Perfusion kinetics in human brain tumor with DCE-MRI derived model and CFD analysis
Introduction
Tumors are abnormal mass of tissues, which usually depend on other normal tissues for their nutritional needs. Tumors contain highly tortuous, fenestrated, discontinuous vessels and large vascular areas, making them highly heterogeneous (Jain, 1987). The pathophysiological state of tumor comprises of accumulated solid stress, abnormal and heterogeneous blood vessel networks, elevated IFP and a dense interstitial structure. This leads to transport barriers such as irregular perfusion, inadequate drug delivery, sporadic and uneven uptake. Further, these barriers cause heterogeneous extravasation of therapeutic agents into tumor tissues that may significantly limit the rate and extent of drug delivery to tumor (Jain et al., 2014, Narang and Varia, 2011). Since transport of macromolecular therapeutic agents in tumor microvasculature is vital for effective treatment of solid tumors, there is an imperative need to develop non-invasive approaches to understand and prevent various transport obstacles.
A number of mathematical models have been developed to study transport of drugs in tumor. Baxter and Jain used a homogeneous porous media model of both uniformly and non-uniformly perfused tumor to solve for interstitial fluid flow and solute transport parameters (Baxter and Jain, 1989, Baxter and Jain, 1990). Eikenberry used a tumor cord model to simulate the delivery of a chemotherapeutic drug to a solid tumor (Eikenberry, 2009). Pozrikidis modelled the tumor capillaries and evaluated blood and interstitial flow (Pozrikidis, 2010). Recently, computational fluid dynamics (CFD) approaches are increasingly being used to predict transport of macromolecules within tissues. For a homogenous tumor model, Soltani and Chen observed that IFP is less than the effective pressure below a certain tumor radius, and transport of chemotherapeutic drug to tumor site is easier (Soltani and Chen, 2011). Zhan et al. modelled heterogeneous vasculature of tumor and concluded that the drug accumulates faster in well vascularized regions and clears out from these regions quickly, resulting in less tumor cell killing (Zhan et al., 2014a). Pishko et al. modelled the tracer transport through a heterogeneous tumor tissue by using a non-voxelized approach (Pishko et al., 2011). Later, Magdoom et al. improved the model by using a voxelized approach that resulted in reduced computational time and increased accuracy (Magdoom et al., 2012).
However, existing studies have a number of limitations. Many of them assumed spherical shape and homogeneous vasculature of tumor, which is far from reality. Even studies employing heterogeneous vasculature of tumor have mainly focused on animal models, with Simple Tofts Kinetics Model used for the analysis of MRI data and the intravascular term ignored. Further, these models did not employ the patient specific AIF and AIF values were taken from literature (also called global AIF). This resulted in inaccurate determination of perfusion kinetic parameters and tracer concentration.
The objective of the present paper is to overcome these limitations by developing a computational model for the transport of contrast agent (tracer) in realistic human brain tumors. Realistic heterogeneous vasculature, permeability and porosity maps of the tumor are determined by analysing the DCE-MRI data. The computational model is employed to model tracer concentration along with IFP and IFV. Similar approach has been used by Magdoom et al. to model interstitial transport in mice. However, the current study introduces realistic heterogeneous human brain tumor and employs patient specific AIF to determine accurate perfusion kinetic parameters with the use of General Tracer Kinetic Model (GTKM). To the best of our knowledge, no study has reported the CFD analysis of realistic human brain tumors based on DCE-MRI data and patient specific AIF.
Section snippets
Methods
In this study, GTKM also called the Extended Tofts Model (Tofts, 1997, Tofts and Parker, 2013) has been used for analyzing DCE-MRI data. The obtained permeability and porosity maps were imported into the computational model developed in OpenFOAM, an open source CFD code, to solve for fluid flow parameters and tracer transport. GTKM model takes the blood volume fraction or intravascular term into account and is known to be more accurate for highly perfused tumors that is the case for humans due
Magnetic resonance imaging (MRI) protocol
DCE-MR imaging was performed on a 1.5-T GE scanner (Signa, Lx Echospeed plus; General Electric Medical Systems, Milwaukee, WI, USA). DCE-MR imaging was done for four patients. Written consent from each patient was obtained before MRI study. Out of those four patients, MR imaging of one patient was done for 14 min, whereas for others it was done for 4 min. DCE imaging was performed using a 3D-SPGR sequence (TR/TE = 5.0 ms/1.4 ms, flip angle = 15°, field of view (FOV) = 240 × 240 mm2, slice thickness = 6 mm,
Tissue transport model
The computational model for the transport of fluid and tracer through tissues is based on flow through porous media. Each point in this porous media transport model consists of vascular and tissue compartment. The governing equations of transport are mentioned in Eqs. (3), (4), (5). IFP is calculated by the continuity equation with added source and sink terms and is expressed aswhere
The first term on right hand side of Eq. (3)
Computational method
To reduce the computation time, only the tumor part and the surrounding normal tissue were taken as the computational domain. A rectangular volume of size 32 × 24 × 72 was created and meshed in a structured Cartesian grid as shown in Fig. 1. The voxel size was taken in accordance with the MRI resolution (0.9375 × 0.9375 × 6 ), maintaining complete analogy between MRI data and CFD model. Tracer kinetic parameters ( and transport properties present in Eqs. (3), (4), (5) of the tissue were
Results and discussion
Fig. 2 shows the pre-contrast and post-contrast images of brain of one slice at two different times. Local AIF (Fig. 2(d)) has been used for the patient in this study as it leads to calculation of accurate kinetic parameters. Permeability and porosity maps obtained from the MRI data are shown in Fig. 3. The porosity values highly depend on the type and grade of tumors. A number of studies have reported that high grade tumors have higher values of porosity as compared to low grade tumors (
Conclusion
A computational model based on MR imaging and governing equations of fluid mechanics was developed to study fluid flow and transport of contrast agent in three-dimensional heterogeneous realistic human brain tumor. The heterogeneous vasculature was determined on voxel scale by processing DCE-MRI data. A good agreement was found between simulated contrast agent concentration and those obtained using the experimental MRI data. Also, simulated IFP and IFV values correlated well with the
Conflict of interest statement
The authors declare that they have no competing interest.
Acknowledgements
The authors thank Dr. R.K. Gupta for providing clinical data and Prof. R.K.S. Rathore for technical support in DCE-MRI data analysis. This research was supported by grants from IIT Kanpur and Science and Engineering Research Board (Grant number: YSS/2014/000092).
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