Homework: AP Simulation Bioengineering 6000 CV Physiology

Homework Assignment Cell Membrane Simulations

Bioengineering 6000 CV PhysiologyHomework: AP Simulation

Question 1: All or Nothing?

• What is all or nothing?– Threshold– Only two states, all, or nothing, independent of variations other than

threshold being reached.• Does the model replicate this behavior?• What consequences does the answer have on subsequent

simulations?– Where to set threshold in later questions?

Bioengineering 6000 CV PhysiologyHomework: AP Simulation

Probing the Stimulation Space

1 2 4 6 8

5

10

15

20

25

No No No No Yes

No No No No Yes

No No No No Yes

No No No No Yes

No No Yes Yes Yes

Stimulus Duration [ms]

Stim

ulus

Am

plitu

de [µ

A/c

m2 ]

Bioengineering 6000 CV PhysiologyHomework: AP Simulation

Probing the Stimulation Space

1 2 4 6 8

5

10

15

20

25

No No No No Yes

No No No No Yes

No No No No Yes

No No No No Yes

No No Yes Yes Yes

Stimulus Duration [ms]

Stim

ulus

Am

plitu

de [µ

A/c

m2 ]

Bioengineering 6000 CV PhysiologyHomework: AP Simulation

Question 1: All or Nothing?Probing the 2D simulation space

Bioengineering 6000 CV PhysiologyHomework: AP Simulation

All or Nothing Example

Stimulus fixed at 8 msVaried in amplitude

The Problem?

Stimulus carries over to the response of the membrane; it is too long.

0

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0 1.25 2.5 3.75 5

y = -6.3003x + 34.033R² = 0.8477

R

2 = 0.85y = �6.3x + 34.0

Bioengineering 6000 CV PhysiologyHomework: AP Simulation

Question #1: Cell Stimulation

Ith (µA/cm^2)

ΔTth

(ms)1/ΔTth

32.5 1 1.0

30 1 1.0

27.5 1.5 0.7

25 1.5 0.7

22.5 1.5 0.7

20 2 0.5

17.5 2 0.5

15 2.5 0.4

12.5 3 0.3

10 3.5 0.3

7.5 5 0.2Intensity vs. Duration

0

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0 1.25 2.5 3.75 5

y = -15.973ln(x) + 30.861R² = 0.9553

R

2 = 0.96y = �16 ln(x) + 30.86

Bioengineering 6000 CV PhysiologyHomework: AP Simulation

Question #1: Cell Stimulation

Intensity vs. Duration

Ith (µA/cm^2)

ΔTth

(ms)1/ΔTth

32.5 1 1.0

30 1 1.0

27.5 1.5 0.7

25 1.5 0.7

22.5 1.5 0.7

20 2 0.5

17.5 2 0.5

15 2.5 0.4

12.5 3 0.3

10 3.5 0.3

7.5 5 0.2

0

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30

40

0 1.25 2.5 3.75 5

y = 1.8931x2 - 17.181x + 46.35

R² = 0.9693

R

2 = 0.97y = 1.89x

2 � 17.2x + 46.4

Bioengineering 6000 CV PhysiologyHomework: AP Simulation

Question #1: Cell Stimulation

Intensity vs. Duration

Ith (µA/cm^2)

ΔTth

(ms)1/ΔTth

32.5 1 1.0

30 1 1.0

27.5 1.5 0.7

25 1.5 0.7

22.5 1.5 0.7

20 2 0.5

17.5 2 0.5

15 2.5 0.4

12.5 3 0.3

10 3.5 0.3

7.5 5 0.2

0

10

20

30

40

0 1.25 2.5 3.75 5

y = 42.559e-0.3805x

R² = 0.9507

Stim

ulus

Inte

nsity

(µA

/cm

2

Duration (ms)

R

2 = 0.95y = 42.6e

�0.38x

Bioengineering 6000 CV PhysiologyHomework: AP Simulation

Question #1: Cell Stimulation

Ith (µA/cm^2)

ΔTth

(ms)1/ΔTth

32.5 1 1.0

30 1 1.0

27.5 1.5 0.7

25 1.5 0.7

22.5 1.5 0.7

20 2 0.5

17.5 2 0.5

15 2.5 0.4

12.5 3 0.3

10 3.5 0.3

7.5 5 0.2

Bioengineering 6000 CV PhysiologyHomework: AP Simulation

Membrane Voltage

E kE Na E Ca

g Na g K g Ca

C m

Outside

Inside

E

Think Charge!

0

10

20

30

40

0 0.25 0.5 0.75 1

y = 30.123x + 2.9395

R² = 0.9387

Stim

ulus

Inte

nsity

(µs/

cm2)

1/Duration (1/ms)

y = mx + b Ith = K(1/Tth) + I0

K = IthTth = Qth

Qth � 30 nC/cm2

Bioengineering 6000 CV PhysiologyHomework: AP Simulation

Question #1: Cell Stimulation

Ith (µA/cm^2)

ΔTth

(ms)1/ΔTth

32.5 1 1.0

30 1 1.0

27.5 1.5 0.7

25 1.5 0.7

22.5 1.5 0.7

20 2 0.5

17.5 2 0.5

15 2.5 0.4

12.5 3 0.3

10 3.5 0.3

7.5 5 0.2

Bioengineering 6000 CV PhysiologyHomework: AP Simulation

Question 2: Effect of [Na+]e

• Interpretation of low [Na+]e– Think of driving

force; even is concentration gradient eliminated potential gradient exists!

– Hypothesis about ICa

– Both hypotheses are easy to test with simulation

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Bioengineering 6000 CV PhysiologyHomework: AP Simulation

When in Doubt, Check the Simulation

Bioengineering 6000 CV PhysiologyHomework: AP Simulation

Be Careful with Axes

Bioengineering 6000 CV PhysiologyHomework: AP Simulation

Scale is Essential

Bioengineering 6000 CV PhysiologyHomework: AP Simulation

Scale is Essential

HumanHair

Bioengineering 6000 CV PhysiologyHomework: AP Simulation

Creating Clear Graphs/Figures

Bioengineering 6000 CV PhysiologyHomework: AP Simulation

Generating Secondary Results

Bioengineering 6000 CV PhysiologyHomework: AP Simulation

More Secondary Results

Bioengineering 6000 CV PhysiologyHomework: AP Simulation

Question 3• Question #3

– Try to motivate with some physiology or pathophysiology– Examine all parameters to try and identify mechanisms– Use the simulations to explore mechanisms--they reveal the

answers many times in a way the experiments cannot!!E.g., Vary Ca+2 concentration

Bioengineering 6000 CV PhysiologyHomework: AP Simulation

Cell Simulation: General I

• Organize simulations– Develop a strategy to answer the question– Vary as few parameters at a time as possible– Use reasonable (physiological) ranges of values– Examine the relevant parameters (often good to start by looking

at all and identify relevant ones)• Develop second order results where appropriate

– e.g., plot of stimulus duration vs. stimulus– e.g., APD vs concentration

• Use results of analysis to motivate more simulations– Use to uncover mechanisms

Bioengineering 6000 CV PhysiologyHomework: AP Simulation

Cell Simulation: General II

• Organization of report– Mimic the flow of the questions and answer all parts

• Plots and graphs– Include axes with labels– Include legends– Include concise captions– Export figures rather than screen capture– Embed all figures into the running text

• Text– Use past tense to report all methods and results– Adopt formal scientific prose style– Strive for concise, clear, accurate descriptions

• Use tables to show sets of results

Bioengineering 6000 CV PhysiologyHomework: AP Simulation

What is Wrong with this Plot?

Bioengineering 6000 CV PhysiologyHomework: AP Simulation

And this one...

Pixelated, especially text

Bioengineering 6000 CV PhysiologyHomework: AP Simulation

And this one...

Rule of thumb: Figure fonts should be approximately the same as surrounding text.

Bioengineering 6000 CV PhysiologyHomework: AP Simulation

And one more... No titles for figures

Caption should not contain interpretation.

Bioengineering 6000 CV PhysiologyHomework: AP Simulation

Mastering MATLAB Plots

Bioengineering 6000 CV PhysiologyHomework: AP Simulation

Including Only What is Useful

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Replace all this with this!

Include only What you Refer To!