, or data sharing, PET imaging has been fundamentally limited in the scope of research hypotheses which could be studied. This method, especially combined with the recent steps taken by the PET imaging community to embrace data sharing, will make it possible to greatly improve the research possibilities and clinical relevance of PET neuroimaging.
Functional support vector machine Xie, Shanghong; Ogden, R Todd
Biostatistics (Oxford, England),
2024-Mar-13, 2024-03-13, 20240313
Journal Article
Peer reviewed
Linear and generalized linear scalar-on-function modeling have been commonly used to understand the relationship between a scalar response variable (e.g. continuous, binary outcomes) and functional ...predictors. Such techniques are sensitive to model misspecification when the relationship between the response variable and the functional predictors is complex. On the other hand, support vector machines (SVMs) are among the most robust prediction models but do not take account of the high correlations between repeated measurements and cannot be used for irregular data. In this work, we propose a novel method to integrate functional principal component analysis with SVM techniques for classification and regression to account for the continuous nature of functional data and the nonlinear relationship between the scalar response variable and the functional predictors. We demonstrate the performance of our method through extensive simulation experiments and two real data applications: the classification of alcoholics using electroencephalography signals and the prediction of glucobrassicin concentration using near-infrared reflectance spectroscopy. Our methods especially have more advantages when the measurement errors in functional predictors are relatively large.
In this paper we first provide an overview of the recently formulated nonlinear constitutive framework for the quasi-static response of electroelastic solids and its isotropic specialization. The ...general theory exhibits a strong nonlinear coupling between electric and mechanical effects. The main part of the paper focuses on the governing equations describing the linearized response of electroelastic solids superimposed on a state of finite deformation in the presence of an electric field for independent incremental changes in the electric displacement and the deformation within the material. The associated incremental changes in the stress and the electric field within the material and the surrounding space and the incremental boundary conditions are derived for mechanically unconstrained and constrained electroelastic solids and in the isotropic specialization. By way of illustration of the incremental theory, we specialize the constitutive law to an electroelastic neo-Hookean material, and consider the stability of a half-space subjected to pure homogeneous deformation in the presence of an applied electric field normal to its surface. We show that stability is crucially dependent on the magnitudes of the electromechanical coupling parameters in the constitutive equation.
In a function‐on‐scalar regression framework, we present some modeling strategies for functional mixed models and also some approaches for making inference about various aspects of the fixed effects. ...This is presented in the context of modeling positron emission tomography (PET) data in order to explore the density of various proteins of interest throughout the human brain. For this application, information about the density of the target protein in a given brain region is encapsulated in the impulse response function (IRF) of the region. Previous work on nonparametric estimation of the IRF is limited in that it is only able to model a single brain region at a time. We propose an extension, based on principles of functional data analysis, that will allow modeling of multiple brain regions simultaneously. Applicable more broadly to functional mixed regression modeling, we discuss two general approaches for permutation testing and describe valid strategies for identifying exchangeable units within the model and building corresponding permutation tests. We illustrate our methods with an application to PET data and explore the effects of depression and sex on the IRF.
This paper is concerned with determining material parameters in incompressible isotropic elastic strain–energy functions on the basis of a non-linear least squares optimization method by fitting data ...from the classical experiments of Treloar and Jones and Treloar on natural rubber. We consider three separate forms of strain-energy function, based respectively on use of the principal stretches, the usual principal invariants of the Cauchy-Green deformation tensor and a certain set of ‘orthogonal’ invariants of the logarithmic strain tensor. We highlight, in particular, (a) the relative errors generated in the fitting process and (b) the occurrence of multiple sets of optimal material parameters for the same data sets. This multiplicity can lead to very different numerical solutions for a given boundary-value problem, and this is illustrated for a simple example.
Objective: The conventional approach to the analysis of dynamic PET data can be described as a two-stage approach. In Stage 1, each individual's kinetic parameter estimates are obtained by modeling ...their PET data. Then in Stage 2, those parameter estimates are treated as though they are the observed data and compared across subjects and groups using standard statistical analyses. In this context, we explore the application of nonlinear mixed-effects (NLME) model under the assumptions of simplified reference tissue model. Methods: In the NLME framework, all subject's PET data are modeled simultaneously and the estimation of kinetic parameters and statistical inference across subjects are performed jointly. Results: In simulated <inline-formula><tex-math notation="LaTeX">{}^{11}</tex-math></inline-formula>CWAY100635 data, this NLME approach shows improved power (6-27% increase) for detecting group differences and greater consistency of population (1.13-1.44 times greater) and individual-level parameter estimation compared to the two-stage approach applying simplified reference tissue model for pharmacokinetic modeling of PET data. We applied our NLME approach to clinical PET data and observed shrinkage of individual-level parameters that is inherent in this modeling structure. Conclusion: The proposed approach is more powerful and accurate than the two-stage approach under the assumptions of simplified reference tissue model in PET data. Significance: The stability of the NLME approach not only improves the efficiency of collected data, but also comes with no additional financial cost and negligible computation cost.
Nonlinear electroelasticity DORFMANN, A; OGDEN, R. W
Acta mechanica,
03/2005, Volume:
174, Issue:
3-4
Journal Article
Peer reviewed
Electro-sensitive (ES) elastomers are "smart materials" whose mechanical properties may be changed significantly by the application of an electric field. In this paper, we provide a theoretical basis ...for the characterization of the nonlinear electroelastic properties of these materials. The theory is then applied to some simple prototype boundary-value problems in order to illustrate the effect of an electric field on the mechanical response. PUBLICATION ABSTRACT
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