Deconvolution-Based CT and MR Brain Perfusion Measurement: Theoretical Model Revisited and Practical Implementation Details

Table 1

Summary of parameters used to derive the indicator-dilution theory and to define clinically relevant tissue perfusion quantities.

Variable	Unit	Description
𝑉voi	mL	Total volume under consideration
𝑉cap	mL	Volume of the capillary bed within the volume 𝑉voi
𝑉^∗voi	mL	Volume 𝑉voi without the volume of the capillary bed,𝑉^∗voi=𝑉voi−𝑉cap
𝜌voi	g/mL	Mean density of the volume 𝑉voi
𝜌^∗voi	g/mL	Mean density of the volume 𝑉^∗voi
𝑚c,voi(𝑡)	g	Total mass of contrast agent in volume 𝑉voi
𝑐art(𝑡)	g/mL	Local contrast agent concentration at the arterial inlet, 𝑐art(𝑡)=d𝑚/d𝑉|𝑡, measured at the arterial inlet
𝑐ven(𝑡)	g/mL	Local contrast agent concentration at the venous outlet,𝑐ven(𝑡)=d𝑚/d𝑉|𝑡, measured at the venous outlet
𝑐voi(𝑡)	g/mL	Average contrast agent concentration in the total volume 𝑉voi,𝑐voi(𝑡)=𝑚𝑐,voi(𝑡)/𝑉voi
𝑐cap(𝑡)	g/mL	Average contrast agent concentration in the capillary bed,𝑐cap(𝑡)=𝑚𝑐,voi(𝑡)/𝑉cap
𝑐^∗voi(𝑡)	g/mL	Average contrast agent concentration corresponding to 𝑉^∗voi, 𝑐^∗voi(𝑡)=𝑚𝑐,voi(𝑡)/𝑉^∗voi
𝐹	mL/s	Volume flow at the arterial inlet and at the venous outlet
ℎ(𝑡)	1/s	Probability density function of the transit times