Uncertainty and bias in contrast concentration measurements using spoiled gradient echo pulse sequences

Abstract

Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) is a widely used technique for assessing tissue physiology. Spoiled gradient echo (SPGR) pulse sequences are one of the most common methods for acquisition of DCE-MRI data, providing high temporal and spatial resolution with strong T 1 -weighting. Conversion of SPGR signal to concentration is briefly reviewed, and a new closed-form expression for concentration measurement uncertainty for finite signal-to-noise ratio (SNR) and baseline scan time is derived. This result is applicable to arbitrary concentrationdependent relaxation rate and is valid over the same domain as the theoretical SPGR signal equation. Expressions for the lower and upper bounds on measurable concentration are also derived. The existence of a concentration-and tissue-dependent optimal flip angle that minimizes concentration uncertainty is demonstrated and it is shown that, for clinically relevant pulse sequence parameters, this optimal flip angle is significantly larger than the corresponding Ernst angle. Analysis of three pulse sequences from the DCE-MRI literature shows that optimization of flip angle using the methods discussed here leads to potential improvements of 10-1166% in effective SNR over the 0.5-5.0 mM concentration range with minimal or no loss of measurement accuracy down to 0.1 mM. In vivo data from three study patients provide further support for our theoretical expression for concentration measurement uncertainty, with predicted and experimental estimates agreeing to within ±30%. Equations for concentration bias resulting from biases in flip angle and from pre-contrast relaxation time and contrast relaxivity (both longitudinal and transverse) are also derived in closed-form. The resulting equations show the potential for significant contributions to bias in concentration measurement arising from even relatively small mis-specification of flip angle and/or pre-contrast longitudinal relaxation time, particularly at high contrast concentrations.

First order correction for T2*‐relaxation in determining contrast agent concentration from spoiled gradient echo pulse sequence signal intensity

“…[4] and [5], E 10 ¼ exp (ÀT R R 10 ) and E Ã 20 ¼ exp (ÀT E R Ã 20 ). E 2 * does not depend on R 20 *.…”

“…Given the pulse sequence settings T R , T E , and a, the CA relaxivities r 1 and r 2 , and the tissue of interests relaxation time T 10 , Eq. [4] can be solved numerically to yield the most accurate solution for the CA concentration C num . Further details can be found in (4), where it is shown that Eq.…”

“…[4] can be solved numerically to yield the most accurate solution for the CA concentration C num . Further details can be found in (4), where it is shown that Eq. [4] has two solutions.…”

“…Further details can be found in (4), where it is shown that Eq. [4] has two solutions. The selection of the appropriate solution is explained in the next section.…”

“…Many studies use spoiled gradient echo pulse (SPGRE) sequences for the monitoring of CA concentration, due to their excellent temporal and spatial resolution properties (3). However, conversion from signal intensity to CA concentration varies between different studies and has been acknowledged as an important error source in pharmacokinetic modeling (4). Several authors assumed a linear relationship between the relative signal enhancement and the CA concentration (2,5,6), which causes severe error in kinetic parameter estimation (7).…”