Andrew J Fagan^{1}, Silvin P Knight^{2}, Matthew Clemence^{3}, and James F Meaney^{2}

The
effects of using a continuous golden-angle
radial k-space sampling trajectory,
with varying degrees of under-sampling and compressed
sensing image reconstruction, on the accuracy and precision of pharmacokinetic
modeling of DCE data, were quantitatively investigated. DCE image temporal resolutions (T_{res})
ranging from 1.85s to 0.09s
(corresponding to radial sampling densities of 100% to 4.68%) produced absolute
accuracy/precision errors in all K^{trans},
v_{e} and k_{ep} values of ≤ 2%/4% (for T_{res} =1.85s)
to ≤ 12%/11% (for T_{res}
=0.09s), respectively.
These results demonstrate that DCE image acquisition protocols can be
designed which constrain pharmacokinetic parameter value errors within
prescribed thresholds.

While an optimum temporal resolution (T_{res})
for dynamic contrast-enhanced (DCE) MRI remains elusive, it is clear that the
accurate measurement of fast-changing contrast time-intensity curve (CTC) shapes
in DCE requires short T_{res} values, particularly for measurements of
patient-specific arterial input function (AIF) used in pharmacokinetic (PK) modelling
on the data^{ [1]}. Compressed sensing (CS) techniques are highly
suited to DCE acquisitions, given the inherent sparsity in the temporal domain,
and thus they present an ideal solution to reducing T_{res} values.
However, to date no studies have investigated quantitatively the effect that
(vastly) undersampling the data has on the fidelity of measuring rapidly
changing CTC shapes, and hence on the consequent PK modelling outputs. Quantification of any effect requires a priori knowledge of the ground truth
CTC curve shapes, which are never known *in
vivo*. A recent study ^{[2]
}described a novel phantom design wherein ground truth values were unambiguously
known prior to MRI scanning, allowing for direct comparisons between the known
ground truth CTCs and those measured on the scanner. In this way, absolute errors as a function of
acquisition parameters could be determined.
The aim of this study was to quantify the accuracy and precision of
DCE-MRI measurements as a function of under-sampling ratio, for data acquired
using a continuous golden-angle radial k-space sampling trajectory using the
model phantom system.

1] Henderson E, Rutt BK, Lee TY. Temporal sampling requirements for the tracer kinetics modeling of breast disease. Magn Reson Imaging. 1998;16:1057-73.

[2] Knight SP, Browne JE, Meaney JF, Smith DS, Fagan AJ. A novel anthropomorphic flow phantom for the quantitative evaluation of prostate DCE-MRI acquisition techniques. Phys Med Biol. 2016;61:7466-83.

[3] Lustig M, Donoho D, Pauly JM. Sparse MRI: The application of compressed sensing for rapid MR imaging. Magn Reson Med. 2007;58:1182-95.

[4] Uecker M, Lai P, Murphy MJ, Virtue P, Elad M, Pauly JM, et al. ESPIRiT — An Eigenvalue Approach to Autocalibrating Parallel MRI: Where SENSE meets GRAPPA. Magn Reson Med. 2014;71:990-1001.