In susceptibility contrast-enhanced MRI of Gd-DTPA bolus injection, relative cerebral blood flow (rCBF) has commonly been analyzed using the deconvolution approach reported by Ostergaard et al. (Ostergaard et al., 1996b
). Another strategy had been suggested by Buxton et al. (Buxton, 2002
) to calculate rCBF by measuring the amount of Gd-DTPA arriving within a time window before any contrast agent has a chance to leave the tissue. That time window is in the order of the tissue mean transit time τ, a quantity known to be a few seconds for gray matter in humans. Given the basic assumption that the contrast agent has not had the chance to leave from the tissue
, the quantity of Gd-DTPA present in the tissue will be proportional to local CBF. We name this rCBF measurement technique which utilizes the early contrast-enhanced MR data points the “early time points” method (ET). The basic assumption, which will be cited repeatedly, will be called ET’s basic assumption for the rest of the manuscript.
A perfusion analysis technique like the deconvolution method utilizes the arterial input function (AIF) from an artery to evaluate flow given by the expression below:
) is the contrast agent concentration curve, a
is the perfusion term, AIF
is arterial input function,
is the convolution symbol and R
) is the residue function which is the probability that a molecule of the agent that entered the capillary bed at t=0 is still there at time t (Buxton, 2002
; Ostergaard et al., 1996b
). Eq (1)
can equally be used to explain the properties of ET. In ET, the residue function R
) = 1 when ET’s basic assumption holds (Buxton, 2002
), leading to Eq (2)
below which shows that perfusion result evaluated by ET is independent of AIF.
The independence of ET results from AIF is associated with an important observation of the early time points. If the shape of AIF changes due to Gd-DTPA injection rate or some other factors, the time course C
) of contrast concentration (ΔR2*) would change accordingly, but Eq (2)
demonstrates that perfusion value estimated using the ET method does not change at all throughout the range of the early time points. A box-shaped or rectangle function rect(t) (Buxton, 2002
) is a good model of a residue function that meets the demand of ET’s basic assumption and will be presented later in the Methods section.
One advantage of ET results being independent of AIF is skipping altogether the long known problem of possible inaccuracies in estimating the “true” AIF (Ellinger et al., 2000
; Kiselev, 2001
; Yamada et al., 2002
), a problem that continues to be receiving a fair amount attention in the perfusion publications. Eq (2)
is valid, however, only if AIF is the same for all pixels. The assumption of a single global AIF is applied throughout the manuscript for our investigation of the properties of ET. In the Discussion section, we will present a discussion on the problem of different AIF’s for different pixels due to delay and dispersion and why we chose to develop our understanding of ET using the global AIF assumption.
When it comes to transit delays of the bolus to the vascular bed, ET inherently requires an accurate correction of the transit delay to be made before the initiation of rCBF evaluation. In this manuscript, whenever the “early time points” or the “bolus time course” is mentioned, the transit delay is expected to have been corrected for the time course. The accuracy of transit delay correction depends, of course, on the accuracy of the estimation of the transit delay, a question that will be explored below.
While ET measures only rCBF, it can also derive absolute CBF the same way the deconvolution method does. It should be pointed out that the deconvolution outputs (the height of the maximum amplitude of the deconvolved residue function) using the method of Ostergaard et al. also yield only rCBF with respect to MR data analysis. One can get absolute CBF only if a proportionality constant, required for absolute CBF estimation, can be obtained independently and separately from a different technique like PET. One compares average PET CBF with the average MR blood flow derived from the deconvolution analysis to obtain the proportionality constant and then calculate absolute CBF. It is as easy for ET as for the deconvolution method to make absolute CBF maps by obtaining a similar proportionality constant using a calibration from PET. In this manuscript we focus only on the rCBF result of the ET analysis of MR data.
Since we are interested in the early time points of the rising bolus time course, a TR acquisition much shorter than the commonly used parameter of TR of ~1.5 sec in clinical perfusion imaging would be preferable. We proposed collecting MR data with echo planar imaging (EPI) acquisition using a short TR of 300ms. While TR=300ms is by no means an absolute requirement, it should cover the low range of τ, allowing a less ambiguous investigation of ET’s properties.
The tradeoff of short TR acquisition is the limited number of slices which reduces the clinical acceptance of ET. Therefore, in addition to applying standard gradient echo EPI (GE EPI) for our main MRI investigation, we briefly introduced at the end of this report a recently developed fast sequence, the Simultaneous Echo Refocusing (SER) EPI technique (Feinberg et al., 2002
; Reese et al., 2002
) which can acquire at least two slices in a single readout. SER could therefore be applied to obtain more slices than standard GE EPI in the same short TR. The utility of SER EPI had been reported in diffusion (Reese et al., 2009
) and fMRI studies (Chan et al., 2008
In order to learn how ET can be used for rCBF calculation, we need to identify the conditions and properties associated with the part of the bolus concentration time course which is compatible with ET’s basic assumption. The effort to clarify those conditions and properties of ET led to the investigation of four technical topics to be presented below. We supported our investigation using contrast-enhanced experimental MRI data and simulated perfusion data created using the algorithm of Wu et al. (Wu et al., 2003b
The four technical topics (Topic I – IV below) of ET we chose to study highlight several of ET’s properties and limitations. Topics I clarifies ET’s limitations due to noise. Topic II deals with a number of different possible techniques used by ET to calculate rCBF. Topic III considers the question of which part of early time points would be useful for rCBF calculation. Topic IV was chosen to demonstrate whether rCBF results by ET would match perfusion results in the literature obtained previously by PET and MRI. All four topics reinforce each other in demonstrating the applicability of ET for rCBF evaluation. With regard to the blood flow terminology we employed in those four topics, we used flow ratio to describe the ratio between different flow levels of simulation data. With experimental contrast-enhanced MRI data, “flow ratio” and “rCBF” were used interchangeably.
Topic I. Background noise at the time of arrival (TOA) of the contrast agent can affect the accuracy of flow ratio calculation
The time of arrival (TOA) of the bolus is a critical ET parameter which has a different value for each pixel. The value of TOA is used for the correction of the transit delay of the bolus for each pixel. Once TOA is found and the transit delay corrected, any single early time point on the rising bolus time curve could theoretically be used for rCBF calculation provided that the same time location is used for every pixel. Unfortunately, the presence of MRI noise makes it difficult to identify the precise location of TOA. The small amount of contrast agent entering the pixel at TOA gives a very low contrast-to-noise ratio (CNR) of the MR signal of the bolus. A misestimated TOA would give an inaccurate evaluation of rCBF by ET.
We must notice there is also a different TOA/noise problem completely separate from the difficulty of identifying the true TOA. It is important to recognize that, even if the true TOA is known, as is the case in noiseless simulation data, low CNR could undermine significantly the accuracy of calculated rCBF results near TOA. In other words, the knowledge of true TOA is not sufficient to secure accurate rCBF results.
Therefore, there are two separate ways for noise around TOA to affect the accuracy of calculated rCBF. First, one may not be able to find the correct TOA due to low CNR at the beginning of the rising concentration time course. Secondly, even if the correct TOA value could somehow be found, low CNR at TOA would still affect the accuracy of calculated rCBF. It is important to analyze these two noise related questions on TOA separately in order not to mix up the interpretation of their different effects.
The usefulness of a TOA searching algorithm to estimate TOA can be assessed first with noiseless simulation data, then with noisy simulation data generated with a predetermined signal to noise ratio (SNR) close to what can be encountered in contrast-enhanced MRI settings. Given that there is currently no accepted optimal way to find TOA, the TOA searching algorithm we selected was just one of many possible options and we did not conduct a comparison of different competing algorithms. Using both noiseless and noisy simulation data (SNR= 20), we proposed to assess the reasonableness of the calculated TOA obtained with our algorithm.
Topic II. Two different methods to perform the rCBF calculation for ET
What procedure can be used to calculate rCBF by ET? Buxton (Buxton, 2002
) proposed to calculate rCBF by measuring the initial slope
of the bolus signal coming in. However, there is no reason to restrict ourselves to only using the initial slope. We can use equally well the signal intensity (ΔR2*) of the early concentration curve to obtain the rCBF value. Eqs (1)
above already showed that the signal intensity was good enough for rCBF evaluation. Eqs (3)
below provided an explanation on why the slope value works equally well as signal intensity:
) is again 1 given ET’s basic assumption, just like Eq (1)
), , AIF
, and R
) have the same meaning as that of Eq (1)
shows that we can use the slope or the signal intensity to obtain the same rCBF values. To our understanding, signal intensity has not been proposed previously to be used for ET to evaluate rCBF. In fact, as long as the assumption of the early contrast agent concentration being proportional to rCBF holds, almost any number of arbitrary ways of manipulating the early rising bolus concentration time course would yield the same rCBF result
. One can equally use the value of the second derivative, the 3rd
derivative, and so on of the rising bolus concentration time course. While all these different methods yield theoretically the same flow results, one method could prove superior to another under specific conditions when noise is present. Eq (4)
, like Eq (2)
, is valid only if the AIF’s of the two pixels under comparison are the same, or if a global AIF is assumed as we have stated earlier for this manuscript. The question on the use of global AIF or local AIF is brought up in the Discussion section as the presence of bolus delay and dispersion between the artery and the tissue is an on-going concern of the research and clinical community.
If random noise is the only concern for our data, the signal intensity approach is in principle having better signal to noise than the slope approach. Due to propagation of error, a derivative evaluated by the simple difference between two time points would have lower signal to noise than the signal intensity alone. On the other hand, when physiological noise of a coherent character is present, the slope result which, being essentially a subtracted difference between subsequent data points, could be less sensitive to the coherent physiological noise oscillation common to the neighboring data points.
In theory, the signal intensity approach needs only one data point while the slope approach needs the difference of at least two neighborhood data points. However, a single data point or the difference of two data points suffers too much from signal fluctuation when the bolus time course is noisy (not just around TOA) and could return inaccurate values for rCBF. In practice, for the signal intensity approach, we used the running average of four time points and called it the signal averaging approach throughout the rest of this manuscript. For the slope approach, we derived a slope using Matlab (MathWorks Inc., MA) based on the linear least squares fit of the same four time points. Demonstration of consistency between rCBF results obtained by two different methods -- the slope method and the signal averaging method – will aid our confidence that the bolus data meet the demand of ET’s basic assumption. With simulation data, flow ratio results from the slope and the signal averaging methods can be checked for their accuracy against the true flow ratio. With experimental data when the true flow ratio is unknown, the flow results obtained by these two different methods can be checked for their consistency with each other.
It should be mentioned that the initial slope method bears resemblance to the maximum gradient-based method (Kimura and Kusahara, 2009
; Koenig et al., 1998
; Miles and Griffiths, 2003
) used in Computed Tomography (CT) and MR perfusion analysis. We leave a more detailed comparison between the maximum gradient-based method and ET to the Discussion section.
Topic III. The useful range of early time points for rCBF calculation: A time segment of steady state flow ratio
For noiseless simulation data, accurate flow ratio calculation is in principle obtainable immediately at TOA. But a very useful property of ET’s basic assumption predicts that flow ratio does not need to be calculated at TOA alone. Indeed, for noiseless data, identical flow ratio values are expected to be obtainable over the whole range going from TOA to TOA+τ, with τ being the time window before the contrast agent starts washing out. For noisy simulation data, useful flow result is not expected to be obtainable over exactly the same range from TOA to TOA+τ. The reason is that inaccuracy of flow ratio is to be expected in the neighborhood TOA even if true TOA is known. However, we do expect the calculated flow ratio at some distance away from TOA (at the higher CNR portion of the bolus time course) to eventually settle into a steady state time course of fluctuating around a mean flow ratio value. This time segment of steady state flow ratio is named FRSS for convenience. Basically, we want to identify the range of FRSS over which ET is expected to yield a steady state mean flow ratio for noisy data. Given the interference of noise at TOA, the beginning of FRSS for noisy data is hypothesized to be TOA+toffset, with toffset being a time delay allowing a more accurate evaluation of rCBF to take place at a better CNR portion of the rising contrast concentration time course. The end of FRSS is to be investigated but it should mark operationally the time when the bolus concentration time course reaches beyond τ.
The existence of FRSS is expected for the simulation data if the chosen model R(t) allows the early time points to meet ET’s basic assumption. For experimental data where R(t) can only be surmised, a successful identification of FRSS will booster the claim that real world data can be compatible with ET’s basic assumption.
Topic IV. Comparing the rCBF values obtained by ET with published literature values
With experimental MRI data, we checked if rCBF results calculated by ET results fell within the published range of rCBF values collected by PET and MRI. Examples of published values can be found at Leender et al. and Ostergaard et al. (Leenders et al., 1990
; Ostergaard et al., 1996a
Data selection and workflow for this manuscript
Our workflow included analyzing simulation data to examine the ideal behavior of ET and investigating experimental MRI data to see how well they matched the expected ideal ET behavior. In collecting experimental data, we imaged an anesthetized macaque in a clinical 3 Tesla MR scanner. While human clinical data would have been ideal, the untested ET technology and the lack of adequate brain coverage at short TR acquisition were some of the reasons why human patient studies are still on hold. Meanwhile, non-human primates were suitable subjects to provide an important model of the human brain. After presenting results to validate ET, we proposed an ET menu to account for the effect of noise and identify a useful range of early time points for rCBF calculation.