12 Apr
2010
12 Apr
'10
11:21 a.m.
Hi Max,
First of all, thanks a lot for your comments.
Some quick answers to your questions. This results are obtained with
the first version of the simulator which only models Brownian motion,
no collision among molecules, and also an infinite space. Now we have a
second version of the simulator which models a limited space and the
collision among molecules.
The transmitted and the received are modeled as a spherical volume of
R=100nm. we are modeling also particles of r=0.2nm (calcium ions) and
the cytoplasm diffusion coefficient 1000nm2/ns.
The negative peak you mentioned from the graph "arriving time maximum
molecule concentration" appears in the receiver located at 1750nm, but
the problem is in the measured data from the previous receiver (a
positive peak). Looking at the concentration from the receiver located
at 1500nm has a peak which does not fit with the shape of the signal,
due to the particle counting noise. This problem is becouse the results
are from 10 receivers but not in average.
The transfer function is obtained with an only receiver.
According to the correlation time you mentioned we will try to decrease
the counting particle noise averaging the measures withing this time.
We will send you more accurate results.
Nora
Hi All,
Since we had some problems to schedule the meeting today, I will write down
some comments I had on the results you obtained from the first version on
the simulator. The we can discuss further in the next meeting... in the
meantime you can prepare questions for me too ;-)
First of all I would like to know if the result of the 10 different
receivers is averaged at the end. I think so, right?
Then, can you summarize here the formulas (or algorithms) you used on the
simulations? You are only simulating the Brownian motion here and not the
collisions between molecules... right?
I can notice a delay in the concentration peak from Rx placed at 1000nm
on... this is in fact a confirmation that there is a delay in the
propagation and this is not possible to result from the solution of Fick's
laws but only either from a simulation of the Brownian motion
(nano-simulation) or from the solution of the Telegraph's equation from the
relativistic diffusion theory. Actually the Telegraph equation should
approach this behavior but at the same time I'm not expecting that it will
model perfectly this delay behavior... as always in physics... the math is
only an approximation of the real behavior, and the relativistic theory is a
"first approximation" of the delay in the diffusion process...
I see there are many fluctuation in the signal and this partly explains what
I'm studying right now: the particle counting noise, which is caused by the
fluctuation in the number of particles going back and forth in and out from
the volume of the receiver... how big is the volume you're using to count
the molecules? This is an important parameter... I assume it is spherical
with a given radius. Well, according to the analysis I did, the power of the
particle counting noise should have inverse proportionality with respect to
this radius... is could be extremely interesting to test this behavior.
I've also analyzed how to cut down the power of the particle counting noise
without having a big received: it looks like the diffusion process has a
sort of correlation time, beyond which we can consider two concentration
measures as independent. If this correlation time, which happens to be equal
to the radius of the receiver volume squared and divided by the diffusion
coefficient, is enough lower than the inverse of the bandwidth of the
system, then we can do multiple measures of the same concentration value
(and consider the concentration quasi-constant) and have a mean value
estimator of the concentration which is less noisy.
From the graph concerning the "arriving time maximum molecule concentration"
the "negative" peak at approx 1750nm is quite interesting... we should
investigate more on why this is happening... I'll think about it too...
The channel transfer function shows a low-pass behavior with some
fluctuations on the top. Are these fluctuations spaced in some regular way?
Like following certain harmonics or a fixed law in frequency? Is the first
graph you show the impulse response at 1micron? How many receivers are there
in this computations? 1 or 10 like before?
When you shift the FFT could you also shift the frequency values having the
zero in the middle of the graph?
So far these are my comments, but I think we can discuss further about these
interesting results and brainstorm a bit on how to proceed.
Thanks a lot and sorry for the delay... many things are going on at the same
time for all of us and I wanted to make this comments without time pressure
;-)
Please, let me know your answers to my comments, as well as any remarks you
have on my explanations.
Max
-----Original Message-----
From: n3-tech-bounces(a)n3cat.upc.edu [mailto:n3-tech-bounces@n3cat.upc.edu]
On Behalf Of garralda(a)ac.upc.edu
Sent: Tuesday, March 23, 2010 3:46 PM
To: n3-tech(a)n3cat.upc.edu
Subject: [N3-tech] simulator results
hello everybody, these are some results obtained using the first version of
the simulator. The pdf contains the graphics we told you (Massimiliano).
if anyone has some data about realistic values for the amount of transmitted
molecules (transmitted power) or any other comment i would appreciate it.
Regards
Nora