Convolution Q: Ca(t) & R(t) for CT Attenuation Model

[JoeBonasia]

SORRY, I figured it was wrong of me to hijack someone elses thread with my query so I will start my own thread, my apologizes in advance for I will also post a thread within the Math forum...

I am new here and I bring a similar question for my first post...

I want to know how to do a convolution where the two functions are:

Ca(t) - arbitrary Input function
(it actually represents the time activity curve of a CT contrast bolus injection in the blood)

R(t) - a piecewise function defined as follows:

R(t) = 1, 0<t<Tm
and E*(exp)^(kt), t>Tm

(this R(t) is called the Impulse Residue Function for the Johnson WIlson model for capillary tracer exchange)

so therefore:

Ca(t)*R(t) = (from 0 to Tm){Ca(t) convolved with 1} + (from Tm to t)E*{Ca(t) convolved with (*exp)^(-kt)}

Can anyone shed some light on this please?!

If anyone is curious the context of this convolution is for determining the representation of CT tissue attenuation in tracer kinetics modelling, considering a distributive parameter model. A background link for those interested is below.

http://www.minervamedica.it/index2.t...9Y2003N03A0171

 

[jordan.nc]

do u want to do it manually or do u want to use a tool??

 

[JoeBonasia]

manual, hand solution..

btw I realized I typed a small error...

the second part of R(t) should read E*(exp)^(-k(t-Tm)), t>Tm

where t is the variable of integration and Tm is a constant