Subjects

The results are based on data from 88 subjects (38 men and 50 women over 50 years of mean age of 67.7±8.02 years). Participants were recruited to participate in clinical trials (ADA 1-06-CR-25; NIH-NINDS 1R01-NS045745-01A2; NIH-NIA 1 R01- AG028760A2; 2009-2011) from community advertisement and through Beth Israel Deaconess Medical Center, Joslin Diabetes Clinic patient registries and the Harvard Cooperative Program on Aging research subject registry. All participants signed the informed consent form for the studies approved by the Institutional Review Board at Beth Israel Deaconess Medical Center (BIDMC), i.e., the Committee on Clinical Investigations (CCI). The participants provided consent to the use of their data in future research. The original protocols were amended to include analyses evaluating the relationships between TCD and MRI; the amendments were approved by the BIDMC CCI. The current retrospective analyses use exclusively de-identified datasets.

The data for this retrospective analysis of 88 subjects were selected from a database of records prospectively collected at the Syncope and Falls in the Elderly Laboratory and the Center for Magnetic Resonance Imaging at BIDMC. The database was composed of records from three completed projects spanning January 2002 to February 2008: Cerebral vasoregulation in the elderly with stroke (March 2003-April 2005); Cerebral vasoregulation in diabetes (January 2002-December 2005); and Cerebral perfusion and cognitive decline in type 2 diabetes (January 2006-December 2008) (see Acknowledgment/Funding Section for grant numbers). Cohort characteristics are summarized in Table 1. BFV and CBF measurements are, ideally, acquired on both the left and right side of the brain for each patient; left and right measurements are considered independently on each side and correspond to a total of 261 measurements. For most patients, 49 of them, one left and one right measurements are available. A total of 32 patients have two left and two right measurements. A full description of the number of available measurements is given in Table 2. Several patients had multiple measurements spanning several projects (i.e., several years); this makes it possible to investigate the predictive values of this type of data, see Results and Discussion below.

A complete dataset for each subject includes: demographic data, laboratory values, plasma hematocrit, TCD-based BFV in MCA, pCASL perfusion, blood pressure end tidal CO₂ at baseline, during hypercapnia, hypocapnia and cognitive challenge; time of flight MR angiography (TOEF MRA) to characterize vessels in the Circle of Willis (CoW) and T1 and T2 weighted images to characterize brain tissue volumes. TCD recordings were visually inspected for signal quality before including in the analysis. Baseline MCA BFV and baseline CBF from 3-D pCASL were acquired on the same day. Patients were on a no caffeine diet 24 hours before the exam. Antihypertensive medications were tapered and stopped on the day of the study; medications not affecting the cardiovascular system were allowed. The TCD and MRI protocols are discussed below.

Inclusion criteria were: (i) Healthy normotensive group: normotensive (BP under 140/90 mm Hg); not being treated for any systemic cardiovascular, renal, or neurological disease; no focal deficit on neurological exam; normal glucose and hemoglobin A1c. (ii) Hypertensive (HTN) group: BP over 140/90 mm Hg or diagnosed/treated for hypertension. (iii) Diabetes (DM) group: diagnosed and treated for type 2 diabetes mellitus for more than one year. (iv) DM-HTN group: with both hypertension and type 2 diabetes. Exclusion criteria were: type 1 DM, major event or surgery within 6 months, stroke history, carotid stenosis, intracranial stenosis, uncontrolled HTN, significant renal, liver, cardiac disease or failure, substance abuse, body mass index over 40, failed TCD insonation.

TCD protocol

About an hour after a light breakfast, participants were instrumented (PMD150 Spencer Technologies, Inc) with continuous monitoring of BFV in major Circle of Willis’ (CoW) vessels (anterior and middle cerebral arteries, ACAs and MCAs); continuous cardiovascular monitoring (beat-to-beat blood pressure, ECG), respiratory tidal volume, flow rate O₂ and CO₂ were simultaneously sampled at 500Hz using Labview. Blood pressure was measured beat-to-beat noninvasively from the finger using a volume-clamp method with a Portapres device (Finapres Medical Systems BV, Amsterdam, The Netherlands). TCD assessments were performed by an experienced sonographer (V.N.). Vessels were insonated bilaterally to record the maximum velocity for each vessel; probes were stabilized with 3D holders. A transtemporal window was used with sample volume set up in the Doppler mode, see Spencer Technologies and [21]. Average insonation depth was 54–57mm. The mean BFV v was calculated as an integral over time of the velocity envelope; systolic and diastolic peak velocities were recorded. Six minute supine baseline was acquired for each vascular territory. Insonation failure incidences were below 10%. Upon completion, participants were escorted to the MRI suite for MRI study.

MRI protocol

CASL [22–26] is one of several Arterial Spin Labeling MRI techniques; it allows the non-invasive measurement of regional perfusion. It is based on electromagnetically labeling arterial blood water in the supplying vessels to an area under study. The CASL protocol uses “continuous” radio frequency pulses (≈ 2 seconds). After some time, the area is imaged; labeled and control states are compared to infer perfusion.

A GE 3 Tesla HDxt scanner with 8 channel brain coil was used. 3D CASL images were acquired with pseudo-continuous labeling, background suppression, and a volumetric stack of spirals fast spin echo acquisition. The resulting pseudocontinuous ASL (pCASL) [27] is a hybrid approach developed in collaboration with GE Healthcare. Modifications to the standard sequence include (i) interleaved labeling and background suppression [28] to enable longer labeling and better signal and (ii) transit time prescan [29, 30] to improve quantification of flow in subjects with vascular pathology or slow flow. Labeling was done at the level of cervical vertebra C1 for whole brain images and at the ICA level for vessel specific labeling [29]. Perfusion and vasoreactivity data were acquired through established protocols and methods [27, 29, 31, 32].

High resolution anatomical images were acquired through 3D magnetization prepared rapid gradient echo (MP-RAGE) and fluid attenuation inversion recovery (FLAIR). Perfusion images were averaged during each condition (6 minutes baseline normocapnia) to improve the signal-to-noise ratio. Perfusion and anatomical MR images (MP-RAGE and FLAIR) was co-registered to a standard template of regional vascular territories and segmented to calculate regional perfusion, gray matter, white matter, and cerebrospinal fluid volumes using the statistical parametric mapping software package (SPM, University College London, UK) [33] and tools written in IDL. ECG, end tidal O₂, CO₂ and blood pressure were simultaneously acquired. An anatomical template (Laboratory of Neuro Imaging, University of California, Los Angles, USA) was applied to measure gray matter (GM), white matter (WM) and intracranial volume (ICV). Vessel diameters were calculated from 3D MR angiography (time of flight, TOF) using the Medical Image Processing, Analysis, and Visualization (MIPAV) software from the Biomedical Imaging Research Services Section, NIH, Bethesda, MD, at 3 locations and averaged, see Fig 1. Based on image resolution, the accuracy of the resulting MCA diameters is conservatively estimated at ±0.4 mm.

Predictor and response variables

We consider the pCASL-MRI CBF measurements y_i, i = 1, …, N, where N is the number of observations, as response variables. The other factors x_i = (x_i,1, …, x_i,14), i = 1, …, N, are predictor variables, namely hematocrit (HCT), intracranial volume (ICV), weight, height, grey matter to ICV fraction (GM/ICV), white matter to ICV fraction (WM/ICV), body mass index (BMI), age, head length (front to back), diabetes (Y/N), hypertension (Y/N), gender, TCD BFV and MCA diameter.

To lower the dimension of the problem and hence help prediction, we only retain one predictor from each group of strongly correlated variables. More precisely, the analysis below does not include GM/ICV or WM/ICV as they are strongly correlated to ICV, neither does it include weight which is determined by BMI and height. The 11 considered predictors are thus HCT, ICV, height, BMI, age, head length, diabetes, hypertension, gender, TCD BFV and MCA diameter. Statistical information about them is presented in Tables 1, 3 and 4. A previous version of this study included all 14 predictors; the difference between the two sets of results is barely detectable.

Random Forests

The above dataset involves noisy measurements, correlated variables and both categorical and numerical inputs. To handle all three difficulties, we base our approach on Random Forests (RF) [34, 35] the principle of which we briefly recall. To describe a RF, we must first introduce regression trees [36, 37] which are essentially piecewise constant approximations based on the given data.

Fig 2 illustrates the construction of a regression tree for a generic problem with two predictors only. The first step of the algorithm consists in dividing the parameter space into two subdomains along either x₁ = t₁ or x₂ = t₁; the split-point t₁ and the split variable, x₁ or x₂, are chosen so that approximation by constants on each side of t₁ results in as small an error as possible. As the best constants are the mean values in each subdomain, the split point is taken so that each subdomain contains data points as similar as possible to each other. This simple recursive partitioning process is then repeated until a stopping criterion is satisfied (for instance, minimum number of data points in each subdomain [35]).

In general, the parameter space is partitioned into K “hyper-rectangular” regions Ω_k, k = 1,…, K, in a space that has the dimension of the number of predictors. The response function is approximated by where x stands for the predictor variables, χ_k is the indicator function of Ω_k and c_k is a simple local model which is usually, as above, taken as the mean response in the leaf Ω_k, i.e., , I_k = {j; x_j ∈ Ω_k}.

While regression trees are fast, simple and robust to irrelevant and/or missing variables, they may suffer from low accuracy and instability as small dataset changes can result in large tree changes. By considering ensembles of trees, RFs [34, 35] partially alleviate these problems. In addition, RF based models allow for correlated parameters, nonlinear interactions, mixed data type (categorical and continuous) and can handle missing data in a natural way (see below). A RF model consists of an ensemble of trees , each tree being grown from a bootstrap sample of the N data points. The process is outlined in Algorithm 1. We take , m = 3, n_min = 5 and p = 11 in the results below.

Algorithm 1 Random Forest

function RF(x, y, , m, n_min)

Output: tree ensemble

 for do

  draw a bootstrap sample with replacement of size N from the data (x, y)

  grow a tree T_t from the bootstrapped data, i.e.

  initiate domain R so as to contain all data

  for all terminal nodes R with |R| ≥ n_min do

   randomly select m variables among the p available variables

   determine the best split among these m variables

   split R into two daughter nodes

  end for

 end for

end function

To make a prediction at a new point x, the values of each of the trees constructed above are averaged there (2) We refer to [35, 38] for additional information about implementation and the treatment of mixed data.

The data set contains N = 261 observations. Only 134 of these observations are complete. The imputation of missing values is an important part of data analysis and is the object of current research [39]. The flexibility of RF methods is here again an asset. We follow the iterative imputation scheme from [40] which has been shown to perform well even for mixed data. More precisely, let ξ be the N × (p + 1) data matrix, i.e., For the s-th variable ξ^(s), s = 1,…, p + 1, we denote by the indices of the missing values in that column and by the rest of the indices. The data matrix ξ is then partitioned in four parts

1. the observed part of ξ^(s): ,
2. the missing part of ξ^(s): ,
3. the part of ξ, without the s-th column, corresponding to : , i = 1,…, s − 1, s + 1,…, p + 1,
4. the part of ξ, without the s-th column, corresponding to : , i = 1,…, s − 1, s + 1,…, p + 1.

The algorithm is initiated by making initial guesses for the missing values of ξ through mean imputation. Then, for each ξ^(s), a RF is learned with predictor and response ; is then predicted by applying RF to and ξ is updated. The process is repeated till convergence of the data matrix.