INTRODUCTION

Perfusion estimates from dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) or arterial spin labelling (ASL) have been proposed for diagnosis, prognosis and monitoring of disease progression and intervention.^1-5 Such perfusion estimations rely on black-box tracer-kinetic models^6-8 and may be vulnerable to systematic errors⁴ depending on the model assumptions and parameter choices. In this work, we present a computational fluid dynamics (CFD) framework for generating synthetic perfusion imaging data. The proposed model can act as a digital reference object with controlled ground-truth parameters. It can be used to study the effect of model assumptions and other processing steps such as, for instance, the effect of ROI placement.

METHODS

CFD model:
The proposed model is based on a coupling between components on various spatial scales. The observable vascular networks above 30-micron radius were described using graph model⁹ and the microvasculature was represented by a fractal network model. Both components were based on Poisseuille's law representing the vessel resistance. In addition, we assumed no leakage from the system. The pressure differences related to node $$$i$$$ can be written as
$$ \sum_{j \in N_i} R_{ij}\gamma \left(P_i-P_j\right) = q_i,$$
where $$$N_i, R_{ij}, \gamma$$$, and $$$q_i$$$ are the connected neighbour nodes to node $$$i$$$, the vessel resistance, the capillary resistance constant(1 for arteries and veins) and the inlet/outlet flow to the node $$$i$$$ (zero for inner nodes), respectively.

Contrast agent (CA) flow:
The contrast agent was assumed to move passively with the bloodstream obtained from the graph model. The CA influx into a small distribution volume $$$\Omega_k$$$ was defined by the product of CA concentration ($$$C_k$$$) and blood flow influx ($$$\textbf{q}_k$$$). It is equivalent to the CA change rate in the distribution volume $$$\Omega_k$$$
$$\frac{d}{dt}\int_{\partial \Omega_k}Cd\textbf{x} = -\frac{1}{\Omega_k} \int_{\partial \Omega_k}C_k (\textbf{q}_k \cdot \textbf{n}) d\textbf{x},$$
where index $$$k$$$ represents a segment in arteries, veins and capillaries. A bolus injection in the arterial root vessel was simulated using a gamma variate function,
$$C_{AIF}(t)=C_0(t - t_0)A.e^{-(t-t_0)/B}$$
for constants $$$t_0 = 6$$$s; $$$A = 3; B = 1; C_0 = 1$$$mM.¹⁰

Numerical experiments:
For illustration, the approach was used to build a CFD model based on a frog tongue vasculature segmentation (Figure 1). The blood circulation was obtained by solving the model based on equation (1). A synthetic perfusion series with a total acquisition time of 120s was generated using the steps outlined above.

The images were analyzed using four models: Maximum Slope (MS), One-compartment Model (1CM), two-compartment Uptake (2CUM) and Exchange Model (2CXM)^5-7 These models are commonly used for quantification of plasma flow (PF) and plasma volume (PV). Reconstructed values for these parameters were compared to the blood flow extracted from the ground truth data. Three different questions were addressed to illustrate the power of the approach: a comparison of analyses with local and global AIFs, a comparison of kinetic models, and an evaluation of the effect of ROI selection. Figure 1 shows the 11 ROIs used for this study.

RESULTS

Figure 2 shows that the CA propagation has the expected behaviour as it flows from the arterial network roots feeding the whole vasculature, spreads to the capillaries and is washed out through the veins. Figure 3 shows the CA signal, which reveals a short CA delay after bolus injection. In addition, four model fits: the MS fit describes the up-slope well; the other three model fits are almost identical.

Figure 4 shows the error in the PF values for each model with a local AIF. The MS model was systematically underestimating PF values. Both the 2C models and the 1C gave similar results for all ROIs, except in ROI 2. This is not unexpected since the model considers intravascular CA only and the kinetics is therefore essentially one-compartmental in nature. Figure 5 shows that the global AIF yields lower PF estimation, consistent with the effects of bolus dispersion.

PV estimation results from 2CXM and 2CUM with local AIFs were relatively accurate with the average error of 4% and 3.9%, respectively. The estimations were robust to AIF selection with the global AIF giving a slightly larger average error (4.7% and 4.4%).

DISCUSSION

We proposed a CFD-based framework to generate computational models of macrovascular and microvascular blood flow and tracer kinetics in a realistic vascular network. We hypothesized that this may provide synthetic ground truth data to compare different perfusion MRI modelling and analysis approaches. We explored the potential of this approach by application to a simple 2D example and by investigating well-known problems of kinetic model selection, AIF selection and ROI selection. We demonstrated that this produces data with the expected behaviour and results that are qualitatively in line with the current understanding of these issues. But unlike previous studies into model dependence, the setup does not rely on synthetic ground truth data that themselves are modelled using simplified black box models.

CONCLUSION

Preliminary experiments show that the proposed CFD framework provides suitable ground truth data that can be used to study the elusive problem of model bias in more depth than was previously possible. Future research will require more in-depth studies with fine-grained vascular networks and a more accurate simulation of key imaging features such as limited spatial resolution and partial volume effects.

Acknowledgements

No acknowledgement found.