A finite element based optimization algorithm to include diffusion into the analysis of DCE-MRI

Abstract

Pharmacokinetic (PK) models are used to extract physiological information from dynamic contrast enhanced magnetic resonance imaging (DCE-MRI) sequences. Some of the most common models employed in clinical practice, such as the standard Tofts model (STM) or the extended Tofts model (ETM), do not account for passive delivery of contrast agent (CA) through diffusion. In this work, we introduce a diffusive term based on the concept of effective diffusivity into a finite element (FE) implementation of the ETM formulation, obtaining a new formulation for the diffusion-corrected ETM (D-ETM). A gradient-based optimization algorithm is developed to characterize the vascular properties of the tumour from the CA concentration curves obtained from imaging clinical data. To test the potential of our approach, several theoretical distributions of CA concentration are generated on a benchmark problem and a real tumour geometry. The vascular properties used to generate these distributions are estimated from an inverse analysis based on both the ETM and the D-ETM approaches. The outcome of these analyses shows the limitations of the ETM to retrieve accurate parameters in the presence of diffusion. The ETM returns smoothed distributions of vascular properties, reaching unphysical values in some of them, while the D-ETM accurately depicted the heterogeneity of KTrans, v$$_{e}$$ e and v$$_{p}$$ p distributions (mean absolute relative difference (ARD) of 16%, 15% and 9%, respectively, for the real geometry case) keeping all their values within their physiological ranges, outperforming the ETM.

Current status in spatiotemporal analysis of contrast‐based perfusion MRI

“…Sainz‐DeMena et al 59 report a two‐compartment system with interstitial diffusion and a vascular input. This model applies a diffusion coefficient, $$$ D $$$, which acts on the total tissue concentration.…”

“…Sainz‐DeMena et al 59 reduce the computational complexity of the inverse problem by considering 2D systems only, and assuming $$$ D $$$ everywhere is a constant known parameter. Minimization was implemented using a Trust Region Reflective algorithm, which handles sparse matrices efficiently.…”

Model discovery approach enables non-invasive measurement of intra-tumoral fluid transport in dynamic MRI

“…Existing data processing approaches for physical interpretation of contrast enhancement data from DCE-MRI use ordinary differential equation (ODE) models applied to individual voxels, though this method largely fails to incorporate the rich spatial data provided by the modality (18). Few methods exist for quantifying the spatially varying effective diffusion coefficient of contrast agent in DCE-MRI (19,20), and similarly few attempt to quantify and investigate interstitial fluid flow (i.e. advection) within the tumor (21)(22)(23).…”

Special Issue: Imaging-based methods in computational medicine

“…Inverse problems, to identify parameters with physical or mechanistic interpretation, is another open area of research that relies on combining imaging data and physics-based modeling. For example, MR imaging can be used to infer properties of tissue, such as transport parameters of tumors, which is needed to determine if drugs are having an effect or not on reducing tumor growth [11]. Another inverse problem showcased in this collection is the identification of activation maps of the heart, with implications for intervention This inverse problem is highly sensitive to patient specific geometries and heterogeneous parameter distributions, requiring new methods as shown in Ruiz Herrera et al [10].…”

“…The musculoskeletal system is the focus of Tajdari et al [15], who created personalized models of spine growth in scoliosis, and that of Crutison and Royston [3], who obtained material parameters from different MR imaging modalities on muscles. Meanwhile, skin [8] and tumors are also studied [7,11].…”