Welcome to the professional web page of Stéphane MOTTIN (SM).
SM is a CNRS researcher (PhD, HDR).
Laboratoire CREATIS, INSALyon, Univ. Lyon1, CNRS UMR5220, Inserm U1294, UJM.
Bâtiment Léonard de Vinci, 21 Av. Jean Capelle, 69100 Villeurbanne, FRANCE.
stephane.mottin arobase creatis.insalyon.fr
Content:
 Research interests
 Short CV
 Teaching
 Administrative functions
 Book Collection “Integrations des Savoirs et SavoirFaire”: 27 books
 Publications
 Softwares
Research interests
SM’s expertise lies in the field of biophotonics, open science, applied mathematics, neurophysiology, animal behavior, and “how to measure concentration (n elements or molecules/volume) in complex/labyrinthique multiphase medium (i.e. tissue in vivo)?”
Keywords: neuroimaging, “NOT numerical methods only closedform form” for partial differential equations , theory of special functions, femtosecond laser, streak camera, neurochemistry in mammals and in birds, brain energy metabolism and waking/sleep states, bioacoustics, social behavior

Cover of JCBFM and Cover of Nature.
some books of the Collection “Integrations des Savoirs et SavoirFaire”.
Closedform analytical solution, Partial differential equation (PDE) and Inverse problems;
Preamble: This part is about deep relations between research in mathematics and research in physics. If you want “the full introduction” and to understand the motivations of this research.
link–>below: Introduction about motivations/results PDE
The contributions of SM are about The inhomogeneous Helmholtz equation :
S(r) ∆u(r) + A(r) u(r) = z(r) , and u is the unknown solution, simplified as ∆u(r) + K(r) u(r) = f(r).
$ r\in \Omega \subset \mathbb{R}^m,$ with m=1, 2 or 3 (and boundary condition on $ \partial \Omega $),
and f is a function with compact support.
Four cases are distinguished in physical mathematics
(physically motivated mathematics = a subfield of mathematical physics which refers to the development of mathematical methods for application in physics),
1/ K(r) is equal to zero> the Laplace equation, 2/ K(r) all times positive> the Helmholtz equation; K(r)= $ k^2 $(r)),
3/ K(r) all times negative> the diffusionreaction equation; K(r)=$ k^2 $(r) and $k$ is an absorption coefficient, 4/ K(r) equal to g $ k^2 $
with g=1 and
\(\class{mymathjaxmathstyle}{g\in \mathbb{C}}\) (Generalized Helmholtz Equation).
SM derived the analytical solution of the Laplace equation with Robin conditions on a sphere with azimuthal symmetry by applying Legendre transform.
$ \left (\frac {\partial u (r, \zeta)} {\partial r} \right) _ {r = 1} + h \text u (r = 1, \zeta) = f\left (\zeta\right) $ , the Robin condition on the unit sphere,
ζ = cos (θ), θ is the azimuthal angle, $ \class{mymathjaxmathstyle}{r\in \mathbb{R}^+} $ and $ \class{mymathjaxmathstyle}{h\in \mathbb{R}^{*+}} $
Many solutions of the boundary value problems in spherical coordinates are available in the form of infinite series of Legendre polynomials but the evaluation of the summing series shows many computational difficulties.
The solution is expressed in terms of the Appell hypergeometric function F1 and also for the following integral
$ \int_0^r \frac{\rho ^{h1}}{\sqrt{12 \zeta \rho +\rho ^2}} \, d\rho $
SM applied this result by some examples of inverse problems in mass and heat transfer, in optics, in biophotonics, in corrosion detection and in geodesy.
SM and Grigory Panasenko, Sivaji Ganesh
shown that the classical homogenization (averaging) approach to the solution of the following equation (1) leading to the approximation (2) with some conditions.
\(\begin{eqnarray}
\Delta\,u_{\epsilon,\delta,\omega} + q\left(\frac{x_1}{\epsilon}\right)
\,u_{\epsilon,\delta,\omega}&=&f.\label{edoeq}
\end{eqnarray}\)
The scattering coefficient is supposed to be constant (S(r) equal to one (adimensionnalisation)) while the absorption coefficient is equal to zero everywhere except for a periodic set of thin parallel strips simulating the blood vessels, where it is a large parameter $ \omega $.
$ x_{1}\in (0,L)$ and L is a characteristic length (i.e. the distance between the source and the detection).
In biophotonics, the equation (2) is considered as a model of the light absorption in vascularized tissues. Usually researchers use the volumic mean value of the absorption $ q $ like an homogeneous medium despite absorption $ q $
takes place only in multiscale vessels and is very low outside these vessels and this ratio depends of the wavelength. Here absorption occurs in the set of parallel thin blood vessels (where $ q=\omega \neq 0$) and this absorption is ignored outside these “vessels”.
The problem contains two other parameters which are small: $ \epsilon $, the ratio of the distance between the axes of vessels to the characteristic macroscopic size, and $ \delta $, the ratio of the thickness of thin vessels and the period.
The goal is to show that the classical homogenization (averaging) approach to the solution of equation leading to the approximation
\(\begin{eqnarray}
\Delta\,u_{0} + <q>
\,u_{0}&=&f.\label{edoeqh}
\end{eqnarray}\)
where $ < q > $ is approximated to the volumic mean value of $ q $.
Indeed, they show that it is right for some combination of magnitudes of parameters
\(\epsilon,\delta,\omega\)
, it can be proved that
\(u_{\epsilon,\delta,\omega} \rightarrow u_{0};\)
but inapplicable for some other combinations.
The authors prove the classical homogenization result in the case
\((A) ~~ \epsilon\to 0,\,\omega\to\infty,\, \delta\to 0, \omega\delta\to\infty,\, \epsilon^2\omega\delta\to 0,\, \mbox{and there exists}\, \gamma>0, \, \mbox{such that,}\,\omega(\epsilon^2\omega\delta)^\gamma = O(1),\)
and they show that the homogeneous model is inapplicable in the case
\((B) ~~ \epsilon\to 0,\,\omega\to\infty,\, \delta\to 0, \epsilon^2\omega\delta^2\to \infty.\)
Future Research Directions: Generalisation Sphere–> Ellipse.
Measurements of endogenous fluorophore (NADH) by picosecond timeresolved spectroscopy in brain deep nucleus with freely moving rodent
In SM’s thesis, they were the first in the world to measure in freely moving animal by optical fiber the variation of chemical concentration in deep nucleus like Raphe Dorsalis nucleus (during many weeks).
–>
for the study of the relation of brain energy metabolism and waking/sleeping states,
–>
for the study of the relation of brain energy metabolism (mitochondrial complex 1) and dose/effect of antibiotics (Chloramphenicol).
During his thesis, SM measured one of the most important neurotransmitter serotonin or 5hydroxytryptamine (5HT) in vitro by a new fiber optic chemical sensor.
Future Research Directions: stop due to the problem of glial scar and the need of surgery. It’s very difficult to manipulate the glial scar for diagnostic and/or therapeutic purposes.
Measurements of variation of hemoglobins and brain energy metabolism in cortex by SM’s patented picosecond functional white laser tomography without surgery and by MRI.
Only mammals and birds dream. The other animals don’t show this third state (only waking, slowwavesleep states).
The paradoxical sleep is the last vital function we don’t know the physiological function! We still need direct in vivo methods to measure fast variations of chemical concentration.
SM decided to develop a new robust functional imaging for small animals to directly measure the coupling between cellular energy metabolism and transport of O2 and CO2
and to apply this one to a model of song bird (zebra finch, Taeniopygia guttata).
First they study optical properties of head tissues in the case of this song birds’model.
In order to study brain activation in response to acoustic stimuli, two different invivo methods (MRIBOLD and this new POT Picosecond Optical Tomography) that are able to assess neuronal activity based on detection of haemodynamic changes were compared within identical experimental settings and under hypercapnia (7% inhaled CO2).
These results provide the first correlation in songbirds of the variations of oxyhemoglobin and deoxyhemoglobin and oxygen saturation level obtained from Nearinfrared spectroscopy NIRS with local BOLD signal variations.
The authors measure in vivo oxyhemoglobin (HbO2) and deoxyhemoglobin (Hb) concentration changes following physiologic stimulation (familiar calls and songs). Picosecond optical tomography showed sufficient submicromolar sensitivity to resolve the fast changes in the hippocampus and auditory forebrain areas with 250 μm resolution.
These new approaches to assess neural activity were selected by Optical Society of America and published in “Optics & Photonics News”.
Future Research Directions: Understanding why CRO (contract research organization) and big pharma don’t use at large scale preclinical 7T 11.7T MRI to measure toxicity of drugs and medical biomaterials. Applied mathematics of biosensing and how to measure molecule’s concentration in medium with complex geometry. New theory about paradoxical sleep.
Measurements of social bonding, animal behavior and bioacoustics
Compared with other mammals, only human sings. Song birds, often deep social animal like mammals, are “perfect” models in bioacoustics and learning process. Specially the zebra finch is a socially monogamous and colonial opportunistic breeder with pronounced sexual differences in singing and plumage coloration. And like all mammals, all birds dream.
Moreover animal vocalizations serve a wide range of “functions” including vocal learning, territorial defense, courtship, begging, and social cohesion.
In this context SM became interested in the concept of Dunbar’s number.
Dunbar suggested cognitive limit to the number of individual with whom one can maintain “stable” social relationships—relationships (in which an individual knows who each “element” is and how each “person” relates to every other “person).
Briefly he theorised that: this limit is a direct function of relative neocortex size, and that this, in turn, limits group size.
Dunbar’s number.
The following work was published in the wellknown world’s leading science journal “Nature” and was selected by the editor for its cover and two comments
( comment in Nature)
The authors prove that the male of a gregarious songbird pays attention to the mating status of conspecific pairs, and uses this information to control its behaviour towards its female partner.
Briefly knowing the mating status of other individu is an important part of social intelligence, and known before only in some primates, this proof has a lot of consequences in many sciences and “playing with the mating status” could be one of the main motors of evolution.
Because the members of a pair (of zebra finch) use distance calls to remain in contact, callbased mate recognition is highly probable in this species.
By analysing the acoustic structure of male calls, the authors investigated the existence of an individual signature and identified the involved acoustic cues.
These experiments suggested that the female uses both the energy spectrum and the frequency modulation of the male signal.
Future Research Directions: Mathematics of bioacoustics specially how birds know the best position for an emitter? And new theory about the link between paradoxical sleep and social intelligence/social bonding
Short CV
 2006 : HDR (Univ. StEtienne, France), president of jury : Michel Jouvet
 1995 : CNRS researcher position in optics
 Oct 1994Oct 1995 : price of young Researcher from Lyonnaise de banque
 SM started a startup “SLeeP” (Système de Lecture et d’enregistrement Polygraphique).
 Oct 1993Oct 1994 : “Attaché de recherche” at Ecole des Mines of StEtienne
 1993 : PhD thesis (Ecole des Mines of StEtienne and Univ. of Grenoble), president of jury : Michel Jouvet.
 1989 : Master degree (DEA) Génie Biologique et Médical, University Lyon1.
 Oct 1987Sept 1988 : civilian service.
 19871984 : Engineer degree at ENSI IGC (Institut Génie chimique) ENSIACET, Toulouse, France.
Teaching
 20032007 : foundation member and director of master Biophotonique at Univ. of StEtienne, (Fac des Sciences (physique et Biologie) and Fac de Médecine)
 optics
 biophotonics
 neurophysiology
 instrumentation
 biosensors
 20052006 and 20162017 : Lectures master M2 “Optique Image Vision” at Univ. of StEtienne
 biophotonics
 instrumentation
 ultrafast laser
Administrative functions
Administrative functions
 Cofounder of the scientific team of the “medical technologies center” of the Loire department with Pr Rieu (Ecole Mines) and Pr Geyssant (PUPH Medicine Univ StEtienne), coadministrator from 19932011. Now Noveka
 Cofounder of the “optdiag” conference (Paris) and member of the scientific committee 19942018. site archive d’optdiag
 Cofounder in 1997 with P. Laporte of the “femtosecond group” at the Curien laboratory (now Radiationmatter Interaction team
 Permanent member of the Technical Commission of Experts “Laser and Photonics” (CNRS markets) from 20012005.
 Cofounder and member of the management committee of GDR 2588 from 2003 to 2014, now GDR IMABIO
 Cofounder of various Thematic networks of the MRCT from 2005 to 2013, now networks miticnrs.
 Founder & Director of the confocal microscopy center at Jean Monnet University from 2004 to 2006.
 Founder & director of the TONI team (optical tomography and neuroimaging) within the Curien laboratory from 2004 to 2009 composed of 5 permanent staff including 2 ITA.
 Cofounder in February 2005 of the FrancoGerman “airbuslike” project Biophoton (220 million €/5 years) stopped in February 2006 because Gerhard Schröder was not reelected in November 2005.
 Founder of the CNRSA2I unit (Industrial Innovation Agency directed by JeanLouis_Beffa), March 2005 under the director of CNRS Bernard Larrouturou.
 Participation in the writing of the “Biophotonics” part of President Jacques Chirac’s speech of April 25, 2005 (during the presentation of the actions of the Industrial Innovation Agency): Chirac’s speech 1
 Participation in the writing of the “Biophotonics” part of President Jacques Chirac’s speech of April 26, 2005 (during the 50th anniversary of the FrancoGerman Chamber of Commerce and Industry): Chirac’s speech 2
 Member of the management committee of the interdisciplinary PID CNRS “neuroInformatique” program, in 2009 directed by Alain Berthoz from the Collège de France.
 Expertise for the Ministry of Research (rue Descarte, Paris) 20092010 with, for example, the organization of a meeting in Alsace for the endowment of more than 10 million euros to Rhénaphotonics for the FrancoSwiss crossborder project with the company Novartis, which ultimately failed due to Novartis’ lack of involvement.
 Elected to the scientific council of the University of StEtienne from 2008 to 2012.
Editor/publisher and Book collection director
Since 2001, SM has founded and directed the “Intégrations des Savoirs et Savoirfaire” collection.
This collection aims to publish summary books in all sciences but also the knowhow of researchers, engineers and technicians: 27 books, and around ~9300 pages.
links for each book
some official links
In the « Système Universitaire de Documentation » (Sudoc), a collective catalogue created by
all french Higher Educational and Research libraries and resource centres, you can get all chapters and authors by book.
in sudoc
in HALCNRS
in zenodoEuropean Open Science
in amazon
The last 3 books were published by EDP Sciences:
in EDPSciences
official permanent id as publisher, book collection, researcher
The DataCite/Figshare Academic Research System of this collection: in Datacite
“Notice de collection éditoriale de la BNF”: BNF
Permanent id as publisher, book collection, researcher:
Identifiant VIAF (Fichier d’autorité international)
isni (International Standard Name Identifier)
Worldcat
Bib. Nationale France
zbmath mathematics
Identifiant Wikidata
other
Publications (only <30)
click on Keywords
Softwares
under progress
link–>below: Introduction about motivations/results
Two main contributions of SM in Applied Mathematics are about the inhomogeneous Helmholtz equation.
This linear PDE has a very wide variety of applications in physics, in biology, in many social sciences… from the smallest particule to the largest galaxies’structures.
And this timeindependent PDE can also solve a lot of timePDE (i.e. operator: $ \displaystyle \left({\frac {1}{c^{n}}}{\frac {\partial ^{n}}{\partial t^{n}}}\right) $) by separation of variables which begins by assuming that the function u(r,t) is in fact separable:
$ \class{mymathjaxmathstyle}{\displaystyle u(\mathbf {r} ,t)=A(\mathbf {r} )T(t)} $
$ \displaystyle \left(\nabla ^{2}{\frac {1}{c^{n}}}{\frac {\partial ^{n}}{\partial t^{n}}}\right)u(\mathbf {r} ,t)=0. \longrightarrow $ $ \displaystyle {\frac {\nabla ^{2}A}{A}}={\frac {1}{c^{n}T}}{\frac {\mathrm {d} ^{n}T}{\mathrm {d} t^{n}}\longrightarrow } $ $\displaystyle {\frac {1}{c^{n}T}}{\frac {\mathrm {d} ^{n}T}{\mathrm {d} t^{n}}}=k^{2}. \longrightarrow $ $ \displaystyle {\frac {\nabla ^{2}A}{A}}=k^{2} $
The contributions of SM are about The inhomogeneous Helmholtz equation :
S(r) ∆u(r) + A(r) u(r) = z(r) , and u is the unknown solution, simplified as ∆u(r) + K(r) u(r) = f(r).
$ r\in \Omega \subset \mathbb{R}^m,$ with m=1, 2 or 3 (and boundary condition on $ \partial \Omega $),
and f is a function with compact support.
Four cases are distinguished in physical mathematics
(physically motivated mathematics = a subfield of mathematical physics which refers to the development of mathematical methods for application in physics),
1/ K(r) is equal to zero> the Laplace equation, 2/ K(r) all times positive> the Helmholtz equation; K(r)= $ k^2 $(r)),
3/ K(r) all times negative> the diffusionreaction equation; K(r)=$ k^2 $(r) and $k$ is an absorption coefficient, 4/ K(r) equal to g $ k^2 $
with g=1 and
\(\class{mymathjaxmathstyle}{g\in \mathbb{C}}\) (Generalized Helmholtz Equation).
The dimension of the quantity $ k $ is meter $^$ $^1 $. If the medium is considered to be not homogeneous (i.e. propagation in a dispersive medium or in a complex absorbing medium)
then $k(r)$ is not a constant. For example Li,1990 published the analytical solution in a semiinfinite linearly inhomogeneous medium
with $k= k _ {0}$(1+ß z)^(1/2) where $k _ {0}$ and ß are positive constants. See below for the homogenization approach when k(r)≠constant.
For inverse problems (i.e. to do ∂/∂k or derivatives of Robin coefficient), it’s crucial to find closedform solution.
It is wellknown that this class of elliptic PDE is related to spherical harmonics:
in (p+2)dimensional Euclidean space with p=1,2,… (Bateman,1953; Bateman_Manuscript_Project] and for the first case (p=1), the Gegenbauer polynomials are the Legendre polynomials.
With this context, the first following article is about the Robin boundary condition on the $ \partial \Omega $ wich is a weighted combination of Dirichlet boundary conditions and Neumann boundary conditions in order to find a closedform solution (“u”) for the Laplace equation in $ \Omega $ = Ball and also outside the Ball by inversive geometry. Many inverse problems are about the absorptionandreflection only on the surface for a wide scale of Balls from atoms to the biggest stars.
The second article is about new research in mathematics in the domain of PDE started around 1975, “Asymptotic homogenization”, and applied to the case 3 with nonhomogeneous medium and TWO rapidly oscillating coefficients.
Averaging the absorption of a composite medium with periodic set of thin parallel strips with high contrast (white/black) could be compared with the questions: what is the grey of “a zebra in fog”?
Isit always “medium” gray? Depending of two geometric parameters and the amplitude of absorption, in some cases the blurry zebra is never “medium” gray!
These results have huge implications not only in optics with scattering medium i.e for all cases of Helmholtz equation when the medium is composite with strong differences of properties, or when surface shows complex absorptionandreflection properties specially when the researchers are interested in two types of results: a/ when the absorption properties are unknown, and we want to find them using observed measurements, it is the harder wellknown inverse problem, b/ when the absorption properties are known, then we can use many strategies to calculate various quantities of interest (i.e. reflectance, transmission, fluence). This is often referred to as the forward problem.
THE END