MATLAB Central Newsreader - need exponential growth function with features

need exponential growth function with features

Matthew — Thu, 05 Nov 2009 22:47:01 -0500

Hi,

I am trying to model the bolus delivery of a pharmeceutical. Theoretically, the delivery shold look like:

1-exp(-rate*abscissa);

However, we are actually delivering the bolus through a syringe with the plunger being pushed by a human, i.e., it is hardly constant. When I try to model the data, I get back a rate, but the fit doesn't seem to model the data very well. It tends to peak a little early, then last longer than it should.

I suspect that I need a model for the injection that has more detail associated with it. Is their a function that would produce an exponential growth with small oscillations in it that could be controlled by very few variables? I am trying to use fminsearch, and I don't want to have to search over a large number of parameters to get a decent fit, but I suspect only fitting the rate is insufficient.

Any ideas?

Thanks

Re: need exponential growth function with features

John D'Errico — Fri, 06 Nov 2009 00:04:01 -0500

"Matthew" <matthew.merritt.nospam@utsouthwestern.edu> wrote in message <hcvkl5$82f$1@fred.mathworks.com>...
> Hi,
>
> I am trying to model the bolus delivery of a pharmeceutical. Theoretically, the delivery shold look like:
>
> 1-exp(-rate*abscissa);
>
> However, we are actually delivering the bolus through a syringe with the plunger being pushed by a human, i.e., it is hardly constant. When I try to model the data, I get back a rate, but the fit doesn't seem to model the data very well. It tends to peak a little early, then last longer than it should.
>
> I suspect that I need a model for the injection that has more detail associated with it. Is their a function that would produce an exponential growth with small oscillations in it that could be controlled by very few variables? I am trying to use fminsearch, and I don't want to have to search over a large number of parameters to get a decent fit, but I suspect only fitting the rate is insufficient.
>
> Any ideas?

No, here are no SIMPLE functions that can handle
this class of model. So why not use something
a bit more generic? You can still compute an
effective (time varying) rate constant.

Use my SLM tools to build a spline model, that is a
monotone decreasing function. You can even force
it to go through the point (x,y) = (0,1) if you wish.

Once you have the function fit as a spline, you can
then use slmeval to evaluate both the spline and
its derivative at many points along the curve. Plot
the function f'(x)/(1-f(x)). This would be a local
effective rate.

HTH,
John

Re: need exponential growth function with features

John D'Errico — Fri, 06 Nov 2009 00:08:01 -0500

"John D'Errico" <woodchips@rochester.rr.com> wrote in message <hcvp5h$ato$1@fred.mathworks.com>...

> Use my SLM tools to build a spline model, that is a
> monotone decreasing function. You can even force

Sorry, I forgot to add a link to SLM:

http://www.mathworks.com/matlabcentral/fileexchange/24443

John