[1] Modeling transport of reactive solutes is a challenging problem, necessary for understanding the fate of pollutants and geochemical processes occurring in aquifers, rivers, estuaries, and oceans. Geochemical processes involving multiple reactive species are generally analyzed using advanced numerical codes. The resulting complexity has inhibited the development of analytical solutions for multicomponent heterogeneous reactions such as precipitation/dissolution. We present a procedure to solve groundwater reactive transport in the case of homogeneous and classical heterogeneous equilibrium reactions induced by mixing different waters. The methodology consists of four steps: (1) defining conservative components to decouple the solution of chemical equilibrium equations from species mass balances, (2) solving the transport equations for the conservative components, (3) performing speciation calculations to obtain concentrations of aqueous species, and (4) substituting the latter into the transport equations to evaluate reaction rates. We then obtain the space-time distribution of concentrations and reaction rates. The key result is that when the equilibrium constant does not vary in space or time, the reaction rate is proportional to the rate of mixing, r T u D ru, where u is the vector of conservative components concentrations and D is the dispersion tensor. The methodology can be used to test numerical codes by setting benchmark problems but also to derive closed-form analytical solutions whenever steps 2 and 3 are simple, as illustrated by the application to a binary system. This application clearly elucidates that in a three-dimensional problem both chemical and transport parameters are equally important in controlling the process.Citation: De Simoni, M., J. Carrera, X. Sánchez-Vila, and A. Guadagnini (2005), A procedure for the solution of multicomponent reactive transport problems, Water Resour. Res., 41, W11410,

Objective:In patients with TIA and ischemic stroke, we validated the total small vessel disease (SVD) score by determining its prognostic value for recurrent stroke.Methods:Two independent prospective studies were conducted, one comprising predominantly Caucasian patients with TIA/ischemic stroke (Oxford Vascular Study [OXVASC]) and one predominantly Chinese patients with ischemic stroke (University of Hong Kong [HKU]). Cerebral MRI was performed and assessed for lacunes, microbleeds, white matter hyperintensities (WMH), and perivascular spaces (PVS). Predictive value of total SVD score for risk of recurrent stroke was determined and potential refinements considered.Results:In 2,002 patients with TIA/ischemic stroke (OXVASC n = 1,028, HKU n = 974, 6,924 patient-years follow-up), a higher score was associated with an increased risk of recurrent ischemic stroke (adjusted hazard ratio [HR] per unit increase: 1.32, 1.16–1.51, p < 0.0001; c statistic 0.61, 0.56–0.65, p < 0.0001) and intracerebral hemorrhage (ICH) (HR 1.54, 1.11–2.13, p = 0.009; c statistic 0.65, 0.54–0.76, p = 0.006). A higher score predicted recurrent stroke in SVD and non-SVD TIA/ischemic stroke subtypes (c statistic 0.67, 0.59–0.74, p < 0.0001 and 0.60, 0.55–0.65, p < 0.0001). Including burden of microbleeds and WMH and adjusting the cutoff of basal ganglia PVS potentially improved predictive power for ICH (c statistic 0.71, 0.60–0.81, phet = 0.45), but not for recurrent ischemic stroke (c statistic 0.60, 0.56–0.65, phet = 0.76) on internal validation.Conclusions:The total SVD score has predictive value for recurrent stroke after TIA/ischemic stroke. Prediction of recurrence in patients with nonlacunar events highlights the potential role of SVD in wider stroke etiology.

Background and Purpose-Arterial stiffening reduces damping of the arterial waveform and hence increases pulsatility of cerebral blood flow, potentially damaging small vessels. In the absence of previous studies in patients with recent transient ischemic attack or stroke, we determined the associations between leukoaraiosis and aortic and middle cerebral artery stiffness and pulsatility. Methods-Patients were recruited from the Oxford Vascular Study within 6 weeks of a transient ischemic attack or minor stroke. Leukoaraiosis was categorized on MRI by 2 independent observers with the Fazekas and age-related white matter change scales. Middle cerebral artery (MCA) stiffness (transit time) and pulsatility (Gosling's index: MCA-PI) were measured with transcranial ultrasound and aortic pulse wave velocity and aortic systolic, diastolic, and pulse pressure with applanation tonometry (Sphygmocor). Results-In 100 patients, MCA-PI was significantly greater in patients with leukoaraiosis (0.91 versus 0.73, PϽ0.0001).Severity of leukoaraiosis was associated with MCA-PI and aortic pulse wave velocity (Fazekas: 2 ϭ0.39, MCA-PI Pϭ0.01, aortic pulse wave velocity Pϭ0.06; age-related white matter change: 2 ϭ0.38, MCA-PI Pϭ0.015; aortic pulse wave velocity Pϭ0.026) for periventricular and deep white matter lesions independent of aortic systolic blood pressure, diastolic blood pressure, and pulse pressure and MCA transit time with MCA-PI independent of age. In a multivariate model (r 2 ϭ0.68, PϽ0.0001), MCA-PI was independently associated with aortic pulse wave velocity (Pϭ0.016) and aortic pulse pressure (PϽ0.0001) and inversely associated with aortic diastolic blood pressure (PϽ0.0001) and MCA transit time (Pϭ0.001). Conclusions-MCA pulsatility was the strongest physiological correlate of leukoaraiosis, independent of age, and was dependent on aortic diastolic blood pressure and pulse pressure and aortic and MCA stiffness, supporting the hypothesis that large artery stiffening results in increased arterial pulsatility with transmission to the cerebral small vessels resulting in leukoaraiosis. (Stroke. 2012;43:2631-2636.)Key Words: arterial stiffness Ⅲ cerebral pulsatility Ⅲ etiology Ⅲ leukoaraiosis Ⅲ white matter disease P revention of premature leukoaraiosis by treating the underlying causes in middle age may reduce the risk of stroke 1 and dementia 2 and other consequences of cerebral small vessel disease, 3,4 but the etiology is not yet fully understood. The relative importance of hemodynamic factors as opposed to a primary microangiopathy 5 in the development of leukoaraiosis is unclear and associations with age, hypertension, and diabetes are consistent with both processes. 6 Previous studies have suggested a relationship between increased middle cerebral artery (MCA) pulsatility measured by transcranial Doppler ultrasound and leukoaraiosis or lacunar infarction in patients with hypertension 7 and diabetes, 8 although not necessarily independent of age. However, increased cerebral pulsatility has often been interpreted as a...

SummaryBackgroundTransient isolated brainstem symptoms (eg, isolated vertigo, dysarthria, diplopia) are not consistently classified as transient ischaemic attacks (TIAs) and data for prognosis are limited. If some of these transient neurological attacks (TNAs) are due to vertebrobasilar ischaemia, then they should be common during the days and weeks preceding posterior circulation strokes. We aimed to assess the frequency of TNAs before vertebrobasilar ischaemic stroke.MethodsWe studied all potential ischaemic events during the 90 days preceding an ischaemic stroke in patients ascertained within a prospective, population-based incidence study in Oxfordshire, UK (Oxford Vascular Study; 2002–2010) and compared rates of TNA preceding vertebrobasilar stroke versus carotid stroke. We classified the brainstem symptoms isolated vertigo, vertigo with non-focal symptoms, isolated double vision, transient generalised weakness, and binocular visual disturbance as TNAs in the vertebrobasilar territory; atypical amaurosis fugax and limb-shaking as TNAs in the carotid territory; and isolated slurred speech, migraine variants, transient confusion, and hemisensory tingling symptoms as TNAs in uncertain territory.FindingsOf the 1141 patients with ischaemic stroke, vascular territory was categorisable in 1034 (91%) cases, with 275 vertebrobasilar strokes and 759 carotid strokes. Isolated brainstem TNAs were more frequent before a vertebrobasilar stroke (45 of 275 events) than before a carotid stroke (10 of 759; OR 14·7, 95% CI 7·3–29·5, p<0·0001), particularly during the preceding 2 days (22 of 252 before a vertebrobasilar stroke vs two of 751 before a carotid stroke, OR 35·8, 8·4–153·5, p<0·0001). Of all 59 TNAs preceding (median 4 days, IQR 1–30) vertebrobasilar stroke, only five (8%) fulfilled the National Institute of Neurological Disorders and Stroke (NINDS) criteria for TIA. The other 54 cases were isolated vertigo (n=23), non-NINDS binocular visual disturbance (n=9), vertigo with other non-focal symptoms (n=10), isolated slurred speech, hemisensory tingling, or diplopia (n=8), and non-focal events (n=4). Only 10 (22%) of the 45 patients with isolated brainstem TNAs sought medical attention before the stroke and a vascular cause was suspected by their physician in only one of these cases.InterpretationIn patients with definite vertebrobasilar stroke, preceding transient isolated brainstem symptoms are common, but most symptoms do not satisfy traditional definitions of TIA. More studies of the prognosis of transient isolated brainstem symptoms are required.FundingWellcome Trust, UK Medical Research Council, Dunhill Medical Trust, Stroke Association, National Institute for Health Research (NIHR), Thames Valley Primary Care Research Partnership, and the NIHR Biomedical Research Centre, Oxford.