Introduction

Drug transport to solid tumors has been shown to be limited [1]. The transport of therapeutic agents to the tumor stroma relies on two mechanisms: convection (dependent on pressure gradients) and diffusion (dependent on concentration gradients) [1, 2]. While convective transport is often hindered by elevated interstitial fluid pressure (IFP) within the tumor, diffusive transport remains the predominant positive transport pathway, but it is both limited and slow, resulting in inadequate drug delivery [2]. The biophysics of drug transport has been extensively reviewed, with the permeability and density of tumor vasculature identified as critical factors controlling IFP [2]. However, patient-specific studies of tumor vasculature properties have been largely lacking due to challenges in addressing both inter- and intra-tumoral heterogeneity. In this context, we utilize dynamic contrast-enhanced MRI (DCE-MRI) as a powerful tool to evaluate tumor vasculature, aiming to construct digital twins of solid tumors.

Methods

Data acquisition
In the context of a translational clinical study (EC/2019/1330, approved by the local ethical committee), we conducted imaging on a patient with peritoneal metastasis using a 3T clinical MR system (PrismaFit, Siemens Healthineers, Germany). The MR imaging protocol encompassed various sequences, including coronal respiratory triggering fat-suppressed HASTE T2-weighted imaging, 3D-T2 weighted coronal SPACE imaging with and without fat-suppression, and transversal 3D gradient echo (3D-GRE) volumetric interpolated breath-hold examination (VIBE) T1-weighted imaging. Additionally, axial breath-hold 3D GRE VIBE T1-weighted imaging was performed without the administration of a contrast agent to establish the anatomical location of the tumor. Finally, a transversal free-breathing prototype 3D GRASP-VIBE dynamic contrast-enhanced scan sequence was continuously acquired [3], achieving an offline-reconstructed temporal resolution of 1.4 seconds. This was done after the intravenous administration of 0.1 mmol/kg of Prohance contrast agent, followed by a 20 ml saline flush at a rate of 2.0 ml/s.
Data analysis
We utilized the open-source software, Quantiphyse [4], for image analysis. Groupwise registration was employed for image motion correction and co-registration [5]. Subsequently, the DCE-MRI data was quantified using the extended-Tofts model [6] to generate the volume transfer constant (K^trans) map. Furthermore, the arterial input function (AIF) was determined from the abdominal aorta, accounting for any bolus arrival delay. The tumor contours were delineated by an experienced radiologist, and based on these contours, the 3D geometry of the tumor was reconstructed.
Computational fluid dynamics (CFD) modeling of IFP
Using the reconstructed 3D geometry, interstitial fluid flow within the tumor was simulated using CFD modeling in COMSOL Multiphysics (Inc., Burlington, USA). The tumor was situated within a normal peripheral region, where the interstitial flow is governed by Darcy’s law (Eq. 1) and the continuity equation. Starling’s law (Eq. 2) is employed to express the interstitial fluid source. Within this framework, the K^trans map was incorporated to address microvascular permeability (L_P) and density (S/V) heterogeneities. It was assumed that no lymphatic vessels were present within the tumor, and the interstitial fluid pressure (IFP) at the boundary of normal tissue, far from the tumor, was set to 0 mmHg (representing normal IFP).
$$u_i=-K\triangledown p_i\hspace{1cm}(Eq.1)\\ \nabla.u_i=L_p\frac{S}{V}(p_v-p_i-\sigma(\pi_v- \pi_i)), L_p=\frac{K^{trans}}{\overline{K^{trans}}}L_{p0}\hspace{1cm}(Eq.2)$$
With p_i the IFP, u_i the interstitial fluid velocity (IFV), S/V the surface area per unit volume, p_v the vascular pressure, σ the osmotic reflection coefficient, π_v the vascular osmotic pressure and π_i the interstitial osmotic pressure [2]. L_p0 is the baseline value for vascular permeability. To enable the evaluation of image-based data effects, a corresponding basic model was generated using the same geometry, but with a uniform value assigned for L_P (i.e. L_p0).

Results

The 3D configuration of the tumor is depicted in Figure 1, with a volume of 27746 mm³. The findings illustrated in Figures 2a and 2b reveal an elevated region of IFP within the tumor. This observation can be correlated with the non-enhancing region depicted in Figure 1. Upon comparing the outcomes of the baseline model (Figure 2c) with the personalized model (Figure 2b), it is apparent that in the basic model, IFP is almost uniformly distributed throughout the tumor, except near the tumor's surface where it rapidly decreases to the normal tissue IFP. In contrast, when incorporating K^trans data, the IFP exhibits greater heterogeneity, particularly at the outer layers of the tumor (Figure 2b).

Discussion and conclusion

An image-based CFD model highlighted the variability in IFP within a solid tumor. The current study, pivotal in creating personalized computational models, gains advantage from enhancements with complex mathematical models and additional patient-specific data. The current study holds the potential to introduce a novel diagnostic tool in clinical oncology.

Acknowledgements

No acknowledgement found.