This educational presentation gives an overview how to analyse data obtained from a Dynamic Contrast Enhanced (DCE) MRI experiment in order to retrieve perfusion and/or perfusion-related parameters.
Introduction
The capillary blood flow in tissue is also called perfusion. Since the blood carries oxygen and nutrition to the tissue through the capillaries, perfusion is important in maintaining tissue viability. There are several clinical applications for studying perfusion due to the changes in capillary blood flow associated with several neurological diseases. Diagnosis, lesion characterisation and follow-up of treatment in oncology, trauma, and dementia are examples where assessment of the level of perfusion is of value. By using dynamic MRI in combination with an exogenous contrast agent, perfusion and perfusion-related parameters can be obtained. One method that utilizes this is Dynamic Contrast Enhanced MRI (DCE-MRI).
Quantification of physiological parameters from contrast agent bolus tracking data is a two- step procedure. In the first step, the signal intensities are converted into contrast agent concentrations by employing MR signal theory. The second step aims to derive the relevant parameters from the time-resolved concentrations by means of tracer-kinetic theory.
Dynamic Contrast Enhanced MRI
The blood-brain-barrier effectively confines contrast agent molecules to the vascular compartment. In case of its disruption, contrast agent may distribute into the extravascular, extracellular space (EES). By injecting a contrast agent and dynamically follow the bolus, often with spoiled gradient echo sequences, information about the hemodynamics in the microvasculature can be obtained using DCE-MRI.
The presence of the contrast agent will create an increase of the longitudinal relaxation rate R1=1/T1. The concentration C is proportional to the change in longitudinal relaxation rate, i.e., C=(1/r1)×ΔR1, where r1 is the longitudinal relaxivity of the contrast agent.
By using curve-fitting approaches employed on the data the hemodynamic parameters can be extracted. Since a large number of unknown parameters might generate unreliable estimates it is common to include the effects of several physiological parameters into one parameter. The volume transfer constant Ktrans [s-1], reflecting the diffusive flux per unit volume of tissue (in mole s-1 m-3) between the blood plasma and the EES is such a combined parameter. The rate of tracer uptake in tissue (per unit volume of tissue) can be expressed as,
$$$\frac{dC_{t}}{dt}=K^{trans}(C_{p}-\frac{C_{t}}{v_{e}})$$$ [1]
where Ct is tissue tracer concentration, Cp tracer concentration in arterial blood plasma and ve is the fractional EES volume. The physiological interpretation of Ktrans depends on the relationship between capillary permeability and blood flow, F. For example, at high permeability, Ktrans represents the plasma blood flow (Ktrans=ρF(1-Hct) where ρ is the tissue density and Hct is the haematocrit), while in the other limiting case, when low permeability limits the tracer leakage, Ktrans reflects the permeability-surface area product (PS) (Ktrans=ρPS). However, PS = 0 is not compatible with Tofts model (Sourbron & Buckley 2011).
The differential equation in Eq. 1 has the following solution (if Cp = Ct = 0 at t = 0): $$$C_{t}(t)=K^{trans}\int_{0}^{t} C_{p}(\tau)e^{-\frac{K^{trans}}{v_{e}}(t-\tau)}d\tau$$$ [2]
The equation, Tofts model (Tofts 1997) (also known as the Kety (Kety 1951) or Larsson (Larsson et al. 1994) model), states that the measured dynamic change in tissue concentration is modelled as a convolution of an exponential kernel and arterial blood or plasma concentration curve (i.e. Arterial Input Function, AIF). If the blood volume cannot be neglected, a modified or extended Tofts model is applied by employing an additional term in Eq. 2, including the fractional plasma volume vp and the arterial plasma concentration over time (Tofts 1997):
$$$C_{t}(t)=v_{p}C_{p}(t)+K^{trans}\int_{0}^{t} C_{p}(\tau)e^{-\frac{K^{trans}}{v_{e}}(t-\tau)}d\tau$$$ [3]
Another model for retrieving perfusion and perfusion-related parameters is the two-compartment exchange model (Brix et al. 2004). There all four parameters F, PS, ve and vp, are retrieved. However this model requires data that will give reliable estimates of the four unknown parameters.
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