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1.  From Quantification to Visualization: A Taxonomy of Uncertainty Visualization Approaches 
Quantifying uncertainty is an increasingly important topic across many domains. The uncertainties present in data come with many diverse representations having originated from a wide variety of disciplines. Communicating these uncertainties is a task often left to visualization without clear connection between the quantification and visualization. In this paper, we first identify frequently occurring types of uncertainty. Second, we connect those uncertainty representations to ones commonly used in visualization. We then look at various approaches to visualizing this uncertainty by partitioning the work based on the dimensionality of the data and the dimensionality of the uncertainty. We also discuss noteworthy exceptions to our taxonomy along with future research directions for the uncertainty visualization community.
PMCID: PMC4319674
uncertainty visualization
3.  Uncertainty Visualization in Forward and Inverse Cardiac Models 
Computing in cardiology  2013;40:57-60.
Quantification and visualization of uncertainty in cardiac forward and inverse problems with complex geometries is subject to various challenges. Specific to visualization is the observation that occlusion and clutter obscure important regions of interest, making visual assessment difficult. In order to overcome these limitations in uncertainty visualization, we have developed and implemented a collection of novel approaches. To highlight the utility of these techniques, we evaluated the uncertainty associated with two examples of modeling myocardial activity. In one case we studied cardiac potentials during the repolarization phase as a function of variability in tissue conductivities of the ischemic heart (forward case). In a second case, we evaluated uncertainty in reconstructed activation times on the epicardium resulting from variation in the control parameter of Tikhonov regularization (inverse case). To overcome difficulties associated with uncertainty visualization, we implemented linked-view windows and interactive animation to the two respective cases. Through dimensionality reduction and superimposed mean and standard deviation measures over time, we were able to display key features in large ensembles of data and highlight regions of interest where larger uncertainties exist.
PMCID: PMC4221850  PMID: 25383390
4.  Performance and Biocompatibility of Extremely Tough Alginate/Polyacrylamide Hydrogels 
Biomaterials  2013;34(33):8042-8048.
Although hydrogels now see widespread use in a host of applications, low fracture toughness and brittleness have limited their more broad use. As a recently described interpenetrating network (IPN) of alginate and polyacrylamide demonstrated a fracture toughness of ∼9000 J/m2, we sought to explore the biocompatibility and maintenance of mechanical properties of these hydrogels in cell culture and in vivo conditions. These hydrogels can sustain a compressive strain of over 90% with minimal loss of Young's Modulus as well as minimal swelling for up to 50 days of soaking in culture conditions. Mouse mesenchymal stem cells exposed to the IPN gel-conditioned media maintain high viability, and although cells exposed to conditioned media demonstrate slight reductions in proliferation and metabolic activity (WST assay), these effects are abrogated in a dose-dependent manner. Implantation of these IPN hydrogels into subcutaneous tissue of rats for 8 weeks led to mild fibrotic encapsulation and minimal inflammatory response. These results suggest the further exploration of extremely tough alginate/PAAM IPN hydrogels as biomaterials.
PMCID: PMC3775708  PMID: 23896005
5.  Baseline Visual Field Findings in the Idiopathic Intracranial Hypertension Treatment Trial (IIHTT) 
To characterize visual field (VF) loss at the baseline visit and to evaluate VF quality control (QC) procedures in the Idiopathic Intracranial Hypertension Treatment Trial (IIHTT).
The Visual Field Reading Center (VFRC) evaluated 660 baseline VFs (1320 hemifields) from 165 enrolled patients. Three readers independently classified each superior and inferior hemifield and identified any abnormalities. A subset (20%) of the hemifields was reread to evaluate within- and between-reader agreements. The QC system addressed test parameters, patient data, and shipment errors.
The majority (60%) of the baseline hemifields consisted of localized nerve fiber bundle-type VF loss. Approximately one-third (31.5%) of all the classifications consisted of partial arcuate defects combined with an enlarged blind spot, making this the most common type of hemifield classification. Inferior hemifield loss was greater than superior loss for both study and nonstudy eyes. Reader agreements were >90% for both inferior and superior hemifields for two out of three readers. Test–retest reliability agreement for individual readers was 95% for both hemifields. There were few QC errors with only 5.48 error points per 100-point VF.
The most common type of IIHTT baseline hemifield abnormality was a localized nerve fiber bundle-like defect. Localized inferior hemifield loss was more common than superior hemifield loss. Quality control and within- and between-reader agreement were excellent for the IIHTT ( number, NCT01003639).
The VFRC at the University of California-Davis was to provide consistent expert analysis and interpretation of visual field data and to ensure high-quality data for subjects participating in a clinical trial. The latter role was accomplished through the use of technician certification and QC.
PMCID: PMC4031894  PMID: 24781936
visual fields; intracranial idiopathic hypertension; optic neuropathy; quality control
6.  Where Do Livestock Guardian Dogs Go? Movement Patterns of Free-Ranging Maremma Sheepdogs 
PLoS ONE  2014;9(10):e111444.
In many parts of the world, livestock guardian dogs (LGDs) are a relatively new and increasingly popular method for controlling the impact of wild predators on livestock. On large grazing properties in Australia, LGDs are often allowed to range freely over large areas, with minimal supervision by their owners. How they behave in this situation is mostly unknown. We fitted free-ranging Maremma sheepdogs with GPS tracking collars on three properties in Victoria, Australia; on two properties, four sheep were also fitted with GPS collars. We investigated how much time the Maremmas spent with their livestock, how far they moved outside the ranges of their stock, and tested whether they use their ranges sequentially, which is an effective way of maintaining a presence over a large area. The 95% kernel isopleth of the Maremmas ranged between 31 and 1161 ha, the 50% kernel isopleth ranged between 4 and 252 ha. Maremmas spent on average 90% of their time in sheep paddocks. Movements away from sheep occurred mostly at night, and were characterised by high-speed travel on relatively straight paths, similar to the change in activity at the edge of their range. Maremmas used different parts of their range sequentially, similar to sheep, and had a distinct early morning and late afternoon peak in activity. Our results show that while free-ranging LGDs spend the majority of their time with livestock, movements away from stock do occur. These movements could be important in allowing the dogs to maintain large territories, and could increase the effectiveness of livestock protection. Allowing LGDs to range freely can therefore be a useful management decision, but property size has to be large enough to accommodate the large areas that the dogs use.
PMCID: PMC4213034  PMID: 25353319
7.  Inverse Electrocardiographic Source Localization of Ischemia: An Optimization Framework and Finite Element Solution 
With the goal of non-invasively localizing cardiac ischemic disease using body-surface potential recordings, we attempted to reconstruct the transmembrane potential (TMP) throughout the myocardium with the bidomain heart model. The task is an inverse source problem governed by partial differential equations (PDE). Our main contribution is solving the inverse problem within a PDE-constrained optimization framework that enables various physically-based constraints in both equality and inequality forms. We formulated the optimality conditions rigorously in the continuum before deriving finite element discretization, thereby making the optimization independent of discretization choice. Such a formulation was derived for the L2-norm Tikhonov regularization and the total variation minimization. The subsequent numerical optimization was fulfilled by a primal-dual interior-point method tailored to our problem’s specific structure. Our simulations used realistic, fiber-included heart models consisting of up to 18,000 nodes, much finer than any inverse models previously reported. With synthetic ischemia data we localized ischemic regions with roughly a 10% false-negative rate or a 20% false-positive rate under conditions up to 5% input noise. With ischemia data measured from animal experiments, we reconstructed TMPs with roughly 0.9 correlation with the ground truth. While precisely estimating the TMP in general cases remains an open problem, our study shows the feasibility of reconstructing TMP during the ST interval as a means of ischemia localization.
PMCID: PMC3727301  PMID: 23913980
Inverse Problem; Electrocardiography; Finite Element Method; PDE Optimization; Myocardial Ischemia; Bidomain Model; Total Variation
8.  Visual Field Profile of Optic Neuritis 
Archives of ophthalmology  2010;128(3):330-337.
To evaluate visual field abnormalities after an episode of optic neuritis among participants in the Optic Neuritis Treatment Trial.
Three readers independently evaluated 10 443 visual fields from 454 patients and classified visual field abnormalities into 21 different monocular categories representing 3 general types of visual loss: diffuse, localized, and artifactual. Classification frequency was determined and reader agreement was evaluated. The association of visual field abnormality classifications with mean deviation, pattern standard deviation, visual acuity, and foveal threshold was assessed.
At baseline, diffuse loss accounted for 66.2% of the abnormalities in the affected eyes but only 6.2% of the abnormalities in the fellow eyes. During years 1 through 15, the affected and fellow eyes exhibited predominantly localized loss in the nerve fiber bundle region (partial arcuate, paracentral, and arcuate defects). At year 1, 35.7% of the abnormalities in the affected eyes and 34.4% in the fellow eyes consisted of localized defects. At year 15, 39.5% of abnormalities in the affected eyes and 26.3% in the fellow eyes consisted of localized defects. Foveal threshold was highly correlated with visual acuity and contrast sensitivity in the affected eye at baseline (−0.82 vs 0.79, respectively), 6 months (−0.84 vs 0.81), and 1 year (−0.84 vs 0.79).
Diffuse and central loss were more predominant in the affected eye at baseline, and nerve fiber bundle defects (partial arcuate, paracentral, and arcuate) were the most predominant localized abnormalities in both the affected and fellow eyes during the study.
PMCID: PMC4107874  PMID: 20212204
9.  Controlled Support MEG imaging 
NeuroImage  2006;33(3):878-885.
In this paper, we present a novel approach to imaging sparse and focal neural current sources from MEG (magnetoencephalography) data. Using the framework of Tikhonov regularization theory, we introduce a new stabilizer that uses the concept of controlled support to incorporate a priori assumptions about the area occupied by focal sources. The paper discusses the underlying Tikhonov theory and its relationship to a Bayesian formulation which in turn allows us to interpret and better understand other related algorithms.
PMCID: PMC4057891  PMID: 16978882
10.  Beyond the disease: Is Toxoplasma gondii infection causing population declines in the eastern quoll (Dasyurus viverrinus)? 
•Seroprevalence of Toxoplasma gondii was investigated in eastern quolls.•Seroprevalence of IgG antibodies was higher at sites where quolls were declining.•T. gondii infection did not reduce quoll survival or reproduction.•Higher seroprevalence signals higher exposure to feral cats at declining sites.
Disease is often considered a key threat to species of conservation significance. For some, it has resulted in localised extinctions and declines in range and abundance. However, for some species, the assertion that a disease poses a significant threat of extinction is based solely on correlative or anecdotal evidence, often inferred from individual clinical case reports. While a species’ susceptibility to a disease may be demonstrated in a number of individuals, investigations rarely extend to measuring the impact of disease at the population level and its contribution, if any, to population declines. The eastern quoll (Dasyurus viverrinus) is a medium-sized Australian marsupial carnivore that is undergoing severe and rapid decline in Tasmania, its last refuge. Reasons for the decline are currently not understood. Feral cats (Felis catus) may be undergoing competitive release following the ongoing decline of the Tasmanian devil (Sarcophilus harrisii), with cats suppressing eastern quolls through increased predation, competition, exclusion or exposure to diseases such as toxoplasmosis. To investigate the effects of Toxoplasma gondii infection, eastern quoll populations at four sites were regularly screened for the seroprevalence of T. gondii-specific IgG antibodies. Seroprevalence was approximately five times higher at sites with declining quoll populations, and there was a negative association between seroprevalence and quoll abundance. However, T. gondii infection did not reduce quoll survival or reproduction. Despite a high susceptibility to T. gondii infection, eastern quoll populations do not appear to be limited by the parasite or its resultant disease. Significantly higher seroprevalence is a signal of greater exposure to feral cats at sites where eastern quolls are declining, suggesting that increased predation, competition or exclusion by feral cats may be precipitating population declines.
PMCID: PMC4142269  PMID: 25161908
Toxoplasmosis; Epidemiology; Feral cat; Felis catus; Population decline
11.  White matter structure assessment from reduced HARDI data using low-rank polynomial approximations 
Assessing white matter fiber orientations directly from DWI measurements in single-shell HARDI has many advantages. One of these advantages is the ability to model multiple fibers using fewer parameters than are required to describe an ODF and, thus, reduce the number of DW samples needed for the reconstruction. However, fitting a model directly to the data using Gaussian mixture, for instance, is known as an initialization-dependent unstable process. This paper presents a novel direct fitting technique for single-shell HARDI that enjoys the advantages of direct fitting without sacrificing the accuracy and stability even when the number of gradient directions is relatively low. This technique is based on a spherical deconvolution technique and decomposition of a homogeneous polynomial into a sum of powers of linear forms, known as a symmetric tensor decomposition. The fiber-ODF (fODF), which is described by a homogeneous polynomial, is approximated here by a discrete sum of even-order linear-forms that are directly related to rank-1 tensors and represent single-fibers. This polynomial approximation is convolved to a single-fiber response function, and the result is optimized against the DWI measurements to assess the fiber orientations and the volume fractions directly. This formulation is accompanied by a robust iterative alternating numerical scheme which is based on the Levenberg-Marquardt technique. Using simulated data and in vivo, human brain data we show that the proposed algorithm is stable, accurate and can model complex fiber structures using only 12 gradient directions.
PMCID: PMC4013549  PMID: 24818174
12.  Delaying Treatment of Ocular Hypertension 
Archives of ophthalmology  2010;128(3):276-287.
To compare the safety and efficacy of earlier vs later treatment in preventing primary open-angle glaucoma (POAG) in individuals with ocular hypertension.
One thousand six hundred thirty-six individuals with intraocular pressure (IOP) from 24 to 32 mm Hg in 1 eye and 21 to 32 mm Hg in the fellow eye were randomized to observation or to topical ocular hypotensive medication. Median time of treatment in the medication group was 13.0 years. After a median of 7.5 years without treatment, the observation group received medication for a median of 5.5 years. To determine if there is a penalty for delaying treatment, we compared the cumulative proportions of participants who developed POAG at a median follow-up of 13 years in the original observation group and in the original medication group.
Main Outcome Measures
Cumulative proportion of participants who developed POAG.
The cumulative proportion of participants in the original observation group who developed POAG at 13 years was 0.22 (95% confidence interval [CI], 0.19–0.25), vs 0.16 (95% CI, 0.13–0.19) in the original medication group (P=.009). Among participants at the highest third of baseline risk of developing POAG, the cumulative proportion who developed POAG was 0.40 (95% CI, 0.33–0.46) in the original observation group and 0.28 (95% CI, 0.22–0.34) in the original medication group. There was little evidence of increased adverse events associated with medication.
Application to Clinical Practice
Absolute reduction was greatest among participants at the highest baseline risk of developing POAG. Individuals at high risk of developing POAG may benefit from more frequent examinations and early preventive treatment.
Trial Registration Identifier: NCT00000125
PMCID: PMC3966140  PMID: 20212196
13.  Refinement of Pointwise Linear Regression Criteria for Determining Glaucoma Progression 
A variety of pointwise linear regression (PLR) criteria have been proposed for determining glaucomatous visual field progression. However, alternative PLR criteria have only been assessed on a limited basis. The purpose of this study was to evaluate a range of PLR slope and significance criteria to define a clinically useful progression decision rule for longitudinal visual field examinations.
Visual field data for each of 140 eyes (one per participant among 96 cases and 44 controls) were evaluated using the Humphrey Field Analyzer II program 24-2 Swedish interactive thresholding algorithm standard test strategy and Goldmann size III stimuli. The pointwise linear regression A2 (PLRA2) method was used to analyze the data, which included nine visual field examinations performed every 6 months for 4 years. Data from the Ocular Hypertension Treatment Study (OHTS) were used to validate the decision rule.
Several slope criteria produced specificities of 0.90 or higher, particularly slope criteria of less than −1.2 dB/y. The use of the slope criterion less than −1.2 dB/y at a significance level of P < 0.04 for classification resulted in a hit rate of 0.38, more than a 2-fold increase compared with a commonly used standard slope criterion of less than −1.0 dB/y at a significance level of P < 0.01. A similar increase in the hit rate was shown for a slope of less than −1.2 dB/y and P < 0.04 compared with the standard criterion in the independent OHTS validation data.
When systematically evaluating criteria for detecting glaucoma progression, PLR criteria can be refined by requiring a stricter slope criterion such as less than −1.2 dB/y and relaxing the significance criterion to P < 0.04. Increasing the hit rate of PLR will be useful for early detection and treatment of glaucoma.
Systematic evaluation of pointwise linear regression (PLR) criteria indicates that trend analysis using PLR can be refined by considering more restrictive declines in slope and relaxing the significance criterion to increase the likelihood of detecting glaucoma progression with PLR.
PMCID: PMC3778872  PMID: 23908183
pointwise linear regression; glaucoma progression; perimetry; trend analysis; visual field
14.  Longitudinal and Cross-Sectional Analyses of Visual Field Progression in Participants of the Ocular Hypertension Treatment Study (OHTS) 
Archives of ophthalmology  2010;128(12):1528-1532.
Visual field progression can be determined by evaluating the visual field by serial examinations (longitudinal analysis), or by a change in classification derived from comparison to age-matched normal data in single examinations (cross-sectional analysis). We determined the agreement between these two approaches in data from the Ocular Hypertension Treatment Study (OHTS).
Visual field data from 3088 eyes of 1570 OHTS participants (median follow-up 7 yrs, 15 tests with static automated perimetry) were analysed. Longitudinal analyses were performed with change probability with total and pattern deviation, and cross-sectional analysis with Glaucoma Hemifield Test, Corrected Pattern Standard Deviation, and Mean Deviation. The rates of Mean Deviation and General Height change were compared to estimate the degree of diffuse loss in emerging glaucoma.
The agreement on progression in longitudinal and cross-sectional analyses ranged from 50% to 61% and remained nearly constant across a wide range of criteria. In contrast, the agreement on absence of progression ranged from 97% to 99.7%, being highest for the stricter criteria. Analyses of pattern deviation were more conservative than total deviation, with a 3 to 5 times lesser incidence of progression. Most participants developing field loss had both diffuse and focal change.
Despite considerable overall agreement, between 40 to 50% of eyes identified as having progressed with either longitudinal or cross-sectional analyses were identified with only one of the analyses. Because diffuse change is part of early glaucomatous damage, pattern deviation analyses may underestimate progression in patients with ocular hypertension.
PMCID: PMC3914151  PMID: 21149774
glaucoma; progression; visual field; change probability; ocular hypertension
15.  Uncertainty Visualization in HARDI based on Ensembles of ODFs 
In this paper, we propose a new and accurate technique for uncertainty analysis and uncertainty visualization based on fiber orientation distribution function (ODF) glyphs, associated with high angular resolution diffusion imaging (HARDI). Our visualization applies volume rendering techniques to an ensemble of 3D ODF glyphs, which we call SIP functions of diffusion shapes, to capture their variability due to underlying uncertainty. This rendering elucidates the complex heteroscedastic structural variation in these shapes. Furthermore, we quantify the extent of this variation by measuring the fraction of the volume of these shapes, which is consistent across all noise levels, the certain volume ratio. Our uncertainty analysis and visualization framework is then applied to synthetic data, as well as to HARDI human-brain data, to study the impact of various image acquisition parameters and background noise levels on the diffusion shapes.
PMCID: PMC3898522  PMID: 24466504
DT-MRI; Uncertainty; HARDI; Rank-k tensor decomp
16.  The Effect of Test Variability on the Structure-Function Relation in Early Glaucoma 
To determine whether the weakness of the structure-function relation could be produced by test variability alone, without implying underlying dissociation between the true rates of structural and functional change.
Perimetric Mean Deviation (MD), and Rim Area (RA) and Cup Volume (CV) from confocal scanning laser ophthalmoscopy, over six visits, were taken from 166 eyes of 92 participants with high risk ocular hypertension or suspected / early glaucoma in the Portland Progression Project. Models were created of each measure’s variability. A further model predicted the rate of functional change from the rate of structural change. These were used to generate realistic simulated sequences of both functional and structural data with different standard deviations σ between the underlying rates of change. ‘Observed’ structure-function relations were calculated. An empirical p-value was derived, equaling the proportion of simulated series for which the ‘observed’ structure-function dissociation was greater than that seen in patient data.
The correlation between the rates of structural (RA) and functional (MD) change was 0.171, consistent with σ<0.02dB/yr. Using CV, the correlation was −0.091, consistent with σ<0.01dB/yr. By comparison, the models predicted that the standard deviation of the rate of functional change for a healthy eye due to test variability would be 0.18dB/yr.
Test variability is sufficiently large that realistic patient data can be simulated without requiring a large variability between the underlying rates of structural and functional change. This absence of implied dissociation is a necessary condition for it to be valid to combine structural and functional measures to improve estimates of functional change and/or to reduce perimetric variability.
PMCID: PMC3763816  PMID: 22527311
Glaucoma; Perimetry; Confocal Scanning Laser Ophthalmoscopy; Structure-Function Relation; Simulation; Variability
17.  Reviewing long-term antidepressants can reduce drug burden: a prospective observational cohort study 
The British Journal of General Practice  2012;62(604):e773-e779.
Antidepressant prescribing continues to rise. Contributing factors are increased long-term prescribing and possibly the use of higher selective serotonin re-uptake inhibitor (SSRI) doses.
To review general practice patients prescribed the same antidepressant long-term (≥2 years) and evaluate prescribing and management pre and post-review.
Design and setting
Prospective observational cohort study using routine data from 78 urban general practices, Scotland.
All patients prescribed antidepressants (excluding amitriptyline) for ≥2 years were identified from records November 2009 to March 2010. GPs selected patients for face-to-face review of clinical condition and medication, December 2009 to September 2010. Pre- and post-review data were collected; average antidepressant doses and changes in prescribed daily doses were calculated. Onward referral to support services was recorded.
8.6% (33 312/388 656) of all registered patients were prescribed an antidepressant, 47.1% (15 689) were defined as long-term users and 2849 (18.2%) were reviewed. 811 (28.5%) patients reviewed had a change in antidepressant therapy: 7.0% stopped, 12.8% reduced dose, 5.3% increased dose, and 3.4% changed antidepressant, resulting in 9.5% (95% CI = 9.1% to 9.8% P<0.001) reduction in prescribed daily dose and 8.1% reduction in prescribing costs. 6.3% were referred onwards, half to NHS Mental Health Services. Pre-review SSRI doses were 10–30% higher than previously reported.
Almost half of all people prescribed antidepressants were long-term users. Appropriate reductions in prescribing can be achieved by reviewing patients. Higher SSRI doses may be contributing to current antidepressant growth.
PMCID: PMC3481518  PMID: 23211181
antidepressant; drug therapy; depression; primary care
18.  Mammalian Fatty Acid Synthase Activity From Crude Tissue Lysates Tracing [13C]-Substrates Using GC Mass Spectrometry 
Analytical biochemistry  2012;428(2):158-166.
Fatty Acid Synthase (FASN, FAS; EC is the sole mammalian enzyme to synthesize fatty acids de novo from acetyl and malonyl coenzyme A esters. A new method is described that directly quantifies uniformly labeled [13C]16-palmitate by tracing [13C]2-acetyl-CoA and [13C]3-malonyl-CoA using an in vitro FASN assay. This method used GC-MS to detect [13C]16-palmitate carboxylate anions (m/z 271) of pentafluorobenzyl derivatives and was highly sensitive at femtomole quantities. Uniformly incorporated [13C]16-palmitate was the primary product of both recombinant and crude tissue lysate FASN. Quantification of FASN protein within crude tissue lysates assured equal FASN amounts, preserved steady state kinetics, and enabled calculation of FASN specific activity. FASN activity determined by [13C]16-palmitate synthesis was consistent with values obtained from NADPH oxidation assays. Analysis of FASN activity from tissue extracts was not hampered by contaminating enzymes or pre-existing fatty acids. Crude mammary gland and liver lysates had significantly different activities at 82 and 65 nmoles minute−1 mg−1 respectively, suggesting tissue specific activity levels differ in a manner unrelated to FASN amount. GC-MS quantification of [13C]16-palmitate synthesis permits sensitive evaluation of FASN activity from tissues of varied physiologic states, and of purified FASN activity in the presence of modifying proteins, enzymes, or drugs.
PMCID: PMC3415257  PMID: 22728958
Fatty Acid Synthase Activity; GC-Mass Spectrometry; Mammary Gland/Liver Lysates; [13C]-substrate incorporation; [13C]16-Palmitic Acid
19.  Perimetric Indices as Predictors of Future Glaucomatous Functional Change 
To evaluate the use of global indices summarizing the current status of a patient’s visual field as predictors of their future rate of change.
Ninety-five subjects with early or suspected glaucoma were studied, of whom 50 exhibited glaucomatous optic neuropathy (GON) at baseline. Subjects underwent seven annual visual field tests. Results from the first test in the sequence were used to predict their subsequent rate of change. Two global indices were considered: mean deviation (MD) and pattern standard deviation (PSD).
Using multiple linear regression, baseline MD predicted subsequent slope of MD significantly better than baseline PSD predicted subsequent slope of PSD (p = 0.017). Using multiple logistic regression, a worse initial MD was predictive of being in the worst tertile for subsequent change in MD (pseudo-R2 = 0.33 for subjects with GON at baseline and 0.31 for those without). Worse initial PSD was not predictive of being in the worst tertile for subsequent change in PSD (pseudo-R2 = 0.09 with GON at baseline, 0.10 without).
Among patients with otherwise similar clinical profiles, a worse visual field at baseline, as measured by the global index MD, is predictive of a more rapid future rate of change. This should be taken into account when clinical decisions are made concerning management of patients who already have some visual field damage at presentation.
PMCID: PMC3746834  PMID: 20966804
glaucoma; perimetry; visual field; progression; data analysis
20.  The Development of a Decision Analytic Model of Changes in Mean Deviation in People with Glaucoma: The COA Model 
Ophthalmology  2012;119(7):1367-1374.
To create and validate a statistical model predicting progression of primary open angle glaucoma (POAG) assessed by loss of visual field as measured in mean deviation (MD) using three landmark studies of glaucoma progression and treatment.
A Markov decision analytic model using patient level data described longitudinal MD changes over seven years.
Patient level data from the Collaborative Initial Glaucoma Treatment Study (CIGTS, n=607), the Ocular Hypertension Treatment Study (OHTS, n=148, only those who developed POAG in the first five years of OHTS) and Advanced Glaucoma Intervention Study (AGIS, n=591), the COA model.
We developed a Markov model with transition matrices stratified by current MD, age, race and intraocular pressure categories and used a microsimulation approach to estimate change in MD over seven years. Internal validation compared model prediction for seven years to actual MD for COA participants. External validation used a cohort of glaucoma patients drawn from university clinical practices.
Main Outcome Measures
Change in visual field as measured in MD in decibels (dB).
Regressing the actual MD against the predicted produced an R2 of 0.68 for the right eye and 0.63 for the left. The model predicted ending MD for right eyes of 65% of participants and for 63% of left eyes within 3 dB of actual results at seven years. In external validation the model had an R2 of 0.79 in the right eye and 0.77 in the left at five years.
The COA model is a validated tool for clinicians, patients and health policy makers seeking to understand longitudinal changes in mean deviation in people with glaucoma..
PMCID: PMC3389134  PMID: 22537616
21.  Morphometric Analysis and Classification of Glaucomatous Optic Neuropathy using Radial Polynomials 
Journal of Glaucoma  2012;21(5):302-312.
To quantify the morphological features of the optic nerve head using radial polynomials, to use these morphometric models as the basis for classification of glaucomatous optic neuropathy glaucomatous optic neuropathy via an automated decision tree induction algorithm, and to compare these classification results with established methods.
A cohort of patients with high-risk ocular hypertension or early glaucoma (n = 179) and a second cohort of normal subjects (n = 96) were evaluated for glaucomatous optic neuropathy using stereographic disc photography and confocal scanning laser tomography. Morphological features of the optic nerve head region were modeled from the tomography data using pseudo-Zernike radial polynomials and features derived from these models were used as the basis for classification by a decision tree induction algorithm. Decision tree classification performance was compared with expert classification of stereographic disc photos and analysis of neural retinal rim thickness by Moorfields Regression Analysis (MRA).
Root mean squared (RMS) error of the morphometric models decreased asymptotically with additional polynomial coefficients, from 62 ± 0.5 μm (32 coefficients) to 32 ± 5.7 μm (256 coefficients). Optimal morphometric classification was derived from a subset of 64 total features and had low sensitivity (69%), high specificity (88%), very good accuracy (80%), and area under the ROC curve (AUROC) was 88% (95% CI = 78 to 98%). By comparison, MRA classification of the same records had a comparatively poorer sensitivity (55%), but had higher specificity (95%), with similar overall accuracy (78%) and AUROC curve, 83% (95 % CI = 70 to 96%).
Pseudo-Zernike radial polynomials provide a mathematically compact and faithful morphological representation of the structural features of the optic nerve head. This morphometric method of glaucomatous optic neuropathy classification has greater sensitivity, and similar overall classification performance (AUROC) when compared with classification by neural retinal rim thickness by MRA in patients with high-risk ocular hypertension and early glaucoma.
PMCID: PMC3163012  PMID: 21423035
Glaucoma; Optic Nerve; Modeling; Classification; Machine Learning
Shock (Augusta, Ga.)  2012;37(6):599-604.
The cellular and biochemical mechanisms leading to acute lung injury and subsequent multiple organ failure are only partially understood. In order to study the potential role of eicosanoids, particularly leukotrienes, as possible mediators of acute lung injury, we used a murine experimental model of acute lung injury induced by hemorrhagic shock after blood removal via cardiac puncture. Neutrophil sequestration as shown by immunofluorescence, and protein leakage into the alveolar space, were measured as markers of injury. We used liquid chromatography coupled to tandem mass spectrometry to unequivocally identify several eicosanoids in the bronchoalveolar lavage fluid of experimental animals. MK886, a specific inhibitor of the 5-lipoxygenase pathway, as well as transgenic mice deficient in 5-lipoxygenase, were used to determine the role of this enzymatic pathway in this model. Leukotriene B4 and leukotriene C4 were consistently elevated in shock-treated mice compared to sham-treated mice. MK886 attenuated neutrophil infiltration and protein extravasation induced by hemorrhagic shock. 5-lipoxygenase-deficient mice showed reduced neutrophil infiltration and protein extravasation after shock treatment, indicating greatly reduced lung injury. These results support the hypothesis that 5-lipoxygenase, most likely through the generation of leukotrienes, plays an important role in the pathogenesis of acute lung injury induced by hemorrhagic shock in mice. This pathway could represent a new target for pharmacological intervention to reduce lung damage following severe primary injury.
PMCID: PMC3357208  PMID: 22392149
multiple organ failure; eicosanoids; leukotrienes; mass spectrometry; inflammation; pharmacological inhibition; transgenic mice
23.  The Nature of Macular Damage in Glaucoma as Revealed by Averaging Optical Coherence Tomography Data 
To better understand the nature of glaucomatous damage, especially to the macula, the inner retinal thickness maps obtained with frequency domain optical coherence tomography (fdOCT) were averaged.
Frequency domain optical coherence tomography macular and optic disc cube scans were obtained from 54 healthy eyes and 156 eyes with glaucomatous optic neuropathy. A manually corrected algorithm was used for layer segmentation. Patients’ eyes were grouped both by mean deviation (MD) and hemifield classification using standard categories and 24-2 (6° grid) visual fields (VFs). To obtain average difference maps, the thickness of retinal nerve fiber (RNF) and retinal ganglion cell plus inner plexiform (RGC+) layers were averaged and subtracted from the average control values.
On the average difference maps, RGC+ and RNF layer thinning was seen in the patient groups with VFs classified as normal. The pattern of the thinning was the same, but the degree of thinning increased with decreased MD and with classification category (from normal to arcuate). This RGC+ thinning was largely within the central four points of the 24-2 (6° grid) field, after correcting for RGC displacement.
1. VF categories represent different degrees of the same pattern of RGC+ and RNFL layer thinning. 2. RGC+ damage occurs in the central macula even in patients with VFs classified as normal. 3. The 6° grid (24-2) pattern is not optimally designed to detect macular damage. 4. A schematic model of RGC projections is proposed to explain the pattern of macular loss, including the greater vulnerability of the inferior retinal region.
Translational relevance
The 24-2 is not an optimal test pattern for detecting or following glaucomatous damage. Further, we suggest clinical fdOCT reports include RGC+ and RNFL probability plots combined with VF information.
PMCID: PMC3634586  PMID: 23626924
glaucoma; optical coherence tomography; perimetry; visual fields; macula
The probability density function (PDF), and its corresponding cumulative density function (CDF), provide direct statistical insight into the characterization of a random process or field. Typically displayed as a histogram, one can infer probabilities of the occurrence of particular events. When examining a field over some two-dimensional domain in which at each point a PDF of the function values is available, it is challenging to assess the global (stochastic) features present within the field. In this paper, we present a visualization system that allows the user to examine two-dimensional data sets in which PDF (or CDF) information is available at any position within the domain. The tool provides a contour display showing the normed difference between the PDFs and an ansatz PDF selected by the user and, furthermore, allows the user to interactively examine the PDF at any particular position. Canonical examples of the tool are provided to help guide the reader into the mapping of stochastic information to visual cues along with a description of the use of the tool for examining data generated from an uncertainty quantification exercise accomplished within the field of electrophysiology.
PMCID: PMC3609671  PMID: 23543120
visualization; probability density function; cumulative density function; generalized polynomial chaos; stochastic Galerkin methods; stochastic collocation methods
25.  Cup Size Predicts Subsequent Functional Change in Early Glaucoma 
To identify structural predictors of functional change in patients with early glaucoma or risk factors for development of glaucoma.
129 participants with either high-risk ocular hypertension, suspected or early glaucoma were followed for ten annual visits. Standard Automated Perimetry was performed at each visit, together with Confocal Scanning Laser Ophthalmoscopy (CSLO). Mean Deviation (MD) at the same visit, and the subsequent rate of change in MD, were predicted by linear regression models based on CSLO parameters together with intraocular pressure, central corneal thickness and treatment status. Models were assessed by comparing the correlations between predicted and observed perimetric results.
The model using rim area predicted MD at the same visit with correlation 0.445. Using cup area the equivalent correlation was r=0.411, lower than the model using rim area with p=0.096. Using cup volume the correlation was r=0.436, and the comparison had p=0.714; using disc area r=0.396 and p=0.011. The model using rim area to predict the subsequent rate of change of MD had r=0.539. Models using cup area (r=0.631), cup volume (r=0.649) or disc area (r=0.602) were significantly better; p=0.003, p=0.001 and p=0.044 respectively.
Lower rim area, as measured by CSLO, is predictive of worse function when measured on the same date in participants with high-risk ocular hypertension, suspected and early glaucoma. However, cup area, cup volume and disc area may all be more predictive of the rate of subsequent functional change. Parameters should be chosen based on the specific purpose intended and questions asked, rather than using the same parameters in all circumstances.
PMCID: PMC3223562  PMID: 21912304
glaucoma; progression; perimetry; confocal scanning laser ophthalmoscopy

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