New measures to capture end of life concerns in Huntington disease: Meaning and Purpose and Concern with Death and Dying from HDQLIFE (a patient-reported outcomes measurement system).

PURPOSE: Huntington disease (HD) is an incurable terminal disease. Thus, end of life (EOL) concerns are common in these individuals. A quantitative measure of EOL concerns in HD would enable a better understanding of how these concerns impact health-related quality of life. Therefore, we developed new measures of EOL for use in HD. METHODS: An EOL item pool of 45 items was field tested in 507 individuals with prodromal or manifest HD. Exploratory and confirmatory factor analyses (EFA and CFA, respectively) were conducted to establish unidimensional item pools. Item response theory (IRT) and differential item functioning analyses were applied to the identified unidimensional item pools to select the final items. RESULTS: EFA and CFA supported two separate unidimensional sets of items: Concern with Death and Dying (16 items), and Meaning and Purpose (14 items). IRT and DIF supported the retention of 12 Concern with Death and Dying items and 4 Meaning and Purpose items. IRT data supported the development of both a computer adaptive test (CAT) and a 6-item, static short form for Concern with Death and Dying. CONCLUSION: The HDQLIFE Concern with Death and Dying CAT and corresponding 6-item short form, and the 4-item calibrated HDQLIFE Meaning and Purpose scale demonstrate excellent psychometric properties. These new measures have the potential to provide clinically meaningful information about end-of-life preferences and concerns to clinicians and researchers working with individuals with HD. In addition, these measures may also be relevant and useful for other terminal conditions.

HDQLIFE: the development of two new computer adaptive tests for use in Huntington disease, Speech Difficulties, and Swallowing Difficulties.

PURPOSE: Huntington disease (HD) is an autosomal dominant neurodegenerative disease which results in several progressive symptoms, including bulbar dysfunction (i.e., speech and swallowing difficulties). Although difficulties in speech and swallowing in HD have a negative impact on health-related quality of life, no patient-reported outcome measure exists to capture these difficulties that are specific to HD. Thus, we developed a new patient-reported outcome measure for use in the Huntington Disease Health-Related Quality of Life (HDQLIFE) Measurement System that focused on the impact that difficulties with speech and swallowing have on HRQOL in HD. METHODS: Five hundred and seven individuals with prodromal and/or manifest HD completed 47 newly developed items examining speech and swallowing difficulties. Unidimensional item pools were identified using exploratory factor analysis and confirmatory factor analysis (EFA and CFA, respectively). Item response theory (IRT) was used to calibrate the final measures. RESULTS: EFA and CFA identified two separate unidimensional sets of items: Speech Difficulties (27 items) and Swallowing Difficulties (16 items). Items were calibrated separately for these two measures and resulted in item banks that can be administered as computer adaptive tests (CATs) and/or 6-item, static short forms. Reliability of both of these measures was supported through high correlations between the simulated CAT scores and the full item bank. CONCLUSIONS: CATs and 6-item calibrated short forms were developed for HDQLIFE Speech Difficulties and HDQLIFE Swallowing Difficulties. These measures both demonstrate excellent psychometric properties and may have clinical utility in other populations where speech and swallowing difficulties are prevalent.

HDQLIFE: development and assessment of health-related quality of life in Huntington disease (HD).

PURPOSE: Huntington disease (HD) is a chronic, debilitating genetic disease that affects physical, emotional, cognitive, and social health. Existing patient-reported outcomes (PROs) of health-related quality of life (HRQOL) used in HD are neither comprehensive, nor do they adequately account for clinically meaningful changes in function. While new PROs examining HRQOL (i.e., Neuro-QoL-Quality of Life in Neurological Disorders and PROMIS-Patient-Reported Outcomes Measurement Information System) offer solutions to many of these shortcomings, they do not include HD-specific content, nor have they been validated in HD. HDQLIFE addresses this by validating 12 PROMIS/Neuro-QoL domains in individuals with HD and by using established PROMIS methodology to develop new, HD-specific content. METHODS: New item pools were developed using cognitive debriefing with individuals with HD, and expert, literacy, and translatability reviews. Existing item banks and new item pools were field tested in 536 individuals with prodromal, early-, or late-stage HD. RESULTS: Moderate to strong relationships between Neuro-QoL/PROMIS measures and generic self-report measures of HRQOL, and moderate relationships between Neuro-QoL/PROMIS and clinician-rated measures of similar constructs supported the validity of Neuro-QoL/PROMIS in individuals with HD. Exploratory and confirmatory factor analysis, item response theory, and differential item functioning analyses were utilized to develop new item banks for Chorea, Speech Difficulties, Swallowing Difficulties, and Concern with Death and Dying, with corresponding six-item short forms. A four-item short form was developed for Meaning and Purpose. CONCLUSIONS: HDQLIFE encompasses both validated Neuro-QoL/PROMIS measures, as well as five new scales in order to provide a comprehensive assessment of HRQOL in HD.

Transient dystonia correlates with parkinsonism after 1-methyl-4-phenyl-1,2,3,6- tetrahydropyridine in nonhuman primates.

Unilateral internal carotid artery 1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine (MPTP) infusion in non-human primates produces transient contralateral hemi-dystonia followed by stable contralateral hemi-parkinsonism; the relationship between dystonia and parkinsonism remains unclear. We hypothesized that transient dystonia severity following MPTP correlates with parkinsonism severity. In male Macaca nemestrina (n = 3) and M. fascicularis (n = 17) we administered unilateral intra-carotid MPTP, then correlated validated blinded ratings of transient peak dystonia and delayed parkinsonism. We also correlated dystonia severity with post-mortem measures of residual striatal dopamine and nigral neuron counts obtained a mean 53 ± 15 days following MPTP, after resolution of dystonia but during stable parkinsonism. Median latency to dystonia onset was 1 day, and peak severity 2.5 days after MPTP; total dystonia duration was 13.5 days. Parkinsonism peaked a median of 19.5 days after MPTP, remaining nearly constant thereafter. Peak dystonia severity highly correlated with parkinsonism severity (r[18] = 0.82, p < 0.001). Residual cell counts in lesioned nigra correlated linearly with peak dystonia scores (r[18] = -0.68, p=<0.001). Dystonia was not observed in monkeys without striatal dopamine depletion (n = 2); dystonia severity correlated with striatal dopamine depletion when residual nigral cell loss was less than 50% ([11] r = -0.83, p < 0.001) but spanned a broad range with near complete striatal dopamine depletion, when nigral cell loss was greater than 50%. Our data indicate that residual striatal dopamine may not reflect dystonia severity. We speculate on mechanisms of transient dystonia followed by parkinsonism that may be studied using this particular NHP MPTP model to better understand relationships of transient dystonia to nigrostriatal injury and parkinsonism.

Effects of deep brain stimulation of dorsal versus ventral subthalamic nucleus regions on gait and balance in Parkinson's disease.

OBJECTIVE: Deep brain stimulation (DBS) of the subthalamic nucleus (STN) improves motor function, including gait and stability, in people with Parkinson's disease (PD) but differences in DBS contact locations within the STN may contribute to variability in the degree of improvement. Based on anatomical connectivity, dorsal STN may be preferentially involved in motor function and ventral STN in cognitive function. METHODS: To determine whether dorsal DBS affects gait and balance more than ventral DBS, a double blind evaluation of 23 PD patients with bilateral STN DBS was conducted. Each participant underwent gait analysis and balance testing off Parkinson's medication under three DBS conditions (unilateral DBS in the dorsal STN region, unilateral DBS in the ventral STN region and both stimulators off) on 1 day. RESULTS: Improvements were seen in Unified Parkinson's Disease Rating Scale (UPDRS)-III scores and velocity in walking trials as fast as possible (Fast gait) and preferred pace (Pref gait), as well as stride length for Fast and Pref gait, with dorsal and ventral stimulation compared with the off condition (post hoc tests, p<0.05). However, there were no differences with dorsal compared to ventral stimulation. Balance, assessed using the multi-item mini-Balance Evaluation Systems Test (mini-BESTest), was similar across conditions. CONCLUSIONS: Absence of differences in gait and balance between the dorsal and ventral conditions suggests motor connections involved in gait and balance may be more diffusely distributed in STN than previously thought, as opposed to neural connections involved in cognitive processes, such as response inhibition, which are more affected by ventral stimulation.

Subthalamic nucleus stimulation-induced regional blood flow responses correlate with improvement of motor signs in Parkinson disease.

Deep brain stimulation of the subthalamic nucleus (STN DBS) improves motor symptoms in idiopathic Parkinson's disease, yet the mechanism of action remains unclear. Previous studies indicate that STN DBS increases regional cerebral blood flow (rCBF) in immediate downstream targets but does not reveal which brain regions may have functional changes associated with improved motor manifestations. We studied 48 patients with STN DBS who withheld medication overnight and underwent PET scans to measure rCBF responses to bilateral STN DBS. PET scans were performed with bilateral DBS OFF and ON in a counterbalanced order followed by clinical ratings of motor manifestations using Unified Parkinson Disease Rating Scale 3 (UPDRS 3). We investigated whether improvement in UPDRS 3 scores in rigidity, bradykinesia, postural stability and gait correlate with rCBF responses in a priori determined regions. These regions were selected based on a previous study showing significant STN DBS-induced rCBF change in the thalamus, midbrain and supplementary motor area (SMA). We also chose the pedunculopontine nucleus region (PPN) due to mounting evidence of its involvement in locomotion. In the current study, bilateral STN DBS improved rigidity (62%), bradykinesia (44%), gait (49%) and postural stability (56%) (paired t-tests: P < 0.001). As expected, bilateral STN DBS also increased rCBF in the bilateral thalami, right midbrain, and decreased rCBF in the right premotor cortex (P < 0.05, corrected). There were significant correlations between improvement of rigidity and decreased rCBF in the SMA (r(s) = -0.4, P < 0.02) and between improvement in bradykinesia and increased rCBF in the thalamus (r(s) = 0.31, P < 0.05). In addition, improved postural reflexes correlated with decreased rCBF in the PPN (r(s) = -0.38, P < 0.03). These modest correlations between selective motor manifestations and rCBF in specific regions suggest possible regional selectivity for improvement of different motor signs of Parkinson's disease.

Neural correlates of STN DBS-induced cognitive variability in Parkinson disease.

BACKGROUND: Although deep brain stimulation of the subthalamic nucleus (STN DBS) in Parkinson disease (PD) improves motor function, it has variable effects on working memory (WM) and response inhibition (RI) performance. The purpose of this study was to determine the neural correlates of STN DBS-induced variability in cognitive performance. METHODS: We measured bilateral STN DBS-induced blood flow changes (PET and [(15)O]-water on one day) in the supplementary motor area (SMA), dorsolateral prefrontal cortex (DLPFC), anterior cingulate cortex (ACC), and right inferior frontal cortex (rIFC) as well as in exploratory ROIs defined by published meta-analyses. STN DBS-induced WM and RI changes (Spatial Delayed Response and Go-No-Go on the next day) were measured in 24 PD participants. On both days, participants withheld PD medications overnight and conditions (OFF vs. ON) were administered in a counterbalanced, double-blind manner. RESULTS: As predicted, STN DBS-induced DLPFC blood flow change correlated with change in WM, but not RI performance. Furthermore, ACC blood flow change correlated with change in RI but not WM performance. For both relationships, increased blood flow related to decreased cognitive performance in response to STN DBS. Of the exploratory regions, only blood flow changes in DLPFC and ACC were correlated with performance. CONCLUSIONS: These results demonstrate that variability in the effects of STN DBS on cognitive performance relates to STN DBS-induced cortical blood flow changes in DLPFC and ACC. This relationship highlights the need to further understand the factors that mediate the variability in neural and cognitive response to STN DBS.

A new measure for end of life planning, preparation, and preferences in Huntington disease: HDQLIFE end of life planning.

BACKGROUND: Huntington disease is a fatal inherited neurodegenerative disease. Because the end result of Huntington disease is death due to Huntington disease-related causes, there is a need for better understanding and caring for individuals at their end of life. AIM: The purpose of this study was to develop a new measure to evaluate end of life planning. DESIGN: We conducted qualitative focus groups, solicited expert input, and completed a literature review to develop a 16-item measure to evaluate important aspects of end of life planning for Huntington disease. Item response theory and differential item functioning analyses were utilized to examine the psychometric properties of items; exploratory factor analysis was used to establish meaningful subscales. PARTICIPANTS: Participants included 508 individuals with pre-manifest or manifest Huntington disease. RESULTS: Item response theory supported the retention of all 16 items on the huntington disease quality of life ("HDQLIFE") end of life planning measure. Exploratory factor analysis supported a four-factor structure: legal planning, financial planning, preferences for hospice care, and preferences for conditions (locations, surroundings, etc.) at the time of death. Although a handful of items exhibited some evidence of differential item functioning, these items were retained due to their relevant clinical content. The final 16-item scale includes an overall total score and four subscale scores that reflect the different end of life planning constructs. CONCLUSIONS: The 16-item HDQLIFE end of life planning measure demonstrates adequate psychometric properties; it may be a useful tool for clinicians to clarify patients' preferences about end of life care.

Association of alpha-synuclein gene haplotypes with Parkinson's disease.

In a previous study, we detected an association between a dinucleotide repeat (Rep1) in the alpha-Synuclein (SNCA) gene and sporadic Parkinson's disease (PD). To extend our previous finding in a larger sample and further determine the role of SNCA in the development of PD, we screened a sample of 194 familial PD (FPD), 327 sporadic PD (SPD), and 215 controls with the Rep1 marker and 2 single nucleotide polymorphisms (SNPs) (770 and int4) in the SNCA gene. There was significant difference in allele frequency between African American and American Indian groups for Rep1 marker (p=0.03). These two samples were excluded from further analysis because of sample size. Comparison of allele frequency differences between PD and controls for the single-locus was significant only for Rep1 and SPD (p=0.017). The global case control association was highly significant for the three loci haplotypes comparisons. Our results indicate that Rep1 locus may be in linkage disequilibrium (LD) with a mutation in the gene or itself could be a risk factor for SPD.

Pathologic correlates of supranuclear gaze palsy with parkinsonism.

INTRODUCTION: Supranuclear gaze palsy (SGP) is a classic clinical feature of progressive supranuclear palsy (PSP) but is not specific for this diagnosis and has been reported to occur in several other neurodegenerative parkinsonian conditions. Our objective was to evaluate the association between SGP and autopsy-proven diagnoses in a large population of patients with parkinsonism referred to a tertiary movement disorders clinic. METHODS: We reviewed clinical and autopsy data maintained in an electronic medical record from all patients seen in the Movement Disorders Clinic at Washington University, St. Louis between 1996 and 2015. All patients with parkinsonism from this population who had subsequent autopsy confirmation of diagnosis underwent further analysis. RESULTS: 221 unique parkinsonian patients had autopsy-proven diagnoses, 27 of whom had SGP documented at some point during their illness. Major diagnoses associated with SGP were: PSP (9 patients), Parkinson disease (PD) (10 patients), multiple system atrophy (2 patients), corticobasal degeneration (2 patients), Creutzfeld-Jakob disease (1 patient) and Huntington disease (1 patient). In none of the diagnostic groups was the age of onset or disease duration significantly different between cases with SGP and those without SGP. In the PD patients, the UPDRS motor score differed significantly between groups (p = 0.01) with the PD/SGP patients having greater motor deficit than those without SGP. CONCLUSION: Although a common feature of PSP, SGP is not diagnostic for this condition and can be associated with other neurodegenerative causes of parkinsonism including PD.

1-Methyl-4-phenyl-1,2,3,6-tetrahydropyridine-induced acute transient dystonia in monkeys associated with low striatal dopamine.

Unilateral intracarotid infusion of 1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine (MPTP) in baboons produces transient contralateral dystonia lasting 2-3 weeks followed by chronic hemiparkinsonism. We now extend this model to Macaca nemestrina and Macaca fascicularis. MPTP was infused unilaterally into the internal carotid artery of two M. nemestrina and 11 M. fascicularis. Effects were assessed with blinded clinical ratings of dystonia and Parkinsonism; [18F]-6-fluoro-DOPA (FDOPA) positron emission tomography; and postmortem measurements of striatal dopamine content. In two M. nemestrina, MPTP 0.4 mg/kg intracarotid produced acute dystonia within 24 h then chronic Parkinsonism starting 3 weeks later. In three M. fascicularis, MPTP 0.4 mg/kg produced acute dystonia within 3-8 h but two others died from large hemispheric infarcts within 1 day. A much lower dose, MPTP 0.1 mg/kg produced no clinical manifestations (n=1), whereas MPTP 0.25 mg/kg produced consistent transient dystonia and ipsiversive turning within 1-3 days followed by chronic Parkinsonism at 3 weeks (n=5). One week after MPTP, striatal FDOPA uptake decreased an average of 69% in M. nemestrina (0.4 mg/kg); and decreased an average of 70+/-21% in M. fascicularis (0.25 mg/kg). Striatal dopamine was reduced an average 66% in the first day (n=2) during acute dystonia, 98% at 3 days (n=1) and 99%+/-2.3% at 2-4 months (n=5). M. nemestrina had a clinical response similar to baboons whereas M. fascicularis seemed more sensitive to MPTP. These findings extend the model of MPTP-induced transient dystonia followed by chronic hemiparkinsonism to M. nemestrina and M. fascicularis and demonstrate that the early dystonic phase is accompanied by striatal dopamine deficiency.

Vibration-induced regional cerebral blood flow responses in normal aging.

Task-induced changes in regional CBF (rCBF) can be measured with positron emission tomography (PET) and provide a powerful tool to map brain function. Many studies using these techniques have investigated responses in healthy young subjects. Since many pathological conditions occur more commonly in older subjects, it is necessary to compare blood flow responses in these patients with appropriately age-matched controls. Furthermore, the effects of normal aging on such blood flow responses remain unknown. For both reasons, we designed this study to determine whether vibration-induced CBF responses change with advancing age in normals. CBF was measured with PET and bolus-administered H2(15)O in 26 subjects from 20 to 72 years old (mean = 39; SD = 19). Regional responses were identified by subtraction-image analysis. Left and right hand vibration produced consistent responses in contralateral primary sensorimotor area (PSA) and supplementary motor area (SMA). Response magnitudes were compared to age by linear regression. There were no substantial relationships between age and responses to vibration for PSA or SMA (PSA r = -0.28, p = 0.054; SMA r = -0.33, p = 0.13). Power analysis demonstrates a high degree of confidence (99.7% for PSA and 87% for SMA) for detecting at least a moderate correlation (r = 0.6) between response magnitude and age. We conclude that the rCBF responses to vibrotactile hand stimulation do not change with normal aging.

Brain blood volume, flow, and oxygen utilization measured with 15O radiotracers and positron emission tomography: revised metabolic computations.

We have revised our methods for calculating regional blood volume, flow, oxygen extraction, and oxygen utilization from positron emission tomography data obtained using 15O-labeled radiotracers. These revisions include radioactive decay explicitly within the model equations instead of requiring all measured activity to be corrected for decay prior to incorporation in the equations. The revised equations yield small but significant differences in the computed values.

PET measured evoked cerebral blood flow responses in an awake monkey.

We have developed a method to measure task-related regional cerebral blood flow (BF) responses in an awake, trained monkey using positron emission tomography (PET) and H215O. We trained an animal with operant conditioning using only positive reinforcement to climb unassisted into a modified primate chair that was then positioned in the PET scanner. A special headholder and acrylic skull cap permitted precise placement and accurate repositioning. We measured BF qualitatively with bolus injection of H215O and 40-s scan. Each session included scans at rest interposed with scans during vibration of a forepaw. Regional responses were identified using subtraction image analysis. After global normalization, a resting image was subtracted on a pixel-by-pixel basis from a comparable image collected during vibration. The region of peak response occurred in contralateral sensorimotor cortex with a mean magnitude of 11.6% (+/- 3.2%) of the global mean value for 10 separate experiments, significantly greater than the mean qualitative BF change (0.4 +/- 3.6%; p less than 0.00001) in the same region for seven rest-rest pairs. This newly developed technique forms the basis for a wide variety of experiments.

In vivo kinetics of [18F](N-methyl)benperidol: a novel PET tracer for assessment of dopaminergic D2-like receptor binding.

A novel D2-like receptor-binding radioligand, [18F](N-methyl)benperidol ([18F]NMB), was evaluated via positron emission tomographic (PET) imaging studies of baboons. [18F]NMB rapidly localized in vivo within dopaminergic receptor-rich cerebral tissues, and striatum-to-cerebellum ratios as high as 35 were achieved after 3 hours. Pretreatment of an animal with unlabeled receptor-specific antagonists before injection of [18F]NMB confirmed that the radioligand bound specifically to central D2-like receptors in vivo, and not to S2- or D1-like receptors. Unlabeled eticlopride displaced striatal [18F]NMB in vivo, showing that D2-like binding is reversible. Receptor-binding by the radioligand was resistant to competitive displacement by synaptic dopamine, as illustrated by the lack of effect of intravenous d-amphetamine on the in vivo localization of [18F]NMB. Studies involving sequential intravenous administration of [18F]NMB, d-amphetamine, and eticlopride show that the radioligand does not undergo agonist-mediated internalization with subsequent trapping. The feasibility of applying a three-compartment non-steady state model for quantification of [18F]NMB receptor binding was demonstrated. These in vivo characteristics give [18F]NMB distinct advantages over the PET radiopharmaceuticals currently used for clinical investigation of D2-like receptor binding.

Regional asymmetries of cerebral blood flow, blood volume, and oxygen utilization and extraction in normal subjects.

Positron emission tomography (PET) and 15O-labeled radiotracers were used to measure regional CBF, cerebral blood volume (CBV), CMRO2, and oxygen extraction in 32 right-handed subjects at rest. Mean left hemispheric CBF (46.2 +/- 6.8 ml/100 g/min) and CMRO2 (2.60 +/- 0.59 ml/100 g/min) were significantly lower than right hemispheric values (47.4 +/- 7.2 and 2.66 +/- 0.61 ml/100 g/min, respectively; p less than 0.0001 for both), whereas left and right hemispheric CBV and oxygen extraction were not significantly different. We further investigated these asymmetries by comparing left- and right-sided values for specific cortical and subcortical regions. We found that left-sided CBF and CMRO2 were significantly lower than right-sided values for sensorimotor, occipital, and superior temporal regions, whereas only left-sided CBF values were lower for anterior cingulum. CBV was asymmetric for the anterior cingulate and mid-frontal regions, and oxygen extraction was asymmetric for the sensorimotor area. No asymmetries were observed in inferior parietal cortex, thalamus, putamen, or pallidum. Knowledge of these normal physiological asymmetries is essential for proper interpretation of PET studies of physiology and pathology. Furthermore, the ability to detect asymmetries with PET may lead to a better understanding of the lateralization of specific functions in the human brain.

Regional correction of positron emission tomography data for the effects of cerebral atrophy.

Given the low spatial resolution of positron emission tomography (PET), regional measurements of neural tissue are often inaccurate because of the presence of non-neural elements and to mixtures of different tissue types within the volume of space influencing the measurements. These effects are significant in scans of brains both with and without atrophy, but are particularly significant when comparing measurements of brains with atrophy with those of normals, as is typically done in studies of aging and dementia. Previous attempts to correct for cerebral atrophy have been limited to global measurements. Using computer simulations, we illustrate the effects of atrophy and describe a method for correcting regional PET data to represent units of actual neural tissue volume.

Standardized mean regional method for calculating global positron emission tomographic measurements.

A new "mean regional" method for calculating global hemispheric values of blood flow, blood volume, and metabolism with positron emission tomography is presented. It is based on a standardized set of regions defined according to coordinates in a stereotactic atlas of the brain. Region locations in each individual scan were determined by a localization technique that is independent of the appearance of the physiological images. Measurements obtained with this mean regional method minimize contributions from nonbrain structures such as ventricles or venous sinuses and provide the necessary basis for comparisons among different subjects and laboratories.

Strategies for in vivo measurement of receptor binding using positron emission tomography.

Dopaminergic ligands labeled with positron-emitting radionuclides have been synthesized for quantitative evaluation of dopaminergic binding in vivo. Two different methods, the explicit method and an operationally simplified ratio method, have been proposed for analysis of these positron emission tomographic (PET) data. The basis for both methods is the same three-compartment model. The two methods differ in the assumptions necessary for practical implementation. We have compared these two approaches using PET data obtained in our laboratory. Sequential scans and serial arterial blood samples from a baboon following intravenous injection of [18F]spiroperidol were collected. Application of the two methods to the same data yielded different values for corresponding parameters. Values calculated by the ratio method for the specific rate constant describing receptor binding varied depending upon the time after tracer injection, thus demonstrating an internal inconsistency in this approach. Tracer metabolism markedly affected the binding measurements calculated with either method and thus cannot be ignored. Our results indicate that the adoption of simplifying assumptions for operational convenience can lead to substantial errors and must be done with caution. Alternatively, we present simple new analytical solutions of the tracer conservation equations describing the complete, unsimplified three-compartment model that vastly reduce the computations necessary to implement the explicit method.