DSC Signal and [Gd]

Is it possible to quantify the actual concentration of Gd from its signal in a DSC study?  

In previous Q&A's we have illustrated how MR signal intensities on T2(*)-weighted DSC images decrease during passage of a gadolinium bolus. From this raw data some potentially useful semiquantitative parameters can be extracted, such as time-to-peak (reflecting blood flow) and negative enhancement integral (reflecting blood volume). The first step toward gaining extracting more accurate and meaningful physiological information from this data is to convert signal intensity information into actual gadolinium concentrations.  

The conversion typically used is to assume that gadolinium concentration [Gd] is proportional to the observed change in T2*-relaxation rate (ΔR2* = 1/ΔT2*), which in turn is proportional to the negative logarithm of relative signal intensity:

Here So is the baseline signal intensity in a given voxel and St is the signal at time t during passage of the gadolinium bolus. The derivation of this equation is given in the Advanced Discussion.

The conversion between signal intensity and gadolinium concentration is essentially a logarithmic transformation, illustrated in the graphs obtained from a commercial perfusion software program below.

DSC ("raw data") signal intensity versus time curve

Transformed concentration curve, fitted with gamma variate

Advanced Discussion (show/hide)»

The following is a brief derivation of the equation relating gadolinium concentration [Gd] and signal intensities given in the text above.

In simple solutions of contrast agents at physiologic concentrations, changes in observed relaxation rates (ΔR2=1/ΔT2 and ΔR2*=1/ΔT2*) are linearly related to gadolinium concentration [Gd]. Thus by measuring the change in relaxation rates within a voxel during passage of a contrast bolus, the approximate Gd concentration at that time and location can be determined.

Recall that the signal (S) generated by a simple gradient echo sequence of the type typically used in a DSC experiment decays exponentially with time given by the expression

S = k e^−TE/T2* = k e^−TE•R2*

where k is a constant that includes a conglomeration of tissue-related (e.g., T1, ρ, χ) and technical (e.g., B_o, TR, NEX, α) factors.

This equation can be solved for R2* by taking logarithms of both sides and rearranging terms.

ln(S/k) = − TE • R2*

R2* = − (1/TE) • ln(S/k)

Before the gadolinium bolus arrives we assume the tissue voxel has an initial relaxation rate R2*_o and signal S_o. At time = t during passage of the bolus, we assume the relaxation rate increases to R2*_t and the signal falls to S_t. In other words

R2*_o = − (1/TE) • ln(S_o /k)

R2*_t = − (1/TE) • ln(S_t /k)

The change in R2*, which is proportional to gadolinium concentration, can be written

ΔR2* = R2*_t − R2*_o = − (1/TE) • [ ln(S_t /k) – ln(S_o /k) ]

Using the logarithmic identity ln(A) − ln(B) = ln(A/B) we can rewrite this last equation as

ΔR2* = − (1/TE) • ln(S_t /S_o)

The major assumption that changes in relaxation rates are proportional to gadolinium concentration may be justifiably challenged. Specifically, such a linear relaxivity relationship holds true only for dilute homogenous aqueous solutions of gadolinium using spin-echo pulse sequences.

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References
     Kiselev VG. On the theoretical basis of perfusion measurements by dynamic susceptibility contrast MRI. Magn Reson Med 2001; 46:1113-1122.
     Østergaard L, Johannsen P, Host-Poulsen P, et al. Cerebral blood flow measurements by magnetic resonance imaging bolus tracking: comparison with [15O]H2O positron emission tomography in humans. J Cerbral Blood Flow Metab 1998; 18:935-940. (Early paper showing good agreement between DSC and PET measurements of cerebral blood flow. However, the MR data had to be "calibrated" to absolute flow rates measured by PET, meaning that absolute quantification of CBF by DSC alone was not possible).
     Simonsen CZ, Østergaard L, Smith DF, et al. Comparison of gradient- and spin-echo imaging: CBF, CBV, and MTT measurements. J Magn Reson Imaging 2000; 12:411-416. (spin-echo techniques may be more accurate than GRE for quantification of microvascular flow)

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Related Questions
     What is meant by the relaxivity of a contrast agent? How is it measured?
     If gadolinium contrast is used to increase signal intensity on routine MR images, why does it decrease signal on DSC perfusion images?  

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