INTRODUCTION

PI-RADS_v2.1 recommends using multi-parametric MRI for the diagnosis and staging of prostate cancer (PCa)^[1]. Pharmacokinetic models, such as the standard Tofts model^[2], are widely used for quantitative analysis of dynamic contrast enhanced (DCE) MRI to extract physiological parameters (K^trans and v_e). However, due to lack of standardization, PI-RADS suggests that DCE-MRI only be analyzed qualitatively. Published literature has demonstrated that there is a large fluctuations of PCa K^trans values, mainly due to huge variations of arterial input functions (AIFs)^[3,4]. It is necessary to standardize physiological parameters for DCE-MRI by minimizing variations of AIFs, so that results can be reasonably compared between different patients and institutions.

In this study, we introduced a novel technique to modulate AIFs using the gluteal muscle as reference to reduce variations of measured AIFs. Prostate DCE-MRI was acquired with a split dose injection (30% and 70% of standard dose (30PSD and 70PSD)) of gadoterate meglumine (Dotarem, Guerbet LLC) so that two different AIFs could be obtained. The original AIFs and modulated AIFs were all used to analyze 70PSD DCE data and results of physiological parameters were compared between AIFs.

METHODS

Normally, physiological parameters (K^trans and v_e) are calculated from cancer and normal tissue of contrast agent concentration curve (C(t)) as function of time (t), using Tofts model:
$$C(t)=K^{trans}\int_{0}^{t}C_p(τ){\cdot}exp(-(t-τ)K^{trans}⁄v_e)dτ,-----(1)$$
where C_p(t) is AIF. Based on previous studies, it is reasonable to assume that the gluteal muscle of each patient has the same K^trans=0.1 (min^-1) and v_e=0.1^[5]. Therefore, for gluteal muscle C_m(t), there is a typical AIF (Ĉ_p(t)) such that:
$$C_m(t)=0.1\int_{0}^{t}C_p(τ)\exp(-(t-τ)0.1/0.1)dτ=0.1\int_{0}^{t}C_p(τ){\cdot}\exp(-(t-τ))dτ.-----(2)$$
Generally, AIF (C_p(t)) obtained from a blood vessel may not satisfy Eq. (2). A simple rational function (f_m(t)) was used to modulate C_p(t), so that $$$Ĉ_p(t)=f_m(t)·C_p(t)$$$, where
$$f_m(t)=\frac{η}{1+θ√t}+ε,-----(3)$$
η, θ≥0, and ε are constant and determined by fitting muscle C_m(t), i.e.:
$$C_m(t)=0.1\int_{0}^{t}(\frac{η}{1+θ√t}+ε){\cdot}C_p (τ)\exp(-(t-τ))dτ.-----(4)$$
In this way, modulated AIF (Ĉ_p(t)) was obtained. To minimize noise effects in the above calculations and to easily compare between AIFs, C_p(t) and Ĉ_p(t) were fitted by an empirical mathematical model (EMM)^[6]:
$$C_p(t)\ {or}\ Ĉ_p(t)=\tan^{-1}⁡(10t)\cdot[1+\sum_{n=1}^2A_n \exp(-(t-τ_n)^2/2σ_n^2)]{\cdot}B\cdot\exp(-βt),-----(5)$$
where A_n and B are scaling constants, τ_n and σ_n (n=1, 2) are the center and width of a Gaussian function, and β is the decay constant. Please note that 30PSD AIF was normalized to the injection dose by multiplying 0.70/0.30, so that it could be used to analyze 70PSD data.

Seventeen patients with biopsy-confirmed PCa were included in this IRB-approved study. MRI data was acquired on a Philips Achieva 3T-TX scanner without an endorectal coil. DCE 3D T1-FFE data was acquired pre- and post- injection of DOTAREM 0.03 mmol/kg (TR/TE=4.153/1.52 ms, FOV=200×200 mm², matrix size=224×224, flip angle=10°, slice thickness=3 mm, number of slices=24, SENSE factor=1.5, half scan factor=0.675) for 95 dynamic scans with a temporal resolution of 3.01 s/image. After two minutes, the DCE 3D protocol was repeated pre- and post- DOTAREM injection of 0.07 mmol/kg (TR/TE=6.115/1.52 ms) for 150 dynamic scans with a temporal resolution of 4.43 s/image.

Regions-of-interest (ROIs) for PCa (n=30) and normal tissue (n=45) in peripheral zone (PZ), transition zone (TZ), and central zone (CZ) were drawn on T2W images and transferred to DCE images. ROIs for blood vessels on the iliac artery and gluteal muscle were traced on DCE images. Average signal intensity as function of time was calculated for each ROI and used to calculate C(t) and C_p(t) using signal intensity model with literature values of T₁(blood)=1.70 s, T₁(prostate-tissue)=1.55 s, and T₁(muscle)=1.42 s at 3Tesla^[7].

One-way ANOVA Test was performed to examine differences for calculated parameters between cancer and normal tissue. The Bland-Altman analysis was performed to evaluate the agreement of physiological parameters obtained between 30PSD and 70PSD modulated AIFs.

RESULTS

Figure 1 shows six examples of AIFs, modulated AIFs and modulation functions obtained for 30PSD and 70PSD data. Figure 2 shows plots of calculated AIFs using average EMM fitting parameters given in the Table. It shows that modulated AIFs were much closer to each other than original AIFs. Figure 3 compares physiological parameter K^trans obtained between original and modulated AIFs from 30PSD and 70PSD. ANOVA tests shows that PCa K^trans is significantly (p<0.05) larger than normal tissue in PZ and CZ, but overlapped with normal tissue in TZ. There is no statistical difference for v_e between PCa and normal tissue (Fig. 4). Finally, Figure 5 shows scatter plots for all ROIs’ K^trans and v_e obtained between 30PSD and 70PSD modulated AIFs. Bland-Altman analysis showed a good agreement for physiological parameters calculated between modulated AIFs.

DISCUSSION

We developed and tested the use of rational function to modulate AIFs with gluteal muscle as reference on two types of AIFs. The fluctuations of physiological parameters obtained with modulated AIFs were much smaller and had better agreement than parameters obtained from original AIFs. Using gluteal muscle K^trans and v_e values, average K^trans(min^-1) calculated from modulated AIFs was approximately 0.70±0.40, 0.35±0.15, 0.60±0.30, and 0.30±0.15 for PCa, and normal tissue in PZ, TZ, and CZ, respectively.

CONCLUSION

By using modulated AIF, the fluctuations of physiological parameters for PCa and normal tissue were reduced significantly, and agreed well between different modulated AIFs. This would allow the physiological parameters to be easily compared between different patients and between different institutions.

References

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