Direct estimation of evoked hemoglobin changes by multimodality fusion imaging

Abstract

In the last two decades, both diffuse optical tomography (DOT) and blood oxygen level dependent (BOLD)-based functional magnetic resonance imaging (fMRI) methods have been developed as noninvasive tools for imaging evoked cerebral hemodynamic changes in studies of brain activity. Although these two technologies measure functional contrast from similar physiological sources, i.e., changes in hemoglobin levels, these two modalities are based on distinct physical and biophysical principles leading to both limitations and strengths to each method. In this work, we describe a unified linear model to combine the complimentary spatial, temporal, and spectroscopic resolutions of concurrently measured optical tomography and fMRI signals. Using numerical simulations, we demonstrate that concurrent optical and BOLD measurements can be used to create cross-calibrated estimates of absolute micromolar deoxyhemoglobin changes. We apply this new analysis tool to experimental data acquired simultaneously with both DOT and BOLD imaging during a motor task, demonstrate the ability to more robustly estimate hemoglobin changes in comparison to DOT alone, and show how this approach can provide cross-calibrated estimates of hemoglobin changes. Using this multimodal method, we estimate the calibration of the 3 tesla BOLD signal to be -0.55%+/-0.40% signal change per micromolar change of deoxyhemoglobin.

Fig. 1. Schematic outline of model

The multimodal fusion model is based on a state-space approach and consists of three components. The set of coefficients to be estimated (β) multiplies a convolution kernel of spatial and temporal basis functions in the multidimensional linear model to model the volumetric changes in oxy- and deoxyhemoglobin due to evoked activation and systemic fluctuations. Linear observation models connect the underlying changes in these hemodynamic variables to expected measurements by both DOT and BOLD technologies. The states are finally estimated by minimizing the error with respect to the experimental data using a Bayesian formulation of the linear inversion operation.

Fig. 2. Basis functions in linear model

A set of spatial and temporal basis functions are used to regularize the model estimates of evoked and systemic hemodynamic changes. To model the different aspects of the physiology, four sets of basis sets are used. In the volume corresponding to either gray or white brain matter, a gamma-variant function (and derivative) was used as a temporal basis (subplot C). These allow the modeling of the differing temporal dynamics of both oxy- and deoxyhemoglobin changes. A spatial basis of overlapping Gaussian spheres is used to reduce the dimensionality of the state space and replace a smoothing operation on the data (subplot B). To model the systemic contributions, the volume corresponding to skin, skull, and cerebral spinal fluid (CSF) layers are grouped into basis functions and given sine and cosine temporal functions to model their dynamics.

Fig. 3. Diffuse optical tomography

Diffuse optical tomography uses spectroscopic measurements of optical absorption changes to record hemoglobin concentration changes. (a) The optical probe was placed over the subject’s primary motor area. (d) The probe contained four source and eight detector positions spaced 2.9 cm apart. (b) and (c) Fiducial markers on the probe were visible in the anatomical MR images. (e) The position of the probe and a segmented layer model for each subject were used to generate the optical sensitivity profiles using Monte Carlo methods.

Fig. 4. Characterization of model quantitative accuracy

The quantitative accuracy of the model was examined with observations simulated from a shallow (18 mm, toprow) and deep (25 mm, bottomrow) inclusion. The simulated inclusions are shown contoured (black) in each image (axial projections). The boundaries of the cortex are outlined in white. Measurement noise was added to achieve a 5:1, 50:1, and 500:1 contrast-to-noise ratio (CNR). Hemoglobin changes were reconstructed using the fusion model and DOT data alone for comparison. Reconstructions were performed at various regularization amounts to examine the dependence of the recovered magnitude of the response on the regularization parameter. The images are shown for the reconstruction at 1/Γ = 1µM (indicated by the vertical red line) for the CNR=50:1 case.

Fig. 5. Direct hemoglobin reconstructions from empirical data

This figure shows (b) the model reconstructions using the DOT alone, BOLD alone, and (a) fusion datasets for deoxy- and oxyhemoglobin changes. Data are represented for subject A. All responses have been normalized for comparison. Reconstructions were performed at a regularization level of 1/Γ = 10µM for the DOT and fusion models and 1/Γ = 10% for the BOLD model. Functional changes are shown masked below the half-max response amplitude. In (a) the approximate location of the optical probe is shown in green. The right-most images show the maximum intensity projections of the activation patterns onto the brain pial surface [surfaces generated using Freesurfer (The Massachusetts General Hospital; see http//surfer.nmr.mgh.harvard.edu)] and displayed using NeuroLens [Université de Montréal; (see http://www.neurolens.org)]. The central sulcus is outlined (green line) in each surface image.

Fig. 6. Comparison of fusion and MRI image reconstructions

In this figure, we show the BOLD (a) and fusion reconstructions (b) for subjects B through E (left to right). Subject A was presented in Fig. 5. Regularization was applied as described for Fig. 5. All images are shown normalized to the maximum response and masked below the half-max amplitude. Axial and coronal projections are shown. The outline of the boundary between the brain and superficial layers is shown in green. The blue rectangle indicates the location of the imaging volume from the fMRI.