Publications by Year: 2007

Gordon Kindlmann, Raúl San José Estépar, Marc Niethammer, Steven Haker, and Carl-Fredrik Westin. 2007. “Geodesic-loxodromes for diffusion tensor interpolation and difference measurement.” Med Image Comput Comput Assist Interv, 10, Pt 1, Pp. 1-9.Abstract
In algorithms for processing diffusion tensor images, two common ingredients are interpolating tensors, and measuring the distance between them. We propose a new class of interpolation paths for tensors, termed geodesic-loxodromes, which explicitly preserve clinically important tensor attributes, such as mean diffusivity or fractional anisotropy, while using basic differential geometry to interpolate tensor orientation. This contrasts with previous Riemannian and Log-Euclidean methods that preserve the determinant. Path integrals of tangents of geodesic-loxodromes generate novel measures of over-all difference between two tensors, and of difference in shape and in orientation.
Seung-Schik Yoo, Ninad Gujar, Peter Hu, Ferenc A Jolesz, and Matthew P Walker. 2007. “The Human Emotional Brain without Sleep - A Prefrontal Amygdala Disconnect.” Curr Biol, 17, 20, Pp. R877-8.
Peter R Lokken, Debra A Gervais, Ronald S Arellano, Kemal Tuncali, Paul R Morrison, Servet Tatli, Peter R Mueller, and Stuart G Silverman. 2007. “Inflammatory nodules mimic applicator track seeding after percutaneous ablation of renal tumors.” AJR Am J Roentgenol, 189, 4, Pp. 845-8.Abstract
OBJECTIVE: The objective of our study was to report the occurrence of benign inflammatory nodules that develop in or near applicator tracks after percutaneous radiofrequency ablation and cryoablation of renal tumors. CONCLUSION: Benign inflammatory nodules occur rarely after percutaneous ablation of renal tumors and may mimic tumor seeding of the applicator track.
Paul L Nguyen, Ming-Hui Chen, Anthony V D'Amico, Clare M Tempany, Graeme S Steele, Michele Albert, Robert A Cormack, David L Carr-Locke, Ronald Bleday, and Warren W Suh. 2007. “Magnetic Resonance Image-guided Salvage Brachytherapy after Radiation in Select Men who Initially Presented with Favorable-risk Prostate Cancer: A Prospective Phase 2 Study.” Cancer, 110, 7, Pp. 1485-92.Abstract

BACKGROUND: The authors prospectively evaluated the late gastrointestinal (GI) and genitourinary (GU) toxicity and prostate-specific antigen (PSA) control of magnetic resonance imaging (MRI)-guided brachytherapy used as salvage for radiation therapy (RT) failure. METHODS: From October 2000 to October 2005, 25 men with a rising PSA level and biopsy-proven, intraprostatic cancer at least 2 years after initial RT (external beam in 13 men and brachytherapy in 12 men) who had favorable clinical features (Gleason score < or =7, PSA < 10 ng/mL, negative pelvic and bone imaging studies), received MRI-guided salvage brachytherapy to a minimum peripheral dose of 137 gray on a phase 1/2 protocol. Estimates of toxicity and cancer control were calculated using the Kaplan-Meier method. RESULTS: The median follow-up was 47 months. The 4-year estimate of grade 3 or 4 GI or GU toxicity was 30%, and 13% of patients required a colostomy and/or urostomy to repair a fistula. An interval < 4.5 years between RT courses was associated with both outcomes with a hazard ratio of 12 (95% confidence interval [95% CI], 1.4-100; P = .02) for grade 3 or 4 toxicity and 25 (95% CI, 1.1-529; P = .04) for colostomy and/or urostomy. PSA control (nadir +2 definition) was 70% at 4 years. CONCLUSIONS: The current results indicated that MRI-guided salvage brachytherapy in men who are selected based on presenting characteristics and post-failure PSA kinetics can achieve high PSA control rates, although complications requiring surgical intervention may occur in 10% to 15% of patients. Prospective randomized studies are needed to characterize the relative cancer control and toxicity after all forms of salvage local therapy.

Lilla Zöllei, Mark Jenkinson, Samson Timoner, and William Wells. 2007. “A marginalized MAP approach and EM optimization for pair-wise registration.” Inf Process Med Imaging, 20, Pp. 662-74.Abstract
We formalize the pair-wise registration problem in a maximum a posteriori (MAP) framework that employs a multinomial model of joint intensities with parameters for which we only have a prior distribution. To obtain an MAP estimate of the aligning transformation alone, we treat the multinomial parameters as nuisance parameters, and marginalize them out. If the prior on those is uninformative, the marginalization leads to registration by minimization of joint entropy. With an informative prior, the marginalization leads to minimization of the entropy of the data pooled with pseudo observations from the prior. In addition, we show that the marginalized objective function can be optimized by the Expectation-Maximization (EM) algorithm, which yields a simple and effective iteration for solving entropy-based registration problems. Experimentally, we demonstrate the effectiveness of the resulting EM iteration for rapidly solving a challenging intra-operative registration problem.
Ayres C Fan, John W Fisher, William M Wells, James J Levitt, and Alan S Willsky. 2007. “MCMC curve sampling for image segmentation.” Med Image Comput Comput Assist Interv, 10, Pt 2, Pp. 477-85.Abstract
We present an algorithm to generate samples from probability distributions on the space of curves. We view a traditional curve evolution energy functional as a negative log probability distribution and sample from it using a Markov chain Monte Carlo (MCMC) algorithm. We define a proposal distribution by generating smooth perturbations to the normal of the curve and show how to compute the transition probabilities to ensure that the samples come from the posterior distribution. We demonstrate some advantages of sampling methods such as robustness to local minima, better characterization of multi-modal distributions, access to some measures of estimation error, and ability to easily incorporate constraints on the curve.
Kemal Tuncali, Paul R Morrison, Carl S Winalski, John A Carrino, S Shankar, JE Ready, Eric Sonnenberg, and Stuart G Silverman. 2007. “MRI-guided percutaneous cryotherapy for soft-tissue and bone metastases: initial experience.” AJR Am J Roentgenol., 189, 1, Pp. 232-9. Publisher's VersionAbstract


We sought to determine the safety and feasibility of percutaneous MRI-guided cryotherapy in the care of patients with refractory or painful metastatic lesions of soft tissue and bone adjacent to critical structures.


Twenty-seven biopsy-proven metastatic lesions of soft tissue (n = 17) and bone (n = 10) in 22 patients (15 men, seven women; age range, 24-85 years) were managed with MRI-guided percutaneous cryotherapy. The mean lesion diameter was 5.2 cm. Each lesion was adjacent to or encasing one or more critical structures, including bowel, bladder, and major blood vessels. A 0.5-T open interventional MRI system was used for cryoprobe placement and ice-ball monitoring. Complications were assessed for all treatments. CT or MRI was used to determine local control of 21 tumors. Pain palliation was assessed clinically in 19 cases. The mean follow-up period was 19.5 weeks.


Twenty-two (81%) of 27 tumors were managed without injury to adjacent critical structures. Two patients had transient lower extremity numbness, and two had both urinary retention and transient lower extremity paresthesia. One patient had chronic serous vaginal discharge, and one sustained a femoral neck fracture at the ablation site 6 weeks after treatment. Thirteen (62%) of the 21 tumors for which follow-up information was available either remained the same size as before treatment or regressed. Eight tumors progressed (mean local progression-free interval, 5.6 months; range, 3-18 months). Pain was palliated in 17 of 19 patients; six of the 17 experienced complete relief, and 11 had partial relief.


MRI-guided percutaneous cryotherapy for metastatic lesions of soft tissue and bone adjacent to critical structures is safe and can provide local tumor control and pain relief in most patients.

Annie M Tang, Daniel F Kacher, Edmund Y Lam, Michael Brodsky, Ferenc A Jolesz, and Edward S Yang. 2007. “Multimodal imaging: simultaneous MRI and ultrasound imaging for carotid arteries visualization.” Conf Proc IEEE Eng Med Biol Soc, 2007, Pp. 2603-6.Abstract
The purpose of this study is to examine the feasibility of simultaneous Magnetic Resonance Imaging (MRI) and Ultrasound (US) imaging in visualizing anatomical structures and functions in human carotid arteries. US has high frame rate in visualizing dynamic changes while high resolution MRI is capable of capturing volumetric structures with the best tissue contrast. Concurrent multi-modal image acquisition allows fusion of US Doppler flow measurement with volumetric MRI. We present a method for acquiring MR images in a known orientation with respect to US image by passive fiducial tracking and demonstrate concurrent real-time imaging in the right Common Carotid Artery (CCA) in both modalities. Preliminary results suggest that US and MRI can operate concurrently with proper shielding. Dispensability measurements are feasible on both modalities at the co-incident plane.
Delphine Nain, Steven Haker, Aaron Bobick, and Allen Tannenbaum. 2007. “Multiscale 3-D shape representation and segmentation using spherical wavelets.” IEEE Trans Med Imaging, 26, 4, Pp. 598-618.Abstract
This paper presents a novel multiscale shape representation and segmentation algorithm based on the spherical wavelet transform. This work is motivated by the need to compactly and accurately encode variations at multiple scales in the shape representation in order to drive the segmentation and shape analysis of deep brain structures, such as the caudate nucleus or the hippocampus. Our proposed shape representation can be optimized to compactly encode shape variations in a population at the needed scale and spatial locations, enabling the construction of more descriptive, nonglobal, nonuniform shape probability priors to be included in the segmentation and shape analysis framework. In particular, this representation addresses the shortcomings of techniques that learn a global shape prior at a single scale of analysis and cannot represent fine, local variations in a population of shapes in the presence of a limited dataset. Specifically, our technique defines a multiscale parametric model of surfaces belonging to the same population using a compact set of spherical wavelets targeted to that population. We further refine the shape representation by separating into groups wavelet coefficients that describe independent global and/or local biological variations in the population, using spectral graph partitioning. We then learn a prior probability distribution induced over each group to explicitly encode these variations at different scales and spatial locations. Based on this representation, we derive a parametric active surface evolution using the multiscale prior coefficients as parameters for our optimization procedure to naturally include the prior for segmentation. Additionally, the optimization method can be applied in a coarse-to-fine manner. We apply our algorithm to two different brain structures, the caudate nucleus and the hippocampus, of interest in the study of schizophrenia. We show: 1) a reconstruction task of a test set to validate the expressiveness of our multiscale prior and 2) a segmentation task. In the reconstruction task, our results show that for a given training set size, our algorithm significantly improves the approximation of shapes in a testing set over the Point Distribution Model, which tends to oversmooth data. In the segmentation task, our validation shows our algorithm is computationally efficient and outperforms the Active Shape Model algorithm, by capturing finer shape details.
Sharon Peled. 2007. “New perspectives on the sources of white matter DTI signal.” IEEE Trans Med Imaging, 26, 11, Pp. 1448-55.Abstract
A minimalist numerical model of white matter is presented, the objective of which is to help provide a biological basis for improved diffusion tensor imaging (DTI) analysis. Water diffuses, relaxes, and exchanges in three compartments-intracellular, extracellular, and myelin sheath. Exchange between compartments is defined so as to depend on the diffusion coefficients and the compartment sizes. Based on the model, it is proposed that an additive "baseline tensor" that correlates with intraaxonal water volume be included in the computation. Anisotropy and tortuosity calculated from such analysis may correspond better to tract ultrastructure than if calculated without the baseline. According to the model, reduced extracellular volume causes increased baseline and reduced apparent diffusion. Depending on the pulse sequence, reduced permeability can cause an increase in both the baseline and apparent diffusion.
Freddy Odille, Cédric Pasquier, Roger Abächerli, Pierre-André Vuissoz, Gary P Zientara, and Jacques Felblinger. 2007. “Noise cancellation signal processing method and computer system for improved real-time electrocardiogram artifact correction during MRI data acquisition.” IEEE Trans Biomed Eng, 54, 4, Pp. 630-40.Abstract
A system was developed for real-time electrocardiogram (ECG) analysis and artifact correction during magnetic resonance (MR) scanning, to improve patient monitoring and triggering of MR data acquisitions. Based on the assumption that artifact production by magnetic field gradient switching represents a linear time invariant process, a noise cancellation (NC) method is applied to ECG artifact linear prediction. This linear prediction is performed using a digital finite impulse response (FIR) matrix, that is computed employing ECG and gradient waveforms recorded during a training scan. The FIR filters are used during further scanning to predict artifacts by convolution of the gradient waveforms. Subtracting the artifacts from the raw ECG signal produces the correction with minimal delay. Validation of the system was performed both off-line, using prerecorded signals, and under actual examination conditions. The method is implemented using a specially designed Signal Analyzer and Event Controller (SAEC) computer and electronics. Real-time operation was demonstrated at 1 kHz with a delay of only 1 ms introduced by the processing. The system opens the possibility of automatic monitoring algorithms for electrophysiological signals in the MR environment.
Neculai Archip, Olivier Clatz, Stephen Whalen, Dan Kacher, Andriy Fedorov, Andriy Kot, Nikos Chrisochoides, Ferenc A Jolesz, Alexandra J Golby, Peter M Black, and Simon K Warfield. 2007. “Non-rigid alignment of pre-operative MRI, fMRI, and DT-MRI with intra-operative MRI for enhanced visualization and navigation in image-guided neurosurgery.” Neuroimage, 35, 2, Pp. 609-24.Abstract

OBJECTIVE: The usefulness of neurosurgical navigation with current visualizations is seriously compromised by brain shift, which inevitably occurs during the course of the operation, significantly degrading the precise alignment between the pre-operative MR data and the intra-operative shape of the brain. Our objectives were (i) to evaluate the feasibility of non-rigid registration that compensates for the brain deformations within the time constraints imposed by neurosurgery, and (ii) to create augmented reality visualizations of critical structural and functional brain regions during neurosurgery using pre-operatively acquired fMRI and DT-MRI. MATERIALS AND METHODS: Eleven consecutive patients with supratentorial gliomas were included in our study. All underwent surgery at our intra-operative MR imaging-guided therapy facility and have tumors in eloquent brain areas (e.g. precentral gyrus and cortico-spinal tract). Functional MRI and DT-MRI, together with MPRAGE and T2w structural MRI were acquired at 3 T prior to surgery. SPGR and T2w images were acquired with a 0.5 T magnet during each procedure. Quantitative assessment of the alignment accuracy was carried out and compared with current state-of-the-art systems based only on rigid registration. RESULTS: Alignment between pre-operative and intra-operative datasets was successfully carried out during surgery for all patients. Overall, the mean residual displacement remaining after non-rigid registration was 1.82 mm. There is a statistically significant improvement in alignment accuracy utilizing our non-rigid registration in comparison to the currently used technology (p<0.001). CONCLUSIONS: We were able to achieve intra-operative rigid and non-rigid registration of (1) pre-operative structural MRI with intra-operative T1w MRI; (2) pre-operative fMRI with intra-operative T1w MRI, and (3) pre-operative DT-MRI with intra-operative T1w MRI. The registration algorithms as implemented were sufficiently robust and rapid to meet the hard real-time constraints of intra-operative surgical decision making. The validation experiments demonstrate that we can accurately compensate for the deformation of the brain and thus can construct an augmented reality visualization to aid the surgeon.

N Archip, S Tatli, Paul Morrison, Ferenc A Jolesz, Simon K Warfield, and S Silverman. 2007. “Non-rigid registration of pre-procedural MR images with intra-procedural unenhanced CT images for improved targeting of tumors during liver radiofrequency ablations.” Med Image Comput Comput Assist Interv, 10, Pt 2, Pp. 969-77.Abstract

In the United States, unenhanced CT is currently the most common imaging modality used to guide percutaneous biopsy and tumor ablation. The majority of liver tumors such as hepatocellular carcinomas are visible on contrast-enhanced CT or MRI obtained prior to the procedure. Yet, these tumors may not be visible or may have poor margin conspicuity on unenhanced CT images acquired during the procedure. Non-rigid registration has been used to align images accurately, even in the presence of organ motion. However, to date, it has not been used clinically for radiofrequency ablation (RFA), since it requires significant computational infrastructure and often these methods are not sufficient robust. We have already introduced a novel finite element based method (FEM) that is demonstrated to achieve good accuracy and robustness for the problem of brain shift in neurosurgery. In this current study, we adapt it to fuse pre-procedural MRI with intra-procedural CT of liver. We also compare its performance with conventional rigid registration and two non-rigid registration methods: b-spline and demons on 13 retrospective datasets from patients that underwent RFA at our institution. FEM non-rigid registration technique was significantly better than rigid (p < 10-5), non-rigid b-spline (p < 10-4) and demons (p < 10-4) registration techniques. The results of our study indicate that this novel technology may be used to optimize placement of RF applicator during CT-guided ablations.

Nicole M Petrovich Brennan, Stephen Whalen, Daniel de Morales Branco, James P O'shea, Isaiah H Norton, and Alexandra J Golby. 2007. “Object naming is a more sensitive measure of speech localization than number counting: Converging evidence from direct cortical stimulation and fMRI.” Neuroimage, 37 Suppl 1, Pp. S100-8.Abstract
Using direct cortical stimulation to map language function during awake craniotomy is a well-described and useful technique. However, the optimum neuropsychological tasks to use have not been detailed. We used both functional MRI (fMRI) and direct cortical stimulation to compare the sensitivity of two behavioral paradigms, number counting and object naming, in the demonstration of eloquent cortical language areas. Fifteen patients with left hemisphere lesions and seven healthy control subjects participated. Patients had both preoperative fMRI at 3 T and direct cortical stimulation. Patients and controls performed object naming and number counting during fMRI at 3 T. Laterality indices were calculated from the fMRI maps for the Number-counting>Object-naming and Object-naming>Number-counting contrasts. The same number-counting and object-naming paradigms were tested during awake craniotomy and assessed for sensitivity to speech disruption. In all patients during intraoperative cortical stimulation, speech disruption occurred at more sites during object naming than during number counting. Subtle speech errors were only elicited with the object-naming paradigm, whereas only speech arrest and/or hypophonia were measured using the number counting paradigm. In both patients and controls, fMRI activation maps demonstrated greater left lateralization for object naming as compared to number counting in both frontal and temporal language areas. Number counting resulted in a more bihemispheric distribution of activations than object naming. Both cortical stimulation testing and fMRI suggest that automated speech tasks such as number counting may not fully engage putative language networks and therefore are not optimal for language localization for surgical planning.
R Sierra, SP DiMaio, J Wada, N Hata, G Székely, Ron Kikinis, and Ferenc A Jolesz. 2007. “Patient specific simulation and navigation of ventriculoscopic interventions.” Stud Health Technol Inform, 125, Pp. 433-5.Abstract

In this paper a comprehensive framework for pre-operative planning, procedural skill training, and intraoperative navigation is presented. The goal of this system is to integrate surgical simulation with surgical planning in order to improve the individual treatment of patients. Various surgical approaches and new, more complex procedures can be assessed using a safe and objective platform that will allow the physicians to explore and discuss possible risks and benefits prior to the intervention. A simulation environment extends the pre-operative planning in a natural way, as it allows for direct evaluation of the surgical approach envisioned for each case. In addition, by providing intraoperative navigation based on this simulation, surgeons can carry out the previously optimized plan with higher precision and greater confidence.

Adam Wittek, Karol Miller, Ron Kikinis, and Simon K Warfield. 2007. “Patient-specific model of brain deformation: application to medical image registration.” J Biomech, 40, 4, Pp. 919-29.Abstract
This contribution presents finite element computation of the deformation field within the brain during craniotomy-induced brain shift. The results were used to illustrate the capabilities of non-linear (i.e. accounting for both geometric and material non-linearities) finite element analysis in non-rigid registration of pre- and intra-operative magnetic resonance images of the brain. We used patient-specific hexahedron-dominant finite element mesh, together with realistic material properties for the brain tissue and appropriate contact conditions at boundaries. The model was loaded by the enforced motion of nodes (i.e. through prescribed motion of a boundary) at the brain surface in the craniotomy area. We suggest using explicit time-integration scheme for discretised equations of motion, as the computational times are much shorter and accuracy, for practical purposes, the same as in the case of implicit integration schemes. Application of the computed deformation field to register (i.e. align) the pre-operative images with the intra-operative ones indicated that the model very accurately predicts the displacements of the tumour and the lateral ventricles even for limited information about the brain surface deformation. The prediction accuracy improves when information about deformation of not only exposed (during craniotomy) but also unexposed parts of the brain surface is used when prescribing loading. However, it appears that the accuracy achieved using information only about the deformation of the exposed surface, that can be determined without intra-operative imaging, is acceptable. The presented results show that non-linear biomechanical models can complement medical image processing techniques when conducting non-rigid registration. Important advantage of such models over the previously used linear ones is that they do not require unrealistic assumptions that brain deformations are infinitesimally small and brain stress-strain relationship is linear.
Mahnaz Maddah, William M Wells, Simon K Warfield, Carl-Fredrik Westin, and Eric WL Grimson. 2007. “Probabilistic clustering and quantitative analysis of white matter fiber tracts.” Inf Process Med Imaging, 20, Pp. 372-83.Abstract
A novel framework for joint clustering and point-by-point mapping of white matter fiber pathways is presented. Accurate clustering of the trajectories into fiber bundles requires point correspondence determined along the fiber pathways. This knowledge is also crucial for any tract-oriented quantitative analysis. We employ an expectation-maximization (EM) algorithm to cluster the trajectories in a Gamma mixture model context. The result of clustering is the probabilistic assignment of the fiber trajectories to each cluster, an estimate of the cluster parameters, and point correspondences along the trajectories. Point-by-point correspondence of the trajectories within a bundle is obtained by constructing a distance map and a label map from each cluster center at every iteration of the EM algorithm. This offers a time-efficient alternative to pairwise curve matching of all trajectories with respect to each cluster center. Probabilistic assignment of the trajectories to clusters is controlled by imposing a minimum threshold on the membership probabilities, to remove outliers in a principled way. The presented results confirm the efficiency and effectiveness of the proposed framework for quantitative analysis of diffusion tensor MRI.
S Larsen, Ron Kikinis, Ion-Florin Talos, D Weinstein, William M Wells III, and Alexandra J Golby. 2007. “Quantitative Comparison of Functional MRI and Direct Electrocortical Stimulation for Functional Mapping.” Int J Med Robot, 3, 3, Pp. 262-70.Abstract

BACKGROUND: Mapping functional areas of the brain is important for planning tumour resections. With the increased use of functional magnetic resonance imaging (fMRI) for presurgical planning, there is a need to validate that fMRI activation mapping is consistent with the mapping obtained during surgery using direct electrocortical stimulation (DECS). METHODS: A quantitative comparison of DECS and fMRI mapping techniques was performed, using a patient-specific conductivity model to find the current distribution resulting from each stimulation site. The resulting DECS stimulation map was compared to the fMRI activation map, using the maximal Dice similarity coefficient (MDSC). RESULTS: Our results show some agreement between these two mapping techniques--the stimulation site with the largest MOSC was the only site that demonstrated intra-operative effect. CONCLUSIONS: There is a substantial effort to improve the techniques used to map functional areas, particularly using fMRI. It seems likely that fMRI will eventually provide a valid non-invasive means for functional mapping.

Hillary K Rolls, Seung-Schik Yoo, Kelly H Zou, Alexandra J Golby, and Lawrence P Panych. 2007. “Rater-dependent accuracy in predicting the spatial location of functional centers on anatomical MR images.” Clin Neurol Neurosurg, 109, 3, Pp. 225-35.Abstract
OBJECTIVES: The determination of eloquent cortex is essential when planning neurosurgical approaches to brain lesions. This study examined the abilities of medical personnel of various backgrounds to predict the location of functional cortex using anatomical information provided by MR imaging. PATIENTS AND METHODS: Neurosurgeons, neuroscientists, neuroradiologists, medical students and MR technologists viewed anatomical MR images acquired from patients with brain tumors and healthy controls. These five groups of raters were then asked to locate the primary motor hand, supplementary motor and primary auditory areas and their predictions were compared to fMRI data acquired from the same subjects. RESULTS: The overall mean distance from the center of the fMRI activation was 2.38 cm. The neuroscientists performed the best and MR technologists performed the worst (mean distance from center of 1.83 and 3.04 cm, respectively, p<0.05). The difference between patients and controls was not significant. The mean distance by ROI was primary motor hand 2.03 cm, auditory area 2.06 cm and supplementary motor area 3.18 cm (p<0.05). Raters also performed best in the medial-lateral direction, compared to superior-inferior and anterior-posterior directions (mean distances from center 0.42, 1.04 and 1.81 cm, respectively). Finally, the approximate minimum fields of view necessary to capture the entire fMRI activations using the raters' predictions ranged from 5 to 15 cm, or 3 to 12 cm larger than the fMRI activations. CONCLUSION: Medical personnel of various training perform poorly when using only anatomical information to predict the location of functional areas of cortex.
Kelly H Zou, James A O'Malley, and Laura Mauri. 2007. “Receiver-operating characteristic analysis for evaluating diagnostic tests and predictive models.” Circulation, 115, 5, Pp. 654-7.