Valentini_subbed.qxp 27/3/09 9:43 am Page 66
Overactive Bladder and Incontinence
Mathematical Models in Urodynamics – Which Method and Why?
a report by
Françoise A Valentini and Pierre P Nelson
French National Institute for Medical Research (ISERM) Unit 731, and Department of Physical Medicine and Rehabilitation, Pierre and Marie Curie University
In order to make a diagnosis and to choose a treatment, physicians require combinations of Q
max
and p
det.Qmax
(Abrams-Griffiths [AG] number
a clinical examination and medical experience. As an example from the p
det.Qmax
-2Q
2
max
and the detrusor coefficient [DECO] number p
det.Qmax
field of urology, when Hunter described, circa 1770, benign prostatic +5Q
3
max
) are used, which lead to meaningful nomograms. It has been
hypertrophy (BPH), the only information at the physician’s disposal were shown
4
that these empirical numbers are strongly correlated with the
the patient’s complaint and a digital rectal examination. Since 1960, value–belief–norm (VBN) parameters of urethral prostatic compression
elaborate devices – i.e. flowmeters, urodynamic units, bladder scan – and detrusor contractility.
5
The value of this two-parameter model is
electromyography, have provided much data. The challenge now is to limited because it does not take into account nervous control
define a disease-associated severity index (SI) and to use the recorded data abnormalities and deviations from the isobaric compartment hypothesis,
to objectively evaluate the SI value for each patient; a comparison of a it does not allow free uroflow (FF) analysis and the values of Q
max
and
patient’s SI with critical values leads to a classification that can be used p
det.
Q
max
need to be frequently corrected using archive data.
6
to make a therapeutic decision. To reach this goal, the only method is the
use of models. Knowledge Models
These were introduced by physicists to explain the phenomena resulting
In this article, we will describe the advancement of modelling in from many well-known elementary phenomena, i.e. why the sky is blue
urodynamics from simple (empirical) models to sophisticated mathematical (Lord Rayleigh circa 1890) or why locomotives and cars were unstable
ones. Benign prostatic enlargement (BPE) has been chosen as an example. (Rocard 1945). Many elementary phenomena add their effects to
produce continence and voiding. Some have been studied separately, in
Empirical Models vivo or in vitro, in men or animals, at any scale from the molecular to the
functional level. Subsequently, knowledge modelling is also applicable for
One-parameter Model urodynamics. The main idea is to use all our knowledge (or at least a well
The maximum flow rate (Q
max
) reached during voiding was the first chosen part of it) to describe each component of the voiding system. The
suggested SI to define the bladder outlet obstruction due to BPE. human mind is unable to handle a lot of data at one time. Therefore,
However, a low Q
max
can be caused by a weak detrusor induced by each elementary phenomenon is described by an equation and
urethral obstruction. mathematics. From 1970 to 1980, equations describing the mechanics of
micturition were formulated, mainly by Griffiths.
7
Unfortunately, many of
Two-parameter Model these equations are of the non-linear differential variety and so unwieldy
To take into account detrusor contractility, a two-parameter classification that the first researchers had to replace them by simplified ones (for
is needed. Therefore, two numbers must be evaluated from the recorded instance, hydrodynamics by an unrealistic urethral resistance). Today,
data. They could be Q
max
and the detrusor pressure at the time of Q
max
high-level mathematicians using modern computers have succeeded
(p
det.Qmax
); unfortunately, p
det
is not recorded. Using the Enhörning in building accurate and fast tools producing easily readable outputs,
hypothesis,
1
p
det
is assumed to be equal to the difference between the e.g. the VBN model.
5
bladder and the rectal pressure (p
det
= p
ves
– p
rec
). Currently, two linear
Knowledge Models of the Mechanical
Part of the Lower Urinary Tract
Françoise A Valentini is a Senior Physician in the Department of Physical Medicine and
Rehabilitation and an Assistant Professor of Chemistry at the Pierre and Marie Curie
Gender, initial bladder volume and nervous excitations of detrusor and
University in Paris, specialising in urodynamics. In association with mathematician Gilbert R
sphincters are the initial computational inputs. The data produced are
Besson and physicist Pierre P Nelson, she developed the value–belief–norm (VBN)
mathematical model of micturition. She completed medical school at the Faculty of Medicine
theoretical curves of flow rate and detrusor pressure versus time, which have
at Pitié-Salpétrière Hospital in Paris and her PhD at Pierre and Marie Curie University. to be compared with the recorded ones. The equations describe the bladder,
E: francoise.valentini@jrs.aphp.fr
the urethra and the sphincter and the hydrodynamics.
Pierre P Nelson is an engineer physicist specialising in the
The Bladder
use of models applied to industrial scientific problems. He is
a graduate of Ecole Polytechnique in Paris and the National
The muscular wall consists of elastic, ‘visco-elastic’ and contractile elements.
School of Advanced Techniques, where he has been a The properties of the elastic and visco-elastic elements have been measured
Professor of Radiative Hydrodynamics.
on pig bladder strips.
7
These elements obey the law of elastic polymers
(thermodynamic equilibrium between folded and unfolded junction of links
in a chain). In fact, the so-called visco-elasticity is a delayed elasticity (slow
transitions between folded and unfolded junction; time constant about 300
66 © TOUCH BRIEFINGS 2008
Page 1  |  Page 2  |  Page 3  |  Page 4  |  Page 5  |  Page 6  |  Page 7  |  Page 8  |  Page 9  |  Page 10  |  Page 11  |  Page 12  |  Page 13  |  Page 14  |  Page 15  |  Page 16  |  Page 17  |  Page 18  |  Page 19  |  Page 20  |  Page 21  |  Page 22  |  Page 23  |  Page 24  |  Page 25  |  Page 26  |  Page 27  |  Page 28  |  Page 29  |  Page 30  |  Page 31  |  Page 32  |  Page 33  |  Page 34  |  Page 35  |  Page 36  |  Page 37  |  Page 38  |  Page 39  |  Page 40  |  Page 41  |  Page 42  |  Page 43  |  Page 44  |  Page 45  |  Page 46  |  Page 47  |  Page 48  |  Page 49  |  Page 50  |  Page 51  |  Page 52  |  Page 53  |  Page 54  |  Page 55  |  Page 56  |  Page 57  |  Page 58  |  Page 59  |  Page 60  |  Page 61  |  Page 62  |  Page 63  |  Page 64  |  Page 65  |  Page 66  |  Page 67  |  Page 68  |  Page 69  |  Page 70  |  Page 71  |  Page 72  |  Page 73  |  Page 74  |  Page 75  |  Page 76  |  Page 77  |  Page 78  |  Page 79  |  Page 80  |  Page 81  |  Page 82  |  Page 83  |  Page 84  |  Page 85  |  Page 86  |  Page 87  |  Page 88  |  Page 89  |  Page 90  |  Page 91  |  Page 92  |  Page 93  |  Page 94  |  Page 95  |  Page 96  |  Page 97  |  Page 98  |  Page 99