CMRO2 Estimating with Multimodality Imaging Using a Multi-Compartment Vascular Model
T.J. Huppert , M.S. Allen , H. Benav , P. Jones , A. Devor , 1 4 1 R.D. Hoge , A. Dale , and D.A. Boas
1 Athinoula 2
1,2
3
1
1
4
A. Martinos Center for Biomedical Imaging Massachusetts General Hospital, Charlestown, MA 02129, USA
Graduate Programs in Biophysics, Harvard University, Boston, MA 02115, USA of Electrical Engineering, University of Texas at Arlington, Arlington, TX 76019, USA
3 Department 4
Neuroscience and Radiology, University of California San Diego, 9500 Gillman Drive, La Jolla CA 92093
[e-mail]
Abstract:
Hemodynamic measurements such as blood flow, volume, or the BOLD signal are composite results of changes in oxygen metabolism and arteriole dilation and also depend on the underlying vascular anatomy and mechanical properties. We describe a multi-compartment model of the vascular anatomy, to inductively estimate the changes in arteriole dilation and CMRO2 from multi-modality hemodynamic measurements. We validate this model with data from optical spectroscopy and laser speckle imaging in a rat model and demonstrate the extension of this model to human imaging.
Validation in Rat Model:
Methods:
Laser speckle and multi-wavelength spectroscopic measurements were made on a total of 7 rats after a thinned skull preparation [6,7]. Stimulus consisted of a 9condition parametric whisker deflection [7]. After deconvolution of the data with the stimulus timing, ROI averages were calculated. The responses for individual rats were normalized to the ninth condition before group averaging.
Comparison of Arteriole Diameter and CMRO2 changes estimated from the Multi- and SingleCompartment Models
Introduction:
Vascular modeling [1,2] has been invaluable in providing interpretations of hemodynamic measures such as optical or fMRI [reviewed by 3]. Recent work has suggested that the single-compartment model is insufficient to explain the higher spatial and temporal resolution data available from imaging in animal models [4]. Here we describe a multi-compartment model of the extra-vascular tissue, arterioles, capillaries, venioles, and veins. The model is based on an inductive framework, and uses a state-space approach with temporal basis functions to model changes in the hemodynamic parameters in each compartment. Interchangeable measurement models relate these parameters to observable hemodynamic variables
We found that the single-compartment model predicted a statistically larger arteriole dilation response (p<2x10-6). Both models predicted a linear response to stimulus condition. There was much more variance in the estimation of CMRO2 changes in the single-compartment model compared to the multi-compartment [both fitting all nine conditions simultaneously]. Differences in the estimate of CMRO2 did not test significant.
Hypercapnic Modulation of Baseline
To further test the model, we repeated the 9-condition stimulus task under a hypercapnic (5% CO2) modulation of the baseline blood flow and volume. CO2 causes vasodilation of the vessels and increases baseline blood volume and flow. Under hypercapnia, the hemodynamic response is dampened, producing a lower amplitude response.
Multi-compartment model fits
The region-of interest averaged responses for all 9 stimulus
R2=0.95 R2=0.98 R2=0.99 conditions were fit using the
Hemodynamic Response during Hypercapnia
Under hypercapnia, the amplitude of the hemodynamic response was lowered (pink lines indicate normalcapnic responses and blue lines indicate hypercapnic responses)
Condition 3 Condition 6 Condition 9
The Model:
State Vector:
A state vector of unknowns (table below) is used to describe the dynamic and structural properties of the model
Multi-Compartment Model
Vascular Model:
++
A multi-compartment vascular model based on [2,4,5] predicts blood flow and volume changes based on changes in arteriole dilation and the underlying vascular structure.
Variable
Data Model Fit
CBF HbT
HbR 2
HbO
model. The model closely replicated the experimental data for all 9 conditions (shown to the right for conditions 3,6 and 9). The state estimates for the structural and baseline variables in the model were consistent for all nine conditions. This was confirmed with a grouped T-test with conditions 1-3, 4-6, and 7-9. A joint fit using data from all 9 stimulus conditions was performed by estimating common structural and baseline parameters, but allowing arteriole dilation and CMRO2 to vary over the nine conditions. This provided a more robust estimate of the states, but remained consistent with the independent fitting results.
R2=0.85
R2=0.92
R2=0.98
Multi-Compartment Model Data CBF HbO Model Fit HbT HbR 2
Arteriole Dilation
Arteriole Resistance [%-Change] 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 1 2 3 4 5 6 7
Normalcapnia Hypercapnia
Oxygen Transport Model:
Dynamic
1
0.94 3.00 2.38 0.53 1.49 1.77 0.73 1.32 0.79 1.27 113.8 0.940 0.709 0.635
2
1.05 3.11 1.97 0.24 1.86 1.15 0.77 1.33 0.68 0.77 118.7 0.940 0.704 0.631
3
1.41 2.96 1.35 0.34 1.68 1.11 0.74 2.27 0.65 0.75 114.3 0.950 0.731 0.656
Stimulus Condition 4 5 6
1.72 3.12 1.15 0.35 1.49 1.72 0.73 2.79 1.31 1.09 133.4 0.972 0.749 0.687 1.69 3.11 1.48 0.22 1.71 1.61 0.76 1.21 0.70 0.59 112.9 0.947 0.740 0.667 1.84 3.03 1.32 0.27 1.91 1.54 0.77 1.14 0.66 0.71 110.7 0.943 0.712 0.635
7
2.57 3.32 1.55 1.28 1.32 2.12 0.66 2.94 0.75 1.40 133.4 0.973 0.732 0.655
8
2.65 3.26 1.56 0.36 1.37 1.84 0.68 1.52 0.62 0.80 92.4 0.939 0.730 0.656
9
3.00 3.22 1.36 0.28 1.27 1.08 0.76 1.19 0.61 0.63 87.7 0.938 0.747 0.673
Mean * *
Fit Together
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CMRO2
1.5 CMRO2 [%-Change]
++
Driven by changes in blood volume and flow predicted by the vascular model and changes in oxygen metabolism, oxygen transport is modeled from the arteriole, capillary, and venial segments into the extravascular space.
Arteriole dilation temporal basis
Observation Models:
Laser Speckle Imaging Spectroscopic Imaging Measurement models based on the biophysics of each modality relate the model's predicted auxiliary states (CBF,CBV,HbR,HbO2) to the observable variables measured. In this example, we use optical spectroscopy and laser speckle imaging.
R A peak CMRO 2 CMRO2 peak temporal basis c R A (0) Windkessel parameters pial [HbT] o SaO2 ScO2 SvO2
1.0
0.5
Normalcapnia Hypercapnia
0.73 1.75 0.75 0.89 113.04 0.95 0.73 0.66
0.79 1.45 0.60 0.96 102.5 0.938 0.694 0.616
Structural
0.0
Hypercapnia produced a significantly smaller arteriole dilation response compared to normal (p<0.003). The estimates in CMRO2 changes were not significantly different between normal and hypercapnia (p=0.34) [2-way T-test].
8
9
1
2
3
4
5
6
7
8
9
Stimulus Condition
Stimulus Condition
Comparison of Baseline Parameters under Hypercapnia
Normalcapnia
YSpeckle
YSpectral
R (Yi - Y^i )2
-1 i i
Observations:
Information from multiple modalities is compared to the model's predictions. A variance-weighted leastsquares routine is used to minimize model residual error.
Measurement noise
Vascular Model:
A vascular model [2,4,5] consists of three compliant vascular compartments (arteriole, capillary, and venial) and a pial venous compartment with constant volume. Vascular changes are driven by arteriole dilation, described using a Gaussian temporal basis function with variable amplitude and time parameters.
The amplitude of arteriole dilation and CMRO2 changes increased linearly with the stimulus amplitude (R2=0.96 and R2= 0.87)[joint fit]. The joint fitting provided a more robust estimate of CMRO2 changes. The plots shown to the right indicate the parametric increases in these variables. The error bars indicate the 75% confidence bounds for each estimate obtained by Markov Chain Monte Carlo techniques.
Baseline CBV and CBF were elevated during hypercapnia. The estimated baseline CMRO2 was higher during hypercapnia, but this difference was not statistically different.
Total Hemoglobin CBV CBF OEF CMRO2
102 1.03 104 0.38 8.6
108 1.08 129 0.34 9.9
Hypercapnia
M mL/100g mL/100g/min mL/100g/min
Extension to Human Imaging
With confidence from the validation of this model in invasive microscopic imaging techniques in the rat model, this work can be directly applied to human measurements.
Model Fit to Human finger-tapping data[11]
HbO2 HbR HbT BOLD ASL
Estimation of Baseline Parameters
A unique feature of this model that is it can calculate baseline blood flow, volume, and oxygen metabolism. In the state vector, baseline total-hemoglobin (HbTo ) is used to scale between the percent changes measured by laser speckle and the micro-molar changes measured by spectroscopy. Using the equations shown to the right, baseline system properties are determined. A hemotocrit (Hct) value of 16 gm/dL was assumed.
The vascular transit time () relates the baseline blood flow (unit normalized) and total Windkessel volume (Vw) [2].
Oxygen Transport Model:
Oxygen transport is modeled between the arteriole, capillary, and venial compartments and the extra-vascular space based on the gradient of oxygen tension and the relative permeability of each vascular segment. In the extra-vascular (parenchyma) space, cerebral oxygen consumption (CMRO2) is described by a Gamma function based temporal basis function, whose amplitude and timing parameters are given by the estimated state-variable. Plasma dissolved oxygen is also calculated to allow this system to model hemodynamic changes under hyperbaric and hyperoxic conditions.
Vw (0) = Fin (0)
Transit time and baseline total hemoglobin are estimated by the model, which allows an absolute value to be given to blood flow.
CBFo = HbTo /( Hct )
Simultaneous NIRS [near-IR spectroscopy] and pASL [pulsed arteriole spin labeling] was used measure of changes in hemoglobin concentration, relative blood flow, and the BOLD signal during a 2second finger-walking task [11].
Model fits to data
0.997 - HbO2 0.987 - HbR 0.999 - HbT 0.996 - ASL 0.991 - BOLD
Probability
Baseline CMRO2 is calculated from flow and oxygen extraction (estimated within model)
Multi-Compartment Model
Consumption:Flow Ratio
<C:F>=0.48
rCMRO2 (0) = CBFo OEF
1
Baseline Flow
87
2
105
Stimulus Condition 3 4 5 6 7
107 61 98 101 107
8
89
9
87
Mean
94 (15)
Fit Together
104 (12) 22.1 (2.6)
mL/100g/min
Literature
56 [8] 70 [9]
Baseline O2 18.6 22.4 22.8 13.1 20.9 21.5 22.9 19.1 delivery Baseline OEF Baseline CMRO2
0.35 0.36 0.33 0.30 0.32 0.35 0.33 6.6 8.0 7.6 4.0 6.7 7.6 7.6 0.33 6.4
18.6 20.0 (3.1)
mL/100g/min
0.31 0.33 (0.02) 0.37 (0.01) 5.9 6.7 (1.3) 8.2 (0.8)
[AU]
The experimental data was fit using the multi-compartment model. A 9.2% (+/2.9%) relative CMRO2 change was estimated. The ratio of consumption to blood flow changes was calculated to be 0.48. Markov Chain Monte Carlo was used to estimate the error in each state (shown to the right)
R2=
0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
Baseline Estimates from Model
Blood Flow Oxygen Delivery Oxygen Extraction CMRO2 35.6 7.83 0.20 1.55 mL/100g/min mL/100g/min mL/100g/min
mL/100g/min
5.6 [9]
Conclusions
*100uM [HbT] assumed
Observation Models
Optical spectroscopic imaging is measures the sum of the changes in oxy- and deoxyhemoglobin from all four vascular compartments. Changes are measured in absolute (i.e. micro-molar) quantities. Laser speckle imaging measures relative changes in cerebral blood flow and is assumed to be the sum over the vascular compartment normalized to the baseline.
YSpectral , HbX (t ) = HbX n (t )
n
Baseline CMRO2, blood flow and volume were calculated from the model fits to the nine stimulus conditions. Baseline flow and CMRO2 slightly higher than expected from literature values [8,9]. This could be due to partial volume errors of the two imaging methods. The estimates of baseline properties were not significantly different among the nine conditions (grouped T-test).
1. The multi-compartment model provides a statistically better fit (p<8x10-5) than the single-compartment model for multi-modality data from the rat cortex. In particular, the multi-compartment model provides better explanation of deoxy-hemoglobin changes (p<8x10-6). 2. The state-space framework of this model allows the estimation of baseline parameters from functional data. Baseline CBF, CBV, and CMRO2 were estimated for the nine stimulus conditions. No statistical differences in the baseline estimates were found over the nine conditions . 3. Hypercapnic modulation of baseline blood flow and volume resulted in lower amplitude hemodynamic responses. However, the change in CMRO2 induced by the stimulus was not statistically different under normal or hypercapnia.
Comparison to single-compartment model
n
YSpeckle (t ) = CBFn (t ) / CBFo
n
State Estimation
A total of 14 states are estimated in the model. The dynamic changes in arteriole dilation and CMRO2 are described using temporal basis functions. Structural parameters describe vascular compliance and the baseline properties of the system.
Symbol Arteriole dilation temporal basis CMRO2 temporal basis R A Description
Change arterial resistance Time to maximum resistance change Width of temporal resistance change Relative change CMRO2 Time to onset of CMRO2 change Width of temporal CMRO2 change Initial arterial resistance Windkessel vascular reserve Vascular transit time Pial venous transit time Total baseline blood volume Baseline arteriole saturation Baseline capillary s...