Impact of fitting algorithms on errors of parameter estimates in dynamic contrast-enhanced MRI

Area of Science:

• Medical Imaging
• Pharmacokinetics
• Computational Biology

Background:

• Dynamic contrast-enhanced MRI (DCE MRI) is crucial for analyzing tissue perfusion and vascularity.
• Parameter estimation in DCE MRI typically uses non-linear least square (NLLS) fitting of pharmacokinetic models.
• The two-compartment exchange model (2CXM) is a common pharmacokinetic model, representable by differential equations or a closed-form solution.

Purpose of the Study:

• To compare the accuracy, robustness, and computational speed of differential equation versus convolution-based solutions for the 2CXM in DCE MRI.
• To evaluate the impact of parameter combinations, arterial input functions, and temporal resolution on parameter estimation.
• To assess the real-world applicability of these methods using patient data.

Main Methods:

• Simulated DCE MRI concentration-time curves were generated for five tissue types and two arterial input functions at varying temporal resolutions.
• NLLS fitting was applied using both numeric integration (Runge-Kutta) and convolution methods to estimate 2CXM parameters.
• Prostate carcinoma and glioblastoma multiforme patient data were analyzed to validate findings.

Main Results:

• The convolution approach demonstrated superior precision, robustness, and computational speed (three orders of magnitude faster) compared to the differential equation method.
• Parameter estimation precision and stability were limited in cases of low blood flow.
• Decreased temporal resolution significantly impacted the accuracy of the differential equation approach, an effect not mitigated by the convolution method.
• The interstitial volume parameter (v_e) exhibited instability and low reliability across all tested scenarios.

Conclusions:

• The convolution method offers a more accurate, robust, and computationally efficient approach for DCE MRI parameter estimation using the 2CXM.
• The differential equation method is sensitive to temporal resolution, particularly at lower sampling rates.
• Careful consideration of temporal resolution and model parameter limitations (e.g., v_e) is essential for reliable DCE MRI analysis.