Statistical Comparison of Commonly Used Kinetic Models for Dynamic Contrast Enhanced Magnetic Resonance Imaging of Rheumatoid Arthritis in the Wrist

Sameer Khanna^{1,2}, Nicolas Pannetier^{1}, Jing Liu^{1}, and Xiaojuan Li^{1}

Ten patients with RA (age 59.6±13.1 years, 8 female, DAS28-CRP: 4.0±2.0 and DAS28-ESR: 4.8±1.8 at baseline checkup) were scanned on a 3.0T MR scanner with an 8-ch phased array wrist coil in coronal view, 3D gradient-echo sequence with a pseudo-random variable-density under the sampling strategy CIRcular Cartesian UnderSampling (CIRCUS) technique (3). Images were reconstructed using combined parallel imaging and compressed sensing technique, k-t SPARSE-SENSE (4).

Arterial input functions were obtained from each patient's radial artery. Four types of ROIs were defined: normal bone marrow (NBM), bone marrow edema (BME), synovitis (SYN), and muscle (MUS). These ROIs were divided into two groups based upon their perfusion characteristics: high perfusion ROIs, consisting of BME and SYN, and low perfusion ROIs, consisting of NBM and MUS.

Reduced chi-squared ( $$$\chi^{2}_{red}$$$) was used to assess the goodness of fit due to the difference in the number of parameters used in each model. $$$\chi^{2}_{red}$$$ can be obtained via the following equation: $$$\chi^{2}_{red}=\frac{\chi^{2}}{\nu}=\frac{\sum \frac{(O-E)^{2}}{\sigma^{2}}}{\nu}$$$, where $$$\nu$$$ is the number of degrees of freedom, $$$\sigma^{2}$$$ is the known variance of the observation, and O – E refers to the difference of the model’s fit to the signal-time curves.

Statistically significant differences were evaluated via the Wilcoxon signed-rank test as we cannot assume normal distribution of chi values. The W test statistic is calculated by the following equation: $$$W = \sum_{i=1}^{N}[sgn(x_{2,i}-x_{1,i})\times R_i]$$$, where N is the sample size, $$$x_i$$$ is a measurement, and $$$R_i$$$ refers to a pair’s rank, determined by the absolute difference of the pair.

Only when a model indicates both statistical significance as well as lower $$$\chi^{2}_{red}$$$ values when compared to another model can it be declared superior for a particular ROI.

For BME and SYN (high perfusion ROIs), both 2CU and 2CX models indicate statistical significance when compared to MT (p < 0.05). 2CU and 2CX also have lower $$$\chi^{2}_{red}$$$ values than MT. No significant difference was found when comparing 2CU to 2CX data.

For MUS and NBM (low perfusion ROIs), 2CX and MT models indicate statistical significance when compared to 2CU. 2CU has lower $$$\chi^{2}_{red}$$$ values than both MT and 2CX. 2CX values also have statistical significance with those of MT. MT has lower $$$\chi^{2}_{red}$$$ values than 2CX.

As indicated by the lack of statistical significance between 2CU and 2CX for high perfusion ROIs, both models performed equally well for this ROI type. It is important to note that 2CU is a more simplified version of 2CX. With fewer parameters needed to calculate, 2CU can ran faster than 2CX. MT’s single transfer coefficient $$$k_{trans}$$$ is not robust enough to fit the data as well for high perfusion regions of interest. This is why MT underperforms when compared to 2CU and 2CX. It is clear that 2CU is the best model for high perfusion parameters in the wrist.

Regions of low perfusion have low efflux of plasma. 2CX performs worse for low perfusion ROIs due to complications introduced by the parameter vascular efflux. $$$K_{trans}$$$, a single-variable parameter that gives information about both influx as well as efflux, causes issues for low perfusion ROIs due to its oversimplified nature; MT performs poorly here as well. Since 2CU assumes that efflux is always near zero, 2CU is the only model to not run into serious issues for low perfusion ROIs. All models are statistically significant to one another, thus they can be ranked from best to worst: 2CU, MT, then 2CX.This study provides guidance for model selection for future studies. Identifying the optimal kinetic modeling technique will allow for more accurate and specific quantification of pathology, which has great potential to provide novel imaging markers for early diagnosis and treatment follow up for RA.

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2. Zierhut ML, Gardner JC, Spilker ME, Sharp JT, Vicini P. Kinetic modeling of contrast-enhanced MRI: an automated technique for assessing inflammation in the rheumatoid arthritis wrist Ann Biomed Eng. 2007;35(5):781-95.

3. Liu J, Saloner D. Accelerated MRI with CIRcular Cartesian UnderSampling (CIRCUS): a variable density Cartesian sampling strategy for compressed sensing and parallel imaging. Quantitative imaging in medicine and surgery. 2014;4(1):57-67.

4. Feng L, Srichai MB, Lim RP, Harrison A, King W, Adluru G, Dibella EV, Sodickson DK, Otazo R, Kim D. Highly accelerated real-time cardiac cine MRI using k-t SPARSE-SENSE. Magn Reson Med. 2013;70(1):64-74.

Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)

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