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

Table 1 Model equations

Model	Fitted parameters	Fitting domain	Tissue impulse response R
Distributed parameter	Myocardial blood flow, T, T_c, T_e	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, τ_0, k	Time	\( R(t)=\frac{1}{ \exp \left[\left(t-{\tau}_0\right)\cdot k\right]+1} \)

Fitted parameters for distributed parameter: myocardial blood flow, T is mean overall transit time, T_c is mean capillary transit time, T_e is mean interstitial (i.e. extravascular-extracellular) transit time. Where s = i ⋅ 2 ⋅ π ⋅ f 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.

ISSN: 1532-429X