Post on 13-Jan-2016
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System physiology – on the design
Petr Marsalek
Class: Advances in biomedical engineering
Graduate course, biomedical engineering
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Outline, part 1What is systems physiology;Description levels:Mathematics level;Physics level;Biology levelDesign of the model;(Case study 1 - ODE solver in Matlab, block design);
? Problems of reverse engineering;Engineering design inspired by biology;(Biomimetic engineering;Neuromimetic engineering;Bionics;)
Outline, part 2
Case study 2:Internet atlas of physiology and pathological
physiology, demo.
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Outline, part 3Case study 3: Model of the flight control inDrospohila Melanogaster (fruit fly)Introduction to flight circuit;Known facts;Power muscles and steering muscles;Neural circuitry, schematics of reflex arcs;Why is feedback needed, the aerodynamics engineer's standpoint;Design of the model;(Methods - ODE solver in Matlab, block design);
Model tuning – sensory neurons emit one spike per wing cycle;Left and right wing, amplitude and phase differences;Modeling the saccade;Exploring parameter space of one "linear" equation;Limited options for the feedback and its function;Towards comparison of model output with real data;Concluding remarks
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Neural sensori-motor circuits
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Known factsNeural circuits consist of neurons talking to each other throughsynapses. Thoracic ganglion is a part of fly brain. Sensory inputs arevisual, mechanical and others (like odors etc.). Motor outputs are realizedby muscles. Motoneurons are last neurons in the circuit.Most of the reflexes are fast (< 5 ms). Some of the reflexes aremonosynaptic.
Halteres – are a pair of club-shaped organs in a dipteran insect thatare the modified second pair of wings and function as sensory flightstabilizers. Drosophila is an example of dipteran insect with one pairof wings and with halteres. Compare e.g. to dragonfly of odonata withtwo pairs of wings.
Flies have two types of flight muscles:(1) power muscles and (2) steering muscles.Experiments: (1) limited kinematics experiments: tethered flight, singlewing preparation; (2) behavioral experiments: free flightDescription of reflex arcs is based on anatomy of neural circuits.
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flightforces
flight
flight trajectory
wing
haltere
Neural sensori-motor circuits
MN
MN
haltere muscle
SN
wing muscle
SN
descendingvisual input
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flightforces
flight
flight trajectory
wing
haltere
Neural sensori-motor circuits
MN
MN
haltere muscle
SN
wing muscle
SN
descendingvisual input
Reflex arcs of halteres
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flightforces
flight
flight trajectory
wing
haltere
Neural sensori-motor circuits
MN
MN
haltere muscle
SN
wing muscle
SN
descendingvisual input
Reflex arcs of wings
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Function of Sensory Inputin Flight Control (Circuit)
Sensory neuron
Mechanoreceptor transduction
Motoneuron
Muscle
Wing
Mechanical coupling
DelaySynapse
Masterpacemaker? NoMechanicalResonance? YesNonlinear oscillator? Yes
Other inputs,visual, from halteres, etc.
50 52 54 56 58 60 62 64 66 68 70-80
-70
-60
-50
time [ms] t
right voltage [mV] V Rleft voltage [mV] V L
Model: Introduction of Leaky Integrator (= RC circuit with threshold)
THL for )( VVVdttV
L VVdt
dV RC
IVVgdt
dVg )( LLL
1L
Rg
Model: Leaky Integrator and Spring Equations
IVVxNpVVhgVVgdt
dVg ))(()()( Na0KALLL
)(SS Vhhdt
dhh
Fxkdt
dx
dt
xdm MRC2
2
TkxkE
xp
B
MRC
02
exp1
1)(
slope ,
half,
SS
exp1
11)(
h
h
V
VVVh
)(LfF
THL for )( VVVdttV
Model: Reordered Equations
IVVxNpVVhgVVgdt
dVg ))(()()( Na0KALLL
)(SS Vhhdt
dhh
Fxkydt
dym MRC
ydt
dx
1. Although leaky integrator and spring equations are linear, threshold, adaptation and mechanoreceptor currents are nonlinear, making the whole DE set nonlinear.2. Spring equation is rewritten to its normal form to be fed into a custom written fixed step Runge-Kutta numerical DE solver (in Matlab).
THL for )( VVVdttV
Wings Model
RR
RRRHR
LL
LLLHL
H2H
2HHHHHH
HHH2H
2HHHHHH
)(
)(
)(
)()(
wx
xtKwxw
wx
xtKwxw
yyxByExFy
xtKxyxByFxEx
Left and right wing is coupled through variable stiffness K(t) to an oscillator =
oscillating power muscle[Vilfan and Duke]
___
___
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-0.5
0
0.5
power oscillator x Hright amplitude x Rleft amplitude x L
50 52 54 56 58 60 62 64 66 68 70-80
-70
-60
-50
time [ms] t
right voltage [mV] V Rleft voltage [mV] V L
Wing amplitudesand traces of leaky integrator
50 52 54 56 58 60 62 64 66 68 70
-0.5
0
0.5
power oscillator x Hright amplitude x Rleft amplitude x L
50 52 54 56 58 60 62 64 66 68 70
-0.5
0
0.5
time t [ms]
right phase Rleft phase L
Wing amplitudes and phases
55 60 65 70 75 80 85 90 95
-0.5
0
0.5
1left amplituderight amplitudephase differenceamplitude difference
55 60 65 70 75 80 85 90 95
-0.4
-0.2
0
0.2
0.4
time [ms]
left stiffness, = 0.5 msright stiffness, = 5 msalpha function, = 0.5 msalpha function, = 5 ms
Feedback formula1LFL for ),6.0)(()( iii ttttgtK
KL(t) is time varying stiffness, gF is gain of the feedback,
L is wing phase. This is the formula for the left wing (L)and analogous formula is for the right (R). [Tu and Dickinson, 96]
50 60 70 80 90 100
-0.5
0
0.5 left amplitude, x L
right amplitude, x R
power oscillator, x H
50 60 70 80 90 100
-0.5
0
0.5 left phase, L
right phase, R
50 60 70 80 90 100
-0.5
0
0.5 left stiffness, K L
right stiffness, K R
50 60 70 80 90 100-80
-70
-60
-50 left voltage, V
L right voltage, V
R
50 60 70 80 90 1000
10
20left relative spike timingright relative spike timing
Variables of a saccade
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Saccade
[Fry et al, 2003]
Investigating parameter values: without and with feedback
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50
0.2
0.4
0.6
0.8
1
1.2
gain g F, stiffness K
Amplitude
(magenta) amplitude, with feedback, varying gain(red) amplitude, no feedback, varying K
Investigating parameter values:wing mass M=1 and M=2
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50
0.2
0.4
0.6
0.8
1
1.2
No feedback, amplitude in dependence on stiffness
stiffness K
(blue) amplitude, mass M=2(green) amplitude, mass M=1
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From model to data
Function of Sensory Input in Flight Control (Wish list)
Things to do, hypotheses, …
Theory: perturbation of the neural circuit will alter flight maneuvers.
Theory: test some of the popular hypotheses (eg. delay line in wing input).
Theory: what entrains/ perturbs wing rhythm?, phase lock, contributions…
Theory: minimal alterations of circuit, not possible in experiments.
Theory… (Theory: any new ideas mostly sought and welcome…)
Theory: in general should (ideally) suggest interesting experiments.
Experiments: should (ideally) suggest interesting theoretical questions.
Experiments: calcium levels recording in mechanoreceptors and neurons.
Experiments: electrophysiological recording in mech.receptors and neurons.
Experiments: flight recording in mutants, in other Drosophila species.
Function of Sensory Input in Flight Control (Wish list)
Things to do, hypotheses, …
Theory: perturbation of the neural circuit will alter flight maneuvers.
Theory: test some of the popular hypotheses (eg. delay line in wing input).
Theory: what entrains/ perturbs wing rhythm?, phase lock, contributions…
Theory: minimal alterations of circuit, not possible in experiments.
Theory… (Theory: any new ideas mostly sought and welcome…)
Theory: in general should (ideally) suggest interesting experiments.
Experiments: should (ideally) suggest interesting theoretical questions.
Experiments: calcium levels recording in mechanoreceptors and neurons.
Experiments: electrophysiological recording in mech.receptors and neurons.
Experiments: flight recording in mutants, in other Drosophila species.
V
+-
V
+-
X
+-
X
X
X+-
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Conclusions1 The aim of the project is to understand the function of sensory
input in Drosophila flight control.
2 Equilibrium reflexes are described in experiments. Their underlying circuitry is mostly unknown.
3 Current model: coupling of mechanoreceptors to spiking of their sensory neuron. Closing of feedback loop from motoneuron to sensory neuron.
4 We described the parameter space and key variables involved in feedback and saccades.
6 What remains to do: to describe effects of feedback and steering in terms of flight aerodynamics, which is the experimental description level.
7 We will analyze new experimental data in near future.