Kamil Uludag1 and Martin Havlicek1
1Maastricht University, Maastricht, Netherlands
Synopsis
Neuronal laminar information reflected in
high-resolution fMRI is reduced due to ascending veins, carrying hemodynamic
changes from various cortical depths to surface draining veins. Here, we
propose an invertible generative hemodynamic model, which takes the effect of
ascending veins to the laminar-specific fMRI signal explicitly into account. We
illustrate the versatility of this novel model to characterize common experimental
observations in laminar fMRI: we show that the spatial increase of laminar fMRI
towards CSF is due to baseline blood volume. In contrast, a peak in the middle
layer is due to higher neuronal activity rather than higher baseline blood
volume.
Introduction
The BOLD signal is an
indirect, vascular reflection of neuronal activity and, thus, comprises both
neuronal and vascular sources of variability1. In particular, in
laminar-resolved fMRI, altered vascular changes in lower layers affect blood
oxygenation and volume in the upper layers via intra-cortical ascending veins,
making it difficult to directly infer neuronal laminar profiles from measured
fMRI data both for gradient- and spin-echo sequences. Hence, modeling blood flow, volume, and oxygenation in the cortical
vasculature is imperative in order to account for vascular biases in the laminar
fMRI signal. Published attempts considering the coupling of vascular changes across
layers were limited because they either only considered two (instead of six or
more) cortical layers, introduced ad hoc vascular-physiological variables not
derived from mass balance principles, and/or exclusively accounted for
steady-state responses2,3. Here, we propose a novel,
invertible dynamic model based on mass balance principles that reliably
discriminates neuronal and vascular effects at this spatial scale.Methods
We expanded a single vascular compartment model (i.e. the balloon model4),
such that the total venous signal of each layer is described by a local (venous
signal of the local microvasculature) and non-local component (ascending vein
carrying deoxyhemoglobin (dHb) changes from the lower layers) (illustrated in Fig.
1). The changes in deoxygenated hemoglobin and volume of the local microvasculature
follow the same equations as in the balloon model and are not repeated here.
According to mass balance principles, the absolute changes in blood volume V and deoxygenated hemoglobin Q of the ascending vein (labeled with d)
in layer k are:
$$ dVd,k(t)/dt=Fmv,k(t)+Fd,k+1(t)-Fd,k(t) $$
$$ dQd,k(t)/dt=Fmv,k(t)Cmv,k(t)+Fd,k+1(t)Cd,k+1(t)-Fd,k(t)Cd,k(t) $$
Here, the variable F and C denote the absolute changes in blood flow and in concentration of
deoxygenated hemoglobin, respectively. In short, the changes in blood volume of
the ascending vein (eq. (1)) is determined by the inflow of blood from the
microvasculature (mv) of that layer k, the inflow from the ascending vein
from the lower layer (i.e. k+1) and
the outflow to the upper layer. Equation (2) describes the changes of
deoxygenated hemoglobin in the ascending vein and is described by the balance
of amount of deoxygenated hemoglobin brought into and washed out (i.e. amount
of deoxygenated hemoglobin is the product of flow and concentration, and
compartments are denoted as in eq. (1)). By normalizing these equations to baseline
values and together with the balloon model equation for the microvasculature5,
dynamic relative fMRI signal for each layer can be calculated for given neuronal
layer-specific activation profile.
Results
In the following, we demonstrate possible sources of
common experimental fMRI observations using this model by assuming typical
physiological values for baseline blood flow, transit time etc. Fig. 2
demonstrates that the commonly-observed spatial increase of the fMRI signal
towards the CSF is not present for constant baseline CBV but is due to spatially
increasing CBV (either of the microvasculature or of the ascending veins).
Occasionally, a “bump” in the fMRI profile is observed. For typical
physiological amplitudes, a local maximum of baseline CBV does only create a
small bump (Fig. 3A, i.e. vascular hypothesis), whereas a higher neuronal
activity in the middle layers evokes a clear bump (Fig. 3B, i.e. neuronal
hypothesis). In Fig. 4, simulations were performed by assuming neuronal
activity in only one layer. It can be observed, as expected, that the upper
layers also show fMRI signal changes, which slowly drop off with distance from
the activation layer (i.e. “leakage”), similar as in3. The leakage
amounts to ~20-30% of the original signal amplitude.Discussion
The proposed
generative hemodynamic model for laminar fMRI (extendable
to any number of cortical layers)
explicitly takes the drainage of deoxygenated hemoglobin and blood volume
changes into account, which experimentally reduces laminar neuronal information.
We illustrated the model on some typical experimental observations. The results
indicate that the spatial increase of fMRI signal is due to increase in
baseline CBV and is not just an effect of drainage of deoxygenated haemoglobin,
as is commonly assumed. In the second example, we demonstrated that the “bump”
in the middle layers cannot be explained by the popular vascular but only by the
neuronal hypothesis. That is, the bump, if present, is most likely due to
higher neuronal activity and not a consequence of higher baseline CBV. The
model can potentially also be used for forward simulations of laminar
hemodynamics (e.g. dip, time-to-peak, post-stimulus undershoot). Importantly,
the model is invertible and identifiable using Bayesian inversion5 that derives spatial distributions of neuronal
activity across cortical depths from experimental laminar fMRI.Acknowledgements
The research was
supported by the Netherlands Organization for Scientific Research (NWO) VIDI
grants 452-11-002 (KU).References
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Uludag, K., Blinder, P. Linking vascular physiology to hemodynamic
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