Skip to main content

Table 1 Model equations

From: Measurement of myocardial blood flow by cardiovascular magnetic resonance perfusion: comparison of distributed parameter and Fermi models with single and dual bolus

Model Fitted parameters Fitting domain Tissue impulse response R
Distributed parameter Myocardial blood flow, T, Tc, Te Laplace \( R(s)=\frac{1- \exp \left[-s\cdot \left(T+s\cdot {T}_c\cdot {T}_e\right)/\left(1+s\cdot {T}_e\right)\right]}{s} \)
Fermi Myocardial blood flow, τ0, k Time \( R(t)=\frac{1}{ \exp \left[\left(t-{\tau}_0\right)\cdot k\right]+1} \)
  1. Fitted parameters for distributed parameter: myocardial blood flow, T is mean overall transit time, Tc is mean capillary transit time, Te is mean interstitial (i.e. extravascular-extracellular) transit time. Where s = i 2 πf and f is the frequency variable in the Fourier transformed data. Fitted parameters for Fermi: myocardial blood flow, τ0 characterized the width of the shoulder of the Fermi function and k determined the decay rate of R(t) due to contrast agent wash-out. t is the time variable.