Vasodilation

Dynamic Causal Modelling is a framework for fitting differential equation models of neuronal activity to brain imaging data using Bayesian inference. The DCM approach can be applied to functional Magnetic Resonance Imaging (fMRI), Electroencephalographic (EEG), Magnetoencephalographic (MEG), and Local Field Potential (LFP) data [22] (link). The empirical work in this paper uses DCM for fMRI. DCMs for fMRI comprise a bilinear model for the neurodynamics and an extended Balloon model [23] (link) for the hemodynamics. The neurodynamics are described by the following multivariate differential equation where indexes continuous time and the dot notation denotes a time derivative. The th entry in corresponds to neuronal activity in the th region, and is the th experimental input.
A DCM is characterised by a set of ‘exogenous connections’, , that specify which regions are connected and whether these connections are unidirectional or bidirectional. We also define a set of input connections, , that specify which inputs are connected to which regions, and a set of modulatory connections, , that specify which intrinsic connections can be changed by which inputs. The overall specification of input, intrinsic and modulatory connectivity comprise our assumptions about model structure. This in turn represents a scientific hypothesis about the structure of the large-scale neuronal network mediating the underlying cognitive function. A schematic of a DCM is shown in Figure 1.
In DCM, neuronal activity gives rise to fMRI activity by a dynamic process described by an extended Balloon model [24] for each region. This specifies how changes in neuronal activity give rise to changes in blood oxygenation that are measured with fMRI. It involves a set of hemodynamic state variables, state equations and hemodynamic parameters, . In brief, for the th region, neuronal activity causes an increase in vasodilatory signal that is subject to autoregulatory feedback. Inflow responds in proportion to this signal with concomitant changes in blood volume and deoxyhemoglobin content . Outflow is related to volume through Grubb's exponent
[20] (link). The oxygen extraction is a function of flow where is resting oxygen extraction fraction. The Blood Oxygenation Level Dependent (BOLD) signal is then taken to be a static nonlinear function of volume and deoxyhemoglobin that comprises a volume-weighted sum of extra- and intra-vascular signals [20] (link)
where is resting blood volume fraction. The hemodynamic parameters comprise and are specific to each brain region. Together these equations describe a nonlinear hemodynamic process that converts neuronal activity in the th region to the fMRI signal (which is additionally corrupted by additive Gaussian noise). Full details are given in [20] (link),[23] (link).
In DCM, model parameters are estimated using Bayesian methods. Usually, the parameters are of greatest interest as these describe how connections between brain regions are dependent on experimental manipulations. For a given DCM indexed by , a prior distribution, is specified using biophysical and dynamic constraints [20] (link). The likelihood, can be computed by numerically integrating the neurodynamic (equation 1) and hemodynamic processes (equation 2). The posterior density is then estimated using a nonlinear variational approach described in [23] (link),[25] (link). Other Bayesian estimation algorithms can, of course, be used to approximate the posterior density. Reassuringly, posterior confidence regions found using the nonlinear variational approach have been found to be very similar to those obtained using a computationally more expensive sample-based algorithm [26] (link).

The methodology for measuring endothelial function and vascular reactivity using DTM has been previously described [21 (link)–25 (link)]. All DTM tests were performed using a VENDYS® 6000 Portable System (Endothelix, Houston, TX), a PC-based system that fully automates the cuff reactive hyperemia protocol. The general test setup and a sample VENDYS test report are shown in Figure 1. During subject preparation, blood pressure cuffs were placed on both of the subject's upper arms, and VENDYS skin temperature sensors were affixed to both of the subject's index fingers. The software-driven DTM test began with an automated measurement of blood pressure and heart rate obtained from the left arm cuff. Following a 5-minute period of patient and temperature stabilization, a 5-minute cuff occlusion (cuff inflated to 30 mmHg above systolic BP) of the right arm was performed. During the cuff occlusion period, fingertip temperature in the right hand decreased because of the absence of warm circulating blood. When the cuff was released after the 5-minute occlusion, hyperemic blood flow to the forearm and hand was restored, and this resulted in a “temperature rebound” in the fingertip that is directly related to the subject's hyperemic blood flow response, endothelial function, and vascular reactivity [21 (link), 22 (link)]. Using the recorded fingertip temperatures, the ambient temperature of the testing room, the observed slope of temperature decline, and a multivariate bioheat formula, the VENDYS software calculated and plotted a zero reactivity curve (ZRC). The ZRC served as an internal control and showed the expected temperature rebound curve, if zero vascular reactivity was present and the other variables remained the same. In other words, the ZRC is the expected temperature curve, if no vasodilatation and subsequent reactive hyperemia had occurred [21 (link)]. Vascular reactivity index (VRI) was determined by taking the maximum difference between the observed temperature rebound curve and the ZRC during the reactive hyperemia period. VRI ranged from 0.0 to 3.5 and was classified as being indicative of poor (0.0 to <1.0), intermediate (1.0 to <2.0), or good (≥2.0) vascular reactivity.
The VENDYS DTM Test Registry includes age, sex, blood pressure, heart rate, VRI, and fingertip temperature measurements recorded during DTM tests. The Registry does not include other health related information. All DTM tests were performed in ambulatory care clinical settings. This study includes a total of 6,084 patients from 18 clinics that volunteered to submit their data to the Registry. The number of each type of medical practice is as follows: cardiology = 9, general/family practice = 4, antiaging = 3, and internal medicine = 2.
Statistical analyses were performed using MATLAB (The MathWorks, Inc., Natick, MA). Variable data were expressed as mean ± SD. VRI scores in men and women were compared using unpaired Student's t-test. Comparisons of categorical data (e.g., proportion of subjects with good VRI in men versus women) were performed using Fisher's exact test. Pairwise correlations were examined using Pearson's correlation coefficient, and correlations between VRI and multiple patient characteristics (i.e., age, sex, blood pressure, and heart rate) were evaluated using multiple linear regression analysis. p value < 0.05 was considered significant. When performing statistical comparisons, tests with missing data were excluded from the comparison. “Cold Finger Flag” was defined as the condition in which the right finger temperature at start of cuff occlusion (time 300 s) is ≤27°C. Previous DTM testing had shown that right finger t300 temperatures < 27°C often resulted in technically poor results. “Sympathetic Response Flag” was defined as the condition in which left finger temperature continuously declines (>0.5°C temperature drop over a 5-minute time period) after right arm-cuff occlusion. When evaluating VRI, tests that exhibited “Cold Finger Flag” (n = 353) or “Sympathetic Response Flag” (n = 294) were excluded from the analyses. In addition to monitoring temperature at the index finger of the right arm, we studied temperature changes at the index finger of the left (nonoccluded) arm and observed interesting signals that are currently under further investigations and not included in the results below.