A physics-based correction model for homogenizing sub-daily temperature series

A new physics-based technique for correcting inhomogeneities present in sub-daily temperature records is proposed. The approach accounts for changes in the sensor-shield characteristics that affect the energy balance dependent on ambient weather conditions (radiation, wind). An empirical model is formulated that reflects the main atmospheric processes and can be used in the correction step of a homogenization procedure. The model accounts for short- and long-wave radiation fluxes (including a snow cover component for albedo calculation) of a measurement system, such as a radiation shield. One part of the flux is further modulated by ventilation. The model requires only cloud cover and wind speed for each day, but detailed site-specific information is necessary. The final model has three free parameters, one of which is a constant offset. The three parameters can be determined, e.g., using the mean offsets for three observation times. The model is developed using the example of the change from the Wild screen to the Stevenson screen in the temperature record of Basel, Switzerland, in 1966. It is evaluated based on parallel measurements of both systems during a sub-period at this location, which were discovered during the writing of this paper. The model can be used in the correction step of homogenization to distribute a known mean step-size to every single measurement, thus providing a reasonable alternative correction procedure for high-resolution historical climate series. It also constitutes an error model, which may be applied, e.g., in data assimilation approaches.

Functional error modeling for uncertainty quantification in hydrogeology

Approximate models (proxies) can be employed to reduce the computational costs of estimating uncertainty. The price to pay is that the approximations introduced by the proxy model can lead to a biased estimation. To avoid this problem and ensure a reliable uncertainty quantification, we propose to combine functional data analysis and machine learning to build error models that allow us to obtain an accurate prediction of the exact response without solving the exact model for all realizations. We build the relationship between proxy and exact model on a learning set of geostatistical realizations for which both exact and approximate solvers are run. Functional principal components analysis (FPCA) is used to investigate the variability in the two sets of curves and reduce the dimensionality of the problem while maximizing the retained information. Once obtained, the error model can be used to predict the exact response of any realization on the basis of the sole proxy response. This methodology is purpose-oriented as the error model is constructed directly for the quantity of interest, rather than for the state of the system. Also, the dimensionality reduction performed by FPCA allows a diagnostic of the quality of the error model to assess the informativeness of the learning set and the fidelity of the proxy to the exact model. The possibility of obtaining a prediction of the exact response for any newly generated realization suggests that the methodology can be effectively used beyond the context of uncertainty quantification, in particular for Bayesian inference and optimization.

Single fluoroscopic image based 2D/3D reconstruction of a scaled, patient-specific vertebral model

Purpose Accurate three-dimensional (3D) models of lumbar vertebrae can enable image-based 3D kinematic analysis. The common approach to derive 3D models is by direct segmentation of CT or MRI datasets. However, these have the disadvantages that they are expensive, timeconsuming and/or induce high-radiation doses to the patient. In this study, we present a technique to automatically reconstruct a scaled 3D lumbar vertebral model from a single two-dimensional (2D) lateral fluoroscopic image. Methods Our technique is based on a hybrid 2D/3D deformable registration strategy combining a landmark-to-ray registration with a statistical shape model-based 2D/3D reconstruction scheme. Fig. 1 shows different stages of the reconstruction process. Four cadaveric lumbar spine segments (total twelve lumbar vertebrae) were used to validate the technique. To evaluate the reconstruction accuracy, the surface models reconstructed from the lateral fluoroscopic images were compared to the associated ground truth data derived from a 3D CT-scan reconstruction technique. For each case, a surface-based matching was first used to recover the scale and the rigid transformation between the reconstructed surface model Results Our technique could successfully reconstruct 3D surface models of all twelve vertebrae. After recovering the scale and the rigid transformation between the reconstructed surface models and the ground truth models, the average error of the 2D/3D surface model reconstruction over the twelve lumbar vertebrae was found to be 1.0 mm. The errors of reconstructing surface models of all twelve vertebrae are shown in Fig. 2. It was found that the mean errors of the reconstructed surface models in comparison to their associated ground truths after iterative scaled rigid registrations ranged from 0.7 mm to 1.3 mm and the rootmean squared (RMS) errors ranged from 1.0 mm to 1.7 mm. The average mean reconstruction error was found to be 1.0 mm. Conclusion An accurate, scaled 3D reconstruction of the lumbar vertebra can be obtained from a single lateral fluoroscopic image using a statistical shape model based 2D/3D reconstruction technique. Future work will focus on applying the reconstructed model for 3D kinematic analysis of lumbar vertebrae, an extension of our previously-reported imagebased kinematic analysis. The developed method also has potential applications in surgical planning and navigation.

Kernel density correlation based non-rigid point set matching for statistical model-based 2D/3D reconstruction

This paper presents a kernel density correlation based nonrigid point set matching method and shows its application in statistical model based 2D/3D reconstruction of a scaled, patient-specific model from an un-calibrated x-ray radiograph. In this method, both the reference point set and the floating point set are first represented using kernel density estimates. A correlation measure between these two kernel density estimates is then optimized to find a displacement field such that the floating point set is moved to the reference point set. Regularizations based on the overall deformation energy and the motion smoothness energy are used to constraint the displacement field for a robust point set matching. Incorporating this non-rigid point set matching method into a statistical model based 2D/3D reconstruction framework, we can reconstruct a scaled, patient-specific model from noisy edge points that are extracted directly from the x-ray radiograph by an edge detector. Our experiment conducted on datasets of two patients and six cadavers demonstrates a mean reconstruction error of 1.9 mm

Pathology hinting as the combination of automatic segmentation with a statistical shape model

With improvements in acquisition speed and quality, the amount of medical image data to be screened by clinicians is starting to become challenging in the daily clinical practice. To quickly visualize and find abnormalities in medical images, we propose a new method combining segmentation algorithms with statistical shape models. A statistical shape model built from a healthy population will have a close fit in healthy regions. The model will however not fit to morphological abnormalities often present in the areas of pathologies. Using the residual fitting error of the statistical shape model, pathologies can be visualized very quickly. This idea is applied to finding drusen in the retinal pigment epithelium (RPE) of optical coherence tomography (OCT) volumes. A segmentation technique able to accurately segment drusen in patients with age-related macular degeneration (AMD) is applied. The segmentation is then analyzed with a statistical shape model to visualize potentially pathological areas. An extensive evaluation is performed to validate the segmentation algorithm, as well as the quality and sensitivity of the hinting system. Most of the drusen with a height of 85.5 microm were detected, and all drusen at least 93.6 microm high were detected.

Closed-loop control of mean arterial blood pressure during surgery with alfentanil: clinical evaluation of a novel model-based predictive controller

BACKGROUND: In contrast to hypnosis, there is no surrogate parameter for analgesia in anesthetized patients. Opioids are titrated to suppress blood pressure response to noxious stimulation. The authors evaluated a novel model predictive controller for closed-loop administration of alfentanil using mean arterial blood pressure and predicted plasma alfentanil concentration (Cp Alf) as input parameters. METHODS: The authors studied 13 healthy patients scheduled to undergo minor lumbar and cervical spine surgery. After induction with propofol, alfentanil, and mivacurium and tracheal intubation, isoflurane was titrated to maintain the Bispectral Index at 55 (+/- 5), and the alfentanil administration was switched from manual to closed-loop control. The controller adjusted the alfentanil infusion rate to maintain the mean arterial blood pressure near the set-point (70 mmHg) while minimizing the Cp Alf toward the set-point plasma alfentanil concentration (Cp Alfref) (100 ng/ml). RESULTS: Two patients were excluded because of loss of arterial pressure signal and protocol violation. The alfentanil infusion was closed-loop controlled for a mean (SD) of 98.9 (1.5)% of presurgery time and 95.5 (4.3)% of surgery time. The mean (SD) end-tidal isoflurane concentrations were 0.78 (0.1) and 0.86 (0.1) vol%, the Cp Alf values were 122 (35) and 181 (58) ng/ml, and the Bispectral Index values were 51 (9) and 52 (4) before surgery and during surgery, respectively. The mean (SD) absolute deviations of mean arterial blood pressure were 7.6 (2.6) and 10.0 (4.2) mmHg (P = 0.262), and the median performance error, median absolute performance error, and wobble were 4.2 (6.2) and 8.8 (9.4)% (P = 0.002), 7.9 (3.8) and 11.8 (6.3)% (P = 0.129), and 14.5 (8.4) and 5.7 (1.2)% (P = 0.002) before surgery and during surgery, respectively. A post hoc simulation showed that the Cp Alfref decreased the predicted Cp Alf compared with mean arterial blood pressure alone. CONCLUSION: The authors' controller has a similar set-point precision as previous hypnotic controllers and provides adequate alfentanil dosing during surgery. It may help to standardize opioid dosing in research and may be a further step toward a multiple input-multiple output controller.

Reconstruction of patient-specific 3D bone surface from 2D calibrated fluoroscopic images and point distribution model

Reconstruction of patient-specific 3D bone surface from 2D calibrated fluoroscopic images and a point distribution model is discussed. We present a 2D/3D reconstruction scheme combining statistical extrapolation and regularized shape deformation with an iterative image-to-model correspondence establishing algorithm, and show its application to reconstruct the surface of proximal femur. The image-to-model correspondence is established using a non-rigid 2D point matching process, which iteratively uses a symmetric injective nearest-neighbor mapping operator and 2D thin-plate splines based deformation to find a fraction of best matched 2D point pairs between features detected from the fluoroscopic images and those extracted from the 3D model. The obtained 2D point pairs are then used to set up a set of 3D point pairs such that we turn a 2D/3D reconstruction problem to a 3D/3D one. We designed and conducted experiments on 11 cadaveric femurs to validate the present reconstruction scheme. An average mean reconstruction error of 1.2 mm was found when two fluoroscopic images were used for each bone. It decreased to 1.0 mm when three fluoroscopic images were used.

Accurate and robust reconstruction of proximal femur from sparse intraoperative data and dense point distribution model for surgical navigation

Constructing a 3D surface model from sparse-point data is a nontrivial task. Here, we report an accurate and robust approach for reconstructing a surface model of the proximal femur from sparse-point data and a dense-point distribution model (DPDM). The problem is formulated as a three-stage optimal estimation process. The first stage, affine registration, is to iteratively estimate a scale and a rigid transformation between the mean surface model of the DPDM and the sparse input points. The estimation results of the first stage are used to establish point correspondences for the second stage, statistical instantiation, which stably instantiates a surface model from the DPDM using a statistical approach. This surface model is then fed to the third stage, kernel-based deformation, which further refines the surface model. Handling outliers is achieved by consistently employing the least trimmed squares (LTS) approach with a roughly estimated outlier rate in all three stages. If an optimal value of the outlier rate is preferred, we propose a hypothesis testing procedure to automatically estimate it. We present here our validations using four experiments, which include 1 leave-one-out experiment, 2 experiment on evaluating the present approach for handling pathology, 3 experiment on evaluating the present approach for handling outliers, and 4 experiment on reconstructing surface models of seven dry cadaver femurs using clinically relevant data without noise and with noise added. Our validation results demonstrate the robust performance of the present approach in handling outliers, pathology, and noise. An average 95-percentile error of 1.7-2.3 mm was found when the present approach was used to reconstruct surface models of the cadaver femurs from sparse-point data with noise added.

A system for 3-D reconstruction of a patient-specific surface model from calibrated X-ray images

This paper presents a system for 3-D reconstruction of a patient-specific surface model from calibrated X-ray images. Our system requires two X-ray images of a patient with one acquired from the anterior-posterior direction and the other from the axial direction. A custom-designed cage is utilized in our system to calibrate both images. Starting from bone contours that are interactively identified from the X-ray images, our system constructs a patient-specific surface model of the proximal femur based on a statistical model based 2D/3D reconstruction algorithm. In this paper, we present the design and validation of the system with 25 bones. An average reconstruction error of 0.95 mm was observed.

Accounting for baseline differences and measurement error in the analysis of change over time

If change over time is compared in several groups, it is important to take into account baseline values so that the comparison is carried out under the same preconditions. As the observed baseline measurements are distorted by measurement error, it may not be sufficient to include them as covariate. By fitting a longitudinal mixed-effects model to all data including the baseline observations and subsequently calculating the expected change conditional on the underlying baseline value, a solution to this problem has been provided recently so that groups with the same baseline characteristics can be compared. In this article, we present an extended approach where a broader set of models can be used. Specifically, it is possible to include any desired set of interactions between the time variable and the other covariates, and also, time-dependent covariates can be included. Additionally, we extend the method to adjust for baseline measurement error of other time-varying covariates. We apply the methodology to data from the Swiss HIV Cohort Study to address the question if a joint infection with HIV-1 and hepatitis C virus leads to a slower increase of CD4 lymphocyte counts over time after the start of antiretroviral therapy.

A Nonstationary Space-Time Gaussian Process Model for Partially Converged Simulations

In the context of expensive numerical experiments, a promising solution for alleviating the computational costs consists of using partially converged simulations instead of exact solutions. The gain in computational time is at the price of precision in the response. This work addresses the issue of fitting a Gaussian process model to partially converged simulation data for further use in prediction. The main challenge consists of the adequate approximation of the error due to partial convergence, which is correlated in both design variables and time directions. Here, we propose fitting a Gaussian process in the joint space of design parameters and computational time. The model is constructed by building a nonstationary covariance kernel that reflects accurately the actual structure of the error. Practical solutions are proposed for solving parameter estimation issues associated with the proposed model. The method is applied to a computational fluid dynamics test case and shows significant improvement in prediction compared to a classical kriging model.

Quantitative 1H-magnetic resonance spectroscopy of human brain: Influence of composition and parameterization of the basis set in linear combination model-fitting

Localized short-echo-time (1)H-MR spectra of human brain contain contributions of many low-molecular-weight metabolites and baseline contributions of macromolecules. Two approaches to model such spectra are compared and the data acquisition sequence, optimized for reproducibility, is presented. Modeling relies on prior knowledge constraints and linear combination of metabolite spectra. Investigated was what can be gained by basis parameterization, i.e., description of basis spectra as sums of parametric lineshapes. Effects of basis composition and addition of experimentally measured macromolecular baselines were investigated also. Both fitting methods yielded quantitatively similar values, model deviations, error estimates, and reproducibility in the evaluation of 64 spectra of human gray and white matter from 40 subjects. Major advantages of parameterized basis functions are the possibilities to evaluate fitting parameters separately, to treat subgroup spectra as independent moieties, and to incorporate deviations from straightforward metabolite models. It was found that most of the 22 basis metabolites used may provide meaningful data when comparing patient cohorts. In individual spectra, sums of closely related metabolites are often more meaningful. Inclusion of a macromolecular basis component leads to relatively small, but significantly different tissue content for most metabolites. It provides a means to quantitate baseline contributions that may contain crucial clinical information.

Statistical model-based segmentation of the proximal femur in digital antero-posterior (AP) pelvic radiographs.

PURPOSE    Segmentation of the proximal femur in digital antero-posterior (AP) pelvic radiographs is required to create a three-dimensional model of the hip joint for use in planning and treatment. However, manually extracting the femoral contour is tedious and prone to subjective bias, while automatic segmentation must accommodate poor image quality, anatomical structure overlap, and femur deformity. A new method was developed for femur segmentation in AP pelvic radiographs. METHODS    Using manual annotations on 100 AP pelvic radiographs, a statistical shape model (SSM) and a statistical appearance model (SAM) of the femur contour were constructed. The SSM and SAM were used to segment new AP pelvic radiographs with a three-stage approach. At initialization, the mean SSM model is coarsely registered to the femur in the AP radiograph through a scaled rigid registration. Mahalanobis distance defined on the SAM is employed as the search criteria for each annotated suggested landmark location. Dynamic programming was used to eliminate ambiguities. After all landmarks are assigned, a regularized non-rigid registration method deforms the current mean shape of SSM to produce a new segmentation of proximal femur. The second and third stages are iteratively executed to convergence. RESULTS    A set of 100 clinical AP pelvic radiographs (not used for training) were evaluated. The mean segmentation error was [Formula: see text], requiring [Formula: see text] s per case when implemented with Matlab. The influence of the initialization on segmentation results was tested by six clinicians, demonstrating no significance difference. CONCLUSIONS    A fast, robust and accurate method for femur segmentation in digital AP pelvic radiographs was developed by combining SSM and SAM with dynamic programming. This method can be extended to segmentation of other bony structures such as the pelvis.

A multi-model comparison of Atlantic multidecadal variability

A multi-model analysis of Atlantic multidecadal variability is performed with the following aims: to investigate the similarities to observations; to assess the strength and relative importance of the different elements of the mechanism proposed by Delworth et al. (J Clim 6:1993–2011, 1993) (hereafter D93) among coupled general circulation models (CGCMs); and to relate model differences to mean systematic error. The analysis is performed with long control simulations from ten CGCMs, with lengths ranging between 500 and 3600 years. In most models the variations of sea surface temperature (SST) averaged over North Atlantic show considerable power on multidecadal time scales, but with different periodicity. The SST variations are largest in the mid-latitude region, consistent with the short instrumental record. Despite large differences in model configurations, we find quite some consistency among the models in terms of processes. In eight of the ten models the mid-latitude SST variations are significantly correlated with fluctuations in the Atlantic meridional overturning circulation (AMOC), suggesting a link to northward heat transport changes. Consistent with this link, the three models with the weakest AMOC have the largest cold SST bias in the North Atlantic. There is no linear relationship on decadal timescales between AMOC and North Atlantic Oscillation in the models. Analysis of the key elements of the D93 mechanisms revealed the following: Most models present strong evidence that high-latitude winter mixing precede AMOC changes. However, the regions of wintertime convection differ among models. In most models salinity-induced density anomalies in the convective region tend to lead AMOC, while temperature-induced density anomalies lead AMOC only in one model. However, analysis shows that salinity may play an overly important role in most models, because of cold temperature biases in their relevant convective regions. In most models subpolar gyre variations tend to lead AMOC changes, and this relation is strong in more than half of the models.