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System physiology – on the design. Petr Marsalek. Class: Advances in biomedical engineering. Graduate course, biomedical engineering. Outline, part 1. What is systems physiology; Description levels: Mathematics level; Physics level; Biology level Design of the model;

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System physiology on the design l.jpg
System physiology – on the design

Petr Marsalek

Class: Advances in biomedical engineering

Graduate course, biomedical engineering


Outline part 1 l.jpg
Outline, part 1

What is systems physiology;

Description levels:

Mathematics level;

Physics level;

Biology level

Design 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 l.jpg
Outline, part 2

Case study 2:

Internet atlas of physiology and pathological physiology, demo.


Outline part 3 l.jpg
Outline, part 3

Case study 3: Model of the flight control in

Drospohila 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



Known facts l.jpg
Known facts

Neural circuits consist of neurons talking to each other through

synapses. Thoracic ganglion is a part of fly brain. Sensory inputs are

visual, mechanical and others (like odors etc.). Motor outputs are realized

by muscles. Motoneurons are last neurons in the circuit.

Most of the reflexes are fast (< 5 ms). Some of the reflexes are

monosynaptic.

Halteres – are a pair of club-shaped organs in a dipteran insect that

are the modified second pair of wings and function as sensory flight

stabilizers. Drosophila is an example of dipteran insect with one pair

of wings and with halteres. Compare e.g. to dragonfly of odonata with

two pairs of wings.

Flies have two types of flight muscles:

(1) power muscles and (2) steering muscles.

Experiments: (1) limited kinematics experiments: tethered flight, single

wing preparation; (2) behavioral experiments: free flight

Description of reflex arcs is based on anatomy of neural circuits.


Neural sensori motor circuits7 l.jpg

flight

forces

SN

MN

SN

MN

Neural sensori-motor circuits

descending

visual input

wing

flight

wing muscle

flight trajectory

haltere

haltere muscle


Neural sensori motor circuits8 l.jpg

flight

forces

SN

MN

SN

MN

Neural sensori-motor circuits

Reflex arcs of halteres

descending

visual input

wing

flight

wing muscle

flight trajectory

haltere

haltere muscle


Neural sensori motor circuits9 l.jpg

flight

forces

SN

MN

SN

MN

Neural sensori-motor circuits

Reflex arcs of wings

descending

visual input

wing

flight

wing muscle

flight trajectory

haltere

haltere muscle


Function of sensory input in flight control circuit l.jpg
Function of Sensory Inputin Flight Control (Circuit)

Other inputs,

visual, from

halteres, etc.

Delay

Synapse

Sensory neuron

Master

pacemaker? No

Mechanical

Resonance? Yes

Nonlinear oscillator? Yes

Motoneuron

Muscle

Mechanoreceptor transduction

Wing

Mechanical coupling


Model introduction of leaky integrator rc circuit with threshold l.jpg
Model: Introduction of Leaky Integrator (= RC circuit with threshold)



Model reordered equations l.jpg
Model: Reordered Equations

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).


Wings model l.jpg
Wings Model

Left and right wing is coupled through variable stiffness K(t) to an oscillator = oscillating power muscle

[Vilfan and Duke]

___

___


Slide15 l.jpg

Wing amplitudesand traces of leaky integrator



Feedback formula l.jpg
Feedback formula

KL(t) is time varying stiffness, gFis gain of the feedback,

Lis wing phase. This is the formula for the left wing (L)

and analogous formula is for the right (R). [Tu and Dickinson, 96]



Saccade l.jpg
Saccade

[Fry et al, 2003]


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Investigating parameter values:without andwithfeedback


Investigating parameter values wing mass m 1 and m 2 l.jpg
Investigating parameter values:wing mass M=1 and M=2



Function of sensory input in flight control wish list l.jpg
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 list24 l.jpg
Function of Sensory Input in Flight Control (Wish list)

V

+-

V

+-

X

+-

X

X

X

+-

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.


Conclusions l.jpg
Conclusions

1 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.


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