Dear Nmusers,
we have rich concentration data from tissues measured with MRI techniques.
>From other results, we know that the following model is a good
approximation of biology
|
C <> T1 <> T2
|
However, we cannot observe T1 and T2 directly, since these are mixed on
cellular level and our resolution in mm-range.
We only see the tissue-average of T1 and T2.
I assume that I have to tweak $ERROR to model the averaging. Could someone
point me to a similar example? I could not find an example on the list that
has a CMT in $ERROR.
Dieter Menne
How to model observed quantity tha is an average over compartments
Hi Dieter,
If you only onserve the average of two quantities you can never estimate the
individual contributions.
You must have some additional information to be able to do this.
Maybe if the time constants are apriori known to be very different, i.e. fast
and slow, then it might be
possible but you would need very rich data. Multiple fast and slow changes in
concentration.
As far as $ERROR is concerned it is quite easy to setup when you use A()
$ERROR
....
CT1=A(1)/V1 ;conc in tissue 1
CT2=A(2)/V2 ;conc in tissue 2
COBS=(CT1+CT2)/2 ;average in tissues
Y=COBS*(1+ERR(1)) ;Just guessing proportional error
...
Hope this helps,
Doug Eleveld
Quoted reply history
-----Original Message-----
From: [email protected] on behalf of Dieter Menne
Sent: Thu 7/29/2010 5:49 PM
To: [email protected]
Subject: [NMusers] How to model observed quantity tha is an average over
compartments
Dear Nmusers,
we have rich concentration data from tissues measured with MRI techniques.
From other results, we know that the following model is a good
approximation of biology
|
C <> T1 <> T2
|
However, we cannot observe T1 and T2 directly, since these are mixed on
cellular level and our resolution in mm-range.
We only see the tissue-average of T1 and T2.
I assume that I have to tweak $ERROR to model the averaging. Could someone
point me to a similar example? I could not find an example on the list that
has a CMT in $ERROR.
Dieter Menne
Thanks, both to Tarjinder and Doug.
The identifiability is a well known problem with (single fit) data of that
sort, and is mostly solved by making an extreme assumption for one of the
coeffs. We hope that the population fit can tweak additional information from
the very rich data (some 100 per set, but this needs long time). As a first
step, assuming that T2 is the only observed quantity gives an excellent fit,
so the mix-in is probably low.
Dieter
----
From: [email protected] [mailto:[email protected]] On
Behalf Of Eleveld, DJ
..
If you only observe the average of two quantities you can never estimate the
individual contributions.
You must have some additional information to be able to do this.
Maybe if the time constants are apriori known to be very different, i.e. fast
and slow, then it might be
possible but you would need very rich data. Multiple fast and slow changes in
concentration.
As far as $ERROR is concerned it is quite easy to setup when you use A()
$ERROR
....
CT1=A(1)/V1 ;conc in tissue 1
CT2=A(2)/V2 ;conc in tissue 2
COBS=(CT1+CT2)/2 ;average in tissues
Y=COBS*(1+ERR(1)) ;Just guessing proportional error
...
Hope this helps,
Doug Eleveld
Quoted reply history
-----Original Message-----
From: [email protected] on behalf of Dieter Menne
Sent: Thu 7/29/2010 5:49 PM
To: [email protected]
Subject: [NMusers] How to model observed quantity tha is an average over
compartments
Dear Nmusers,
we have rich concentration data from tissues measured with MRI techniques.
>From other results, we know that the following model is a good
approximation of biology
|
C <> T1 <> T2
|
However, we cannot observe T1 and T2 directly, since these are mixed on
cellular level and our resolution in mm-range.
We only see the tissue-average of T1 and T2.
I assume that I have to tweak $ERROR to model the averaging. Could someone
point me to a similar example? I could not find an example on the list that
has a CMT in $ERROR.
Dieter Menne
Dieter,
"As a first step, assuming that T2 is the only observed quantity gives
an excellent fit, so the mix-in is probably low."
Some questions:
What if you assumed that both tissues have the same time-constant,
wouldn't you also get an excellent fit?
Does that imply something different about mix-in?
What if T1 was the only observed quantity?
Don't let your reasoning be led by excellent fits alone, you need some
bad fits as well.
Model 1: Assume mix-in is low -> excellent fit
Model 2: Assume mix-in is high -> bad fit
Then you can infer based on your data that mix-in is probably low.
But if you have this:
Model 1: Assume mix-in is low -> excellent fit
Model 2: Assume mix-in is high -> excellent fit
Then you cant really say anything about mix-in.
An excellent fit in the case you sketch suggests that your observations
are not sufficient to differentiate the two-tissue system you described
from a one-tissue system. Then you cant differentiate anything about the
two tissues, purely based on the observations.
But if you bring in information from some other source about the
tissues, you might be able to make some inferences about the two
different tissues. This can be apriori or determined by some other
technique.
Doug Eleveld
-----Oorspronkelijk bericht-----
Quoted reply history
Van: Dieter Menne [mailto:[email protected]]
Verzonden: July 30, 2010 8:05 AM
Aan: Eleveld, DJ; [email protected]
Onderwerp: RE: [NMusers] How to model observed quantity tha is an
average over compartments
Thanks, both to Tarjinder and Doug.
The identifiability is a well known problem with (single fit) data of
that sort, and is mostly solved by making an extreme assumption for one
of the coeffs. We hope that the population fit can tweak additional
information from the very rich data (some 100 per set, but this needs
long time). As a first step, assuming that T2 is the only observed
quantity gives an excellent fit, so the mix-in is probably low.
Dieter
----
From: [email protected] [mailto:[email protected]]
On Behalf Of Eleveld, DJ ..
If you only observe the average of two quantities you can never estimate
the individual contributions.
You must have some additional information to be able to do this.
Maybe if the time constants are apriori known to be very different, i.e.
fast and slow, then it might be possible but you would need very rich
data. Multiple fast and slow changes in concentration.
As far as $ERROR is concerned it is quite easy to setup when you use A()
$ERROR
....
CT1=A(1)/V1 ;conc in tissue 1
CT2=A(2)/V2 ;conc in tissue 2
COBS=(CT1+CT2)/2 ;average in tissues
Y=COBS*(1+ERR(1)) ;Just guessing proportional error ...
Hope this helps,
Doug Eleveld
-----Original Message-----
From: [email protected] on behalf of Dieter Menne
Sent: Thu 7/29/2010 5:49 PM
To: [email protected]
Subject: [NMusers] How to model observed quantity tha is an average over
compartments
Dear Nmusers,
we have rich concentration data from tissues measured with MRI
techniques.
From other results, we know that the following model is a good
approximation of biology
|
C <> T1 <> T2
|
However, we cannot observe T1 and T2 directly, since these are mixed on
cellular level and our resolution in mm-range.
We only see the tissue-average of T1 and T2.
I assume that I have to tweak $ERROR to model the averaging. Could
someone point me to a similar example? I could not find an example on
the list that has a CMT in $ERROR.
Dieter Menne