CONFERENCES - CONFERENCIAS - CONFÊRENCIAS

El Nov 16, 2001 7:55 am, Douglas McLean dijo:

As the author, I'd like to apologise for not having
included my email address in my conference.

I can be contacted at:

d.mclean@cmcsm.ac.uk

Douglas.

El Nov 16, 2001 8:02 am, Douglas McLean dijo:

Addendum:

Equation (11) in Part II of the conference should read:

A(t) = sum_{i=1}^n(t) [ g_0 + g(t) ]^2

and not as printed (with an additional term -n_0 g_0^2).

Douglas McLean
(author).

El Nov 17, 2001 3:14 pm, María dijo:

ypu are right that tha mathematical modelling in medicine is at an embryonic stage.

But I'm surprised by "that the rate of change of nephrons was independent of the disease process."
Could you explain any more the experiment you have done ?

Thanks!

El Nov 19, 2001 8:54 am, Douglas McLean dijo:

Maria:

Thanks for your comment! When I mentioned that the rate of
change of nephrons was independent of the disease process,
I was commenting on the mathematical model of Chaturvedi &
Insana (1997) [CI97]. It is my belief that the rate of
change of nephrons is implicitly linked to the disease
process.

CI97 model a population of healthy nephrons as a decreasing
exponential function of time whilst modelling the inter-
play between sclerosis index and hypertrophy entirely
separately. In this way, the disease process for a single
nephron cannot influence the global disease process for a
kidney (i.e. the population of nephrons). Additionally,
CI97 do not accomodate the fact that a diseased nephron
will still filtrate until it becomes too sclerosed.

In my model, an initial insult will bring some nephrons
onto a disease course. Those nephrons must ultrafiltrate
and will eventually become completely sclerosed. Now, the
body must maintain a healthy glomerular filtration rate,
GFR, and the only way to do this is to have a large enough
surface area for filtration. The body must hypertrophy just
enough nephrons so that it can maintain the GFR. But
nephrons on a disease path will themselves become too
sclerosed to participate in filtration. Eventually, too
many nephrons are sclerosed to maintain sufficient renal
function and renal failure occurs.

My model is purely mathematical at present. However, it
should not be too difficult to test it in the way that CI97
have done with their model.

I hope this helps. Please ask me more questions and/or
give me more comments! Thanks,

Douglas.

Discussion on-line

[21:51] *** DMcLean (webchat@useraw83.uk.uudial.com) has joined #cin

[22:15] (Speaker> Mathematical Modelling and Simulation of Biological Systems in Renal Transplantation and Renal Disease

[22:16] (Speaker> DR DOUGLAS R MCLEAN, Scotland

[22:16] (Speaker> Here, I discuss two different approaches to mathematical modelling in renal research. Part I discusses the development of a discrete event simulation along with some results related to the outcome, in terms of patient numbers, associated with cardiovascular risk. The model is based on a retrospective study of renal graft patients> attending treatment at the Western Infirmary Renal Unit in Glasgow, Scotland. Part II discusses mathematical models of progressive renal disease.

[22:16] (Speaker> To date, the literature on such models is scarce. However, one such ..................................
[22:17] (Speaker> ........................
[22:17] (Speaker> ........................
[22:18] (Speaker> ........................

Text in ../../../../cin2001/conf/mclean/index.html

[22:22] (Speaker> ...... Mathematicians should take heart from the fact that problems arising in medicine are very challenging and the clinicians should try to reap the rewards that mathematical modelling can offer. It must be a happy partnership.

[22:22] (Speaker> thanks!

[22:22] (MJesus> plas plas plas plas plas plas plas plas plas plas
[22:22] (MJesus> plas plas plas plas plas plas plas plas plas plas
[22:22] (MJesus> plas plas plas plas plas plas plas plas plas plas
[22:22] (MJesus> plas plas plas plas plas plas plas plas plas plas
[22:23] (Oroz> plas :)

[22:23] (DMcLean1> Thank you

[22:24] (MJesus> it is too difficult the math for any doctor dr. mclean

[22:25] (MJesus> comments ?

[22:26] (DMcLean11> Sorry if the maths is too, hard.

[22:26] (DMcLean11> Would you like a *short* run thru of the work?

[22:26] (MJesus> yes.. if it possible

[22:26] (DMcLean11> I discuss 2 different models

[22:27] (DMcLean11> One is more statistical

[22:27] (DMcLean11> the other more mathematical

[22:27] (DMcLean11> but it is not too hard to explain

[22:27] (DMcLean11> In part I, I have developped a

[22:27] (gtorres> the art of the medicine is lost with the matematicas?

[22:27] (DMcLean11> discrete event simulation

[22:27] (DMcLean11> Hello!

[22:27] (DMcLean11> I don't believe so

[22:28] (DMcLean11> Anyway, medicine is fast becoming scientific! Not so?

[22:28] (MJesus> hummmm scientific .. yes

[22:28] (gtorres> yes .....

[22:28] (DMcLean11> I'll 1st talk about the discrete event simulation

[22:29] (DMcLean11> I have been working in

[22:29] (DMcLean11> collaboration with the

[22:29] (DMcLean11> Western Infirmary Renal Unit

[22:29] (DMcLean11> in Glasgow, Scotland

[22:29] (DMcLean11> My principal collaborator is Dr Alan Jardine

[22:29] (DMcLean11> Does anyone know him?

[22:29] (DMcLean11> Basically, Alan approached my centre

[22:29] (DMcLean11> (a centre for maths in medicine

[22:29] (MJesus> I have heard about Dr,. Jardim

[22:30] (DMcLean11> based in Glasgow Uni)

[22:30] (DMcLean11> Alan says he's heard of you too, Maria!

[22:30] (DMcLean11> So, Alan approached my centre for some

[22:30] (DMcLean11> maths help.

[22:30] (DMcLean11> He wanted something more than the usual stats

[22:31] (DMcLean11> stuff that is used so much in medicine

[22:31] (zafra> what clinical aplications can we infer from your model?

[22:31] (DMcLean11> You know, test and hypothesis - T- F-tests etc

[22:31] (DMcLean11> Clinical Appls

[22:31] (DMcLean11> Yes

[22:31] (DMcLean11> The simulation model aims to predict

[22:32] (DMcLean11> what the effects will be

[22:32] (DMcLean11> of new strategies aimed at

[22:32] (DMcLean11> reducing cardiovascular risk.

[22:32] (DMcLean11> For example

[22:32] (DMcLean11> Suppose that in the next 20 or so years

[22:32] (DMcLean11> (in the next "professional lifetime of a renal unit")

[22:32] (MJesus> aja...

[22:33] (DMcLean11> that immunosuppresant drugs

[22:33] (DMcLean11> improved the rate of acute rejection episodes

[22:33] (DMcLean11> Suppose that

[22:33] (DMcLean11> Then what would be the eventual benefits to

[22:33] (DMcLean11> the UK (or any other) health service?

[22:33] (DMcLean11> In other words

[22:33] (DMcLean11> Acute rejection rate goes down

[22:34] (DMcLean11> More people are alive with a functioning renal graft

[22:34] (DMcLean11> less people are on haemodialysis

[22:34] (DMcLean11> so it costs the health service less

[22:34] (DMcLean11> There are other risk factors too...

[22:35] (DMcLean11> eg diabetes, smoking, ischaemia, ...

[22:35] (DMcLean11> Progression of medical science

[22:35] (DMcLean11> would indicate that we will be able to reduce these rates

[22:35] (DMcLean11> Thus, how do we quantify

[22:35] (DMcLean11> (1) the number of patients alive on the waiting list

[22:36] (DMcLean11> (2) the # of patients alive on the grafted list

[22:36] (DMcLean11> (3) the graft failure rates and patient death rates

[22:36] (DMcLean11> Go on! How do we do that?

[22:36] (DMcLean11> This is the essence

[22:36] (DMcLean11> of my work with Alan Jardine at the Renal Unit in Glasgow

[22:36] (DMcLean11> Any questions thus far?

[22:37] (zafra> if I understand well, your model proposes a kind of "punishment" to smokers; it is true? or it is only they have worse life expectancy

[22:37] (DMcLean11> No, it is not punishment!

[22:37] (DMcLean11> The model asked various questions

[22:38] (DMcLean11> about "how many people alive if?" scenarios

[22:38] (DMcLean11> In my model

[22:38] (DMcLean11> I supposed that in the future there might be

[22:38] (DMcLean11> say, 50% less smokers around in

[22:38] (DMcLean11> the population as a whole

[22:38] (DMcLean11> So, then I am in a position to project what numbers

[22:39] (DMcLean11> will there be on

[22:39] (DMcLean11> the patient waiting list and

[22:39] (DMcLean11> on the grafted list

[22:39] (DMcLean11> Perhaps I should explain the model a little bit

[22:39] (DMcLean11> The Renal Unit has performed a retrospective study

[22:40] (DMcLean11> into the prevalence of cardiovascular risk

[22:40] (DMcLean11> on renal transplantation

[22:40] (DMcLean11> For a follow-up period

[22:40] (DMcLean11> of around 20 years

[22:40] (DMcLean11> they have survivial data and CV risk factors

[22:40] (gtorres> I know that Dr zafra and me are in favour punishing smokers...

[22:40] (DMcLean11> (CV = cardiovascular)

[22:41] (DMcLean11> Oh yes? I was in Madrid this year

[22:41] (DMcLean11> they smoke quite a bit in Spain

[22:41] (DMcLean11> (more than in Scotland, perhaps! :-)

[22:41] (zafra> it is true

[22:41] (DMcLean11> Ok

[22:42] (DMcLean11> So, the renal unit has 434 complete records

[22:42] (DMcLean11> It has survivor functions too

[22:42] (DMcLean11> Cox prop hazards model survivor functions

[22:42] (DMcLean11> for the risk factors (like smoking!)

[22:42] (DMcLean11> They have two survivor functions:

[22:43] (DMcLean11> one for patient survival and

[22:43] (DMcLean11> one for graft survival

[22:43] (DMcLean11> with various censoring techniques employed

[22:43] (DMcLean11> when a patient dies with a functioning graft for example

[22:43] (DMcLean11> So, we have 434 records and survival curves

[22:43] (DMcLean11> We can use these to drive

[22:44] (DMcLean11> a simulation

[22:44] (DMcLean11> in "pseudo-time" / real time

[22:44] (DMcLean11> to see how many patients will be alive

[22:44] (DMcLean11> as a time series

[22:44] (DMcLean11> Is everyone ok?

[22:44] (zafra> do you consider necessary to have unless a renal biposy to applie your model on crhonic renal failure porgression? or it is not necessary

[22:45] (DMcLean11> I'm not sure what you mean

[22:45] (DMcLean11> I'm losing the connexion

[22:46] (DMcLean11> Can you explain more, Dr Zafra

[22:46] (zafra> if we need a biopsie

[22:47] (zafra> in order to count glomerular sclerosis

[22:47] (zafra> or health glomerulous

[22:48] (DMcLean11> As far as I understand, this is not taken into account

[22:48] (DMcLean11> I speak about my patient numbers simulation

[22:48] (DMcLean11> not about the progressive model

[22:48] (DMcLean11> progressive renal disease model

[22:48] (DMcLean11> I'm talking about the quantification of patient numbers

[22:49] (DMcLean11> following a 20 yr follow up study

[22:49] (DMcLean11> with CV risk factors tabulated for each patient

[22:49] (gtorres> models of the creatinine? are good predicting of the renal progression ?

[22:50] (DMcLean11> Would you rather I spoke solely about my renal

[22:50] (DMcLean11> disease model?

[22:50] (din> thanks a lot...

[22:50] (gtorres> excuse me

[22:51] (RRobles> So that, this model is useful just for wide population trends. Can it be used to predict individual evolution?

[22:51] (DMcLean11> OK

[22:51] (DMcLean11> The 1st model is statistical for wide pop'n trends

[22:52] (DMcLean11> The 2nd model is for predicting the time course

[22:52] (DMcLean11> of progressive renal disease

[22:52] (DMcLean11> My article is split into 2 distinct sections - separate

[22:52] (DMcLean11> So, in the 2nd model

[22:52] (DMcLean11> I have developed a system

[22:53] (DMcLean11> of differential equations which

[22:53] (DMcLean11> describe the disease course of

[22:53] (DMcLean11> an individual nephron

[22:53] (DMcLean11> I then use an idea from the GFR

[22:53] (DMcLean11> glomer'l filt'n rate

[22:53] (DMcLean11> to build a model of a kidney

[22:54] (DMcLean11> The idea for the disease model is this:

[22:54] (DMcLean11> I define what is known as the sclerosis index "s"

[22:54] (DMcLean11> for an individual nephron.

[22:55] (DMcLean11> I am following on from and improving a similar model

[22:55] (DMcLean11> that has been published by Chaturvedi and Insana (1997)

[22:56] (DMcLean11> They model the nature of progressive renal disease

[22:56] (DMcLean11> for a subtotal nephrectomy rat model

[22:56] (DMcLean11> in terms of the sclerosis index "s" and

[22:56] (DMcLean11> in terms of the glomerular hypertrophy "g"

[22:57] (DMcLean11> They have based their maths model on an experimental

[22:57] (DMcLean11> rat model done by Yoshida et al (1989).

[22:58] (DMcLean11> Yoshida was able to measure the degree of sclerosis

[22:58] (DMcLean11> and the amount of hypertrophy for many nephrons

[22:58] (DMcLean11> in various diseased states.

[22:58] (DMcLean11> Chaturvedi et al took the data and put a mathematical

[22:58] (DMcLean11> framework around it.

[22:59] (DMcLean11> The framework is in terms of differential equations.

[22:59] (DMcLean11> So sclerosis and hypertrophy are functions of time.

[22:59] (DMcLean11> And the disease progression model is defined in

[22:59] (DMcLean11> terms of some initial state at time zero

[23:00] (DMcLean11> and in terms of the rate of change of sclerosis and

[23:00] (DMcLean11> hypertrophy.

[23:00] (DMcLean11> Additional to this

[23:00] (DMcLean11> (for this is a model for a single nephron so far)

[23:01] (DMcLean11> they put another equation in to model the rate of

[23:01] (DMcLean11> decrease in the number of nephrons.

[23:01] (DMcLean11> So all is fine and dandy.

[23:01] (DMcLean11> The trouble is, they seem to be modelling the disease

[23:01] (DMcLean11> process in two different ways

[23:02] (DMcLean11> This didn't seem quite right to me.

[23:02] (DMcLean11> The nephrons become diseased at some arbitrary

[23:02] (DMcLean11> rate which is unrelated to the progression of the disease

[23:02] (DMcLean11> in a single nephron.

[23:03] (DMcLean11> This can't be! Surely, it is linked?!

[23:03] (DMcLean11> So, this got me thinking. How to improve the model so

[23:03] (DMcLean11> that the disease process is an integrated one.

[23:03] (DMcLean11> My idea was this:

[23:04] (DMcLean11> Let's keep the differential equations for the sclerosis and

[23:04] (DMcLean11> the hypertrophy. Let's try and improve what CI97 did.

[23:04] (DMcLean11> What was a bit strange in their model was that the

[23:05] (DMcLean11> sclerosis index just seemed to keep increasing and

[23:05] (DMcLean11> increasing without bound

[23:05] (DMcLean11> once a nephron entered a diseased state.

[23:05] (DMcLean11> So I decided we needed to have 2 states for any nephron.

[23:05] (DMcLean11> A health state and a fully sclerosed state.

[23:06] (DMcLean11> Further more, the healthy state had to be one which is

[23:06] (DMcLean11> unstable

[23:06] (DMcLean11> Why?

[23:06] (DMcLean11> Because we know that a nephron on a disease path

[23:06] (DMcLean11> will continue on that path until completely sclerosed.

[23:07] (DMcLean11> And once it is sclerosed 100% it can never become healthy

[23:07] (DMcLean11> again

[23:08] (RRobles> This one way evolution is undoubtly, but are we sure that it is a non-stop process?

[23:11] (zafra> Are you ready?...Do we need a special software to calculate your model?

[23:11] (DMcLean> Are people still interested?

[23:11] (zafra> yes, we are

[23:11] (gtorres> yes

[23:11] (DMcLean> I seemed to be rattling on and on...

[23:11] (DMcLean> OK

[23:11] (DMcLean> RE: software for model

[23:11] (DMcLean> The model is being developed now

[23:12] (DMcLean> I guess I will write it in the language C

[23:12] (DMcLean> The final aim would be to work out a time

[23:12] (DMcLean> for complete (or say, 95%) sclerosis.

[23:13] (DMcLean> You say the maths is hard?

[23:13] (DMcLean> Well, it is sufficiently hard that I would not be able

[23:13] (DMcLean> to write an analytical solution by pen on a piece of paper

[23:13] (DMcLean> However, I can program a computer to work out a

[23:13] (DMcLean> numerical solution.

[23:13] (DMcLean> As I was saying, I had a single nephron model.

[23:14] (DMcLean> The model has two steady states.

[23:14] (DMcLean> One state is unstable - that is the healthy state.

[23:14] (DMcLean> One state is stable - the unhealthy state.

[23:14] (DMcLean> And any small perturbation will send healthy nephron A

[23:15] (DMcLean> to completely sclerosed nephron A after a finite time.

[23:15] (DMcLean> But we need to make the model work for a kidney!

[23:15] (DMcLean> Single nephron models are no use!

[23:15] (DMcLean> How to do that?

[23:15] (DMcLean> This is where Chaturvedi and Insana went slightly

[23:15] (DMcLean> off the rails.

[23:16] (DMcLean> They prescribed some other completely arbitrary rate

[23:16] (DMcLean> which was unrelated to the initial disease process (the single nephron model)

[23:16] (DMcLean> I argue that we need to introduce the idea of the

[23:16] (DMcLean> glomerular filtration rate.

[23:16] (DMcLean> GFR

[23:17] (DMcLean> Imaging now, that we have a population of nephrons.

[23:17] (DMcLean> As many as we need for a whole kidney.

[23:17] (MJesus> impressive !

[23:17] (DMcLean> Then, the filtration rate is related to

[23:18] (DMcLean> the entire surface are available for filtration

[23:18] (DMcLean> which is presented by all the nephrons.

[23:18] (DMcLean> It is now important to note that ALL the nephrons are

[23:18] (DMcLean> taken into account.

[23:18] (DMcLean> Even the partially sclerosed ones.

[23:18] (DMcLean> I'll explain why.

[23:19] (DMcLean> Imagine there is an initial insult to the kidney

[23:19] (DMcLean> Imagine that a proportion of nephrons are removed

[23:19] (DMcLean> as is the case in a partially nephrectomy.

[23:20] (DMcLean> Then, my idea was that the GFR would decrease

[23:20] (DMcLean> or at least, initially, anyway.

[23:20] (DMcLean> Then, the body would try to counteract this by

[23:20] (DMcLean> bringing onto a disease path

[23:20] (DMcLean> a number of nephrons.

[23:20] (DMcLean> Why would it do this?

[23:21] (DMcLean> Because, on the disease path, the nephrons become

[23:21] (DMcLean> (1) sclerosed and (2) hypertrophied.

[23:21] (DMcLean> here hypertrophy is a good thing.

[23:21] (DMcLean> It is a good thing because it increases the available

[23:21] (DMcLean> area for filtration.

[23:21] (DMcLean> Thus, by sclerosing nephrons, the body maintains

[23:21] (DMcLean> renal function.

[23:22] (DMcLean> But you can see where this will all lead.

[23:22] (DMcLean> Eventually, there will be insufficient nephrons available

[23:22] (DMcLean> so that the body cannot possibly maintain a

[23:22] (DMcLean> "healthy" GFR indefinitely.

[23:22] (DMcLean> This is the progressive nature of the disease.

[23:23] (DMcLean> Hence, GFR must be reduced and at a rate which

[23:23] (DMcLean> gets faster and faster and faster.

[23:23] (DMcLean> Eventually, we have only 5% renal function and

[23:23] (DMcLean> complete renal failure.

[23:24] (DMcLean> My model allows to plot the time progression of the

[23:24] (DMcLean> disease.

[23:24] (DMcLean> Initially, the model would not include therapeutic techniques

[23:24] (DMcLean> to slow renal failure.

[23:24] (DMcLean> This allows to understand the nature of the disease.

[23:24] (DMcLean> Once this is fairly well understood, we can augment

[23:25] (DMcLean> the model with additional ideas from renal care therapy

[23:25] (DMcLean> So!

[23:25] (DMcLean> ABout software to do calculation... :-)

[23:25] (DMcLean> Initially, I'd write it in C

[23:26] (MJesus> C++ ?

[23:26] (DMcLean> It wouldn't be that user friendly - a research tool

[23:26] (DMcLean> !!!

[23:26] (DMcLean> But once it looks good, we could make it into a

[23:26] (DMcLean> clinical application which IS easy to use.

[23:26] (DMcLean> Yes , why not C++? I can stretch almost that far!!!

[23:27] (DMcLean> Does anyone want to criticise the model?

[23:27] (DMcLean> Constructively, bien sur !!!

[23:27] (DMcLean> My idea would certainly be

[23:28] (DMcLean> that there be a clinical use for such a tool.

[23:28] (zafra> It would be very interesting for clinicians as we are that we could predict renal function evolution

[23:28] (DMcLean> I am losing the connexxion again/....!

[23:28] (DMcLean> Yes! Indeed.

[23:28] (MJesus> no... you are well

[23:29] (zafra> any more questions...

[23:29] (DMcLean1> I am back!

[23:30] (DMcLean1> Obviously we must

[23:30] (MJesus> re welcome

[23:30] (DMcLean1> tie the model into experimental results

[23:30] (DMcLean1> This is very important

[23:30] (DMcLean1> as many mathematicians like to stop at a couple of

[23:30] (DMcLean1> differential equations!!!

[23:31] (DMcLean1> (Not me, j'ajoute !)

[23:31] (DMcLean1> But I am also a statistician

[23:31] (DMcLean1> and although I have no parameters really to speak of

[23:31] (DMcLean1> in my model right now

[23:31] (DMcLean1> I explicitly made it this way for clarity

[23:32] (DMcLean1> We can certainly put the parameters into the model

[23:32] (DMcLean1> and go ahead and estimate them using statistical

[23:32] (DMcLean1> techniques from the data.

[23:32] (DMcLean1> We can even test to see if the model is any good

[23:32] (DMcLean1> statistically.

[23:33] (zafra> we are in our last fives minutes..

[23:33] (DMcLean1> Ok!

[23:33] (DMcLean1> Does anyone want to add/say anything?

[23:33] (DMcLean1> Criticize?

[23:33] (DMcLean1> Is it a good idea?

[23:33] (zafra> we are not able to criticize

[23:34] (zafra> properly your conference

[23:34] (MJesus> I like to remark our acknowledgment for this explanation

[23:34] (DMcLean1> Thanks

[23:34] (DMcLean1> If people are interested in helping me to develop this

[23:34] (zafra> because we need to know to improve our maths level

[23:34] (DMcLean1> model further, please do get in touch with me by

[23:34] (DMcLean1> email

[23:35] (zafra> ok

[23:35] (DMcLean1> Oh no!

[23:35] (DMcLean1> Don't worry about the maths!

[23:35] (DMcLean1> Seriously!

[23:35] (MJesus> plas plas plas plas plas plas plas plas plas plas plas plas
[23:35] (MJesus> plas plas plas plas plas plas plas plas plas plas plas plas
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[23:35] (DMcLean1> Thanks!

[23:35] (zafra> thanks to you

[23:35] (MJesus> I'm little less afraid !

[23:35] (zafra> we are very glad to you

[23:36] (DMcLean1> Thank you!

[23:36] (gtorres> good night , thanks

[23:36] (zafra> for having an excelent teacher as you

[23:36] (DMcLean1> Thanks for listening.

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[23:36] (DMcLean1> It is a pleasure

[23:36] (zafra> thank you very much

[23:37] (DMcLean1> IF anyone wants to know more, get in touch!

[23:37] (DMcLean1> I don't bite!!!

[23:37] (MJesus> the log was placed in the web

[23:37] (DMcLean1> That's great.

[23:37] (zafra> and good night to Dr, Mac Lean

[23:37] (DMcLean1> Thank you for inviting me.

[23:37] (DMcLean1> Good night everyone!

[23:37] (MJesus> good night

[23:38] (DMcLean1> Good night and stay in touch :-))

[23:38] (zafra> ok

[23:38] (DMcLean1> I'll let you know what I make of the model.

[23:38] (zafra> it would be interesting

[23:39] (DMcLean1> And feel free to add to it/complain! as you like :-)