Neurovascular Coupling Mark Freeman Adam Mauskopf Shuyan Mei Kimberly Stanke Zihao Yan Fields Institute August 26, 2014 Neuro Group August 26, 2014 1 / 1
Neuron Network Model Adam Mauskopf, Shuyan Mei August 27, 2014 Adam Mauskopf, Shuyan Mei Neuron Network Model August 27, 2014 1 / 22
Background 1 Why are we studying the neuron network model? 2 What did we study for the neuron network model? Adam Mauskopf, Shuyan Mei Neuron Network Model August 27, 2014 2 / 22
Model Description 1 Single Neuron Dynamics 2 Neuron Network Dynamics Adam Mauskopf, Shuyan Mei Neuron Network Model August 27, 2014 3 / 22
Model Description Physical Parameters Of The Neurons Considered 1 Voltage, Sodium, Potassium, Chlorine, Calcium, 2 Gating Variables n and h. Adam Mauskopf, Shuyan Mei Neuron Network Model August 27, 2014 4 / 22
Network Schismatic Adam Mauskopf, Shuyan Mei Neuron Network Model August 27, 2014 5 / 22
Model Description Difference between single and network neuron model 1 Leak Current 2 Synaptic Current 3 Potassium Adam Mauskopf, Shuyan Mei Neuron Network Model August 27, 2014 6 / 22
Single Neuron Current Equations: I Na = − g Na [ m ∞ ( V )] 3 h ( V − V Na ) − g NaL ( V − V Na ) . I K = − ( g K n 4 + g AHP [ Ca ] i )( V − V K ) − g KL ( V − V K ) . 1 + [ Ca ] i I Cl = − g Cl L ( V − V Cl ) . ρ 1 . 0 I pump = ( 1 + exp (( 25 . 0 − [ Na ] i )/ 3 . 0 ))( 1 . 0 + exp ( 5 . 5 − [ K ] o )) . G glia I glia = 1 . 0 + exp (( 18 − [ K ] o )/ 2 . 5 ) . I diff = ǫ ([ K ] o − k 0 , ∞ ) . Adam Mauskopf, Shuyan Mei Neuron Network Model August 27, 2014 7 / 22
Single Neuron Differential Equations: C dV dt = I Na + I K + I Cl . dq dt = φ [ α q ( V )( 1 − q ) − β q ( V ) q ] , q = n , h . d [ Ca ] i − 0 . 002 g Ca ( V − V Ca ) 1 + exp (−( V + 25 )/ 2 . 5 ) − [ Ca ] i / 80 . = dt d [ K ] o = − 0 . 33 I K − 2 β I pump − I glia − I diff . dt d [ Na ] i = 0 . 33 I Na β − 3 I pump . dt Adam Mauskopf, Shuyan Mei Neuron Network Model August 27, 2014 8 / 22
Single Neuron Supporting Equations: m ∞ ( V ) = α m ( V )/( α m ( V ) + β m ( V )) . α m ( V ) = 0 . 1 ( V + 30 )/( 1 − exp ( − 0 . 1 ( V + 30 ))) . β m ( V ) = 4 exp ( − ( V + 55 )/ 18 )) . α n ( V ) = 0 . 01 ( V + 34 )/( 1 − exp ( − 0 . 1 ( V + 34 ))) . β m ( V ) = 0 . 125 exp ( − ( V + 44 )/ 80 )) . α h ( V ) = 0 . 07 ( − ( V + 44 )/ 20 ) . β h ( V ) = 1 /[ 1 + exp ( − 0 . 1 ( V + 4 ))] . Adam Mauskopf, Shuyan Mei Neuron Network Model August 27, 2014 9 / 22
Neuron Network Current Equations: ∞ ( V e / i )] 3 h e / i ( V e / i − V e / i I e / i Na = − g Na [ m e / i Na ) . = −( g K [ n e / i ] 4 + g AHP [ Ca ] e / i )( V e / i − V e / i I e / i i K ) . K 1 + [ Ca ] e / i i = − g L ( V e / i − V e / i I e / i L ) . L ( V e j − V ee ) ( V e j − V ie ) N N I e syn = − g ee jk s e k χ e jk − g ie jk s i k χ i ∑ ∑ jk . N N k = 1 k = 1 ( V i j − V ei ) ( V i j − V ii ) N N I i syn = − g ei jk s e k χ e jk − g ii jk s i k χ i ∑ ∑ jk . N N k = 1 k = 1 Adam Mauskopf, Shuyan Mei Neuron Network Model August 27, 2014 10 / 22
Neuron Network Current Equations Cont’d: 1 . 25 1 . 0 I e / i pump = ( )( ) . 1 + exp (( 25 . 0 − [ Na ] e / i 1 . 0 + exp ( 8 . 0 − [ K ] e / i )/ 3 . 0 ) o ) i G glia I e / i glia = . 1 . 0 + exp (( 18 − [ K ] e / i o )/ 2 . 5 ) I e / i diff = ǫ ([ K ] e / i − k 0 , ∞ ) . o Adam Mauskopf, Shuyan Mei Neuron Network Model August 27, 2014 11 / 22
Neuron Network Differential Equations: C dV e / i = I e / i Na + I e / i + I e / i + I e / i syn + I e / i ext + I e / i rand . K L dt τ e / i ds e / i = φσ ( V e / i )( 1 − s e / i ) − s e / i . dt d η e / i = γ e / i ( V e / i − V b ) − ˜ γη e / i . dt d [ K ] e / i D o = 0 . 33 I e / i − 2 β I e / i pump − I e / i diff − I e / i glia + K ∆ x 2 dt ([ K ] e / i o (+) + [ K ] e / i o (−) + [ K ] i / e − 3 [ K ] e / i o ) . o d [ Na ] e / i = 0 . 33 I e / i β − 3 I e / i i Na pump . dt Adam Mauskopf, Shuyan Mei Neuron Network Model August 27, 2014 12 / 22
Neuron Network Supporting Equations: σ ( V e / i ) = 1 /[ 1 + exp ( − ( V e / i + 20 )/ 4 )] . jk = { exp ( − η e / i / v ) η e / i > 5 . 0 χ e / i 1 otherwise − 30 < V e / i < − 10 γ e / i = { 0 . 4 0 otherwise = 26 . 64 ln ([ K ] e / i + 0 . 065 [ Na ] e / i + 0 . 6 [ Cl ] e / i ) . o o V e / i i [ K ] e / i + 0 . 065 [ Na ] e / i + 0 . 6 [ Cl ] e / i L o i i Adam Mauskopf, Shuyan Mei Neuron Network Model August 27, 2014 13 / 22
Single Neuron Simulation Results The dynamics of membrane voltage, sodium, potassium at 100 ms. Adam Mauskopf, Shuyan Mei Neuron Network Model August 27, 2014 14 / 22
Single Neuron Simulation Results The dynamics of membrane voltage, sodium, potassium at 10000 ms. Adam Mauskopf, Shuyan Mei Neuron Network Model August 27, 2014 15 / 22
Single Neuron Simulation Results The dynamics of membrane voltage, sodium, potassium at 100000 ms. Adam Mauskopf, Shuyan Mei Neuron Network Model August 27, 2014 16 / 22
Neuron Network Simulation Results With 5 Neurons The dynamics of first neuron’s membrane voltage, sodium, potassium at 100 ms. Adam Mauskopf, Shuyan Mei Neuron Network Model August 27, 2014 17 / 22
Neuron Network Simulation Results With 5 Neurons The dynamics of first neuron’s membrane voltage, sodium, potassium at 1000 ms. Adam Mauskopf, Shuyan Mei Neuron Network Model August 27, 2014 18 / 22
Neuron Network Simulation Results With 5 Neurons The dynamics of first neuron’s membrane voltage, sodium, potassium at 10000 ms. Adam Mauskopf, Shuyan Mei Neuron Network Model August 27, 2014 19 / 22
Neuron Network Simulation Results With 5 Neurons The dynamics of third neuron’s membrane voltage, sodium, potassium at 100 ms. Adam Mauskopf, Shuyan Mei Neuron Network Model August 27, 2014 20 / 22
Neuron Network Simulation Results With 5 Neurons The dynamics of third neuron’s membrane voltage, sodium, potassium at 1000 ms. Adam Mauskopf, Shuyan Mei Neuron Network Model August 27, 2014 21 / 22
Neuron Network Simulation Results With 5 Neurons The dynamics of third neuron’s membrane voltage, sodium, potassium at 10000 ms. Adam Mauskopf, Shuyan Mei Neuron Network Model August 27, 2014 22 / 22
Circulation Model Mark Freeman and Kimberly Stanke Fields Institute markfreeman@college.harvard.edu kmstanke@mtu.edu August 26, 2014 Mark Freeman and Kimberly Stanke Fields August 26, 2014 1 / 10
FETAL HYPOXIA: WHAT IS IT? Episodes of low oxygenation in the fetus Often caused by occlusion of the umbilical cord, especially during labour Triggers deceleration of the fetal heart Mark Freeman and Kimberly Stanke Fields August 26, 2014 2 / 10
FETAL HYPOXIA: WHY STUDY IT? Tissues need steady supply of oxygen to stay alive Oxygen deprivation lowers blood pH and can lead to brain damage, but can also be asymptomatic Currently diagnosed based on fetal heart rate, but this is not a reliable predictor of whether the hypoxia is damaging Modelling fetal circulation could lead to better understanding, diagnostic methods Mark Freeman and Kimberly Stanke Fields August 26, 2014 3 / 10
THE BEATRIJS MODEL Combines previously published models of various components of the maternal and fetal cardiovascular system: Sarcomere movement in the maternal and fetal hearts [Bovendeered, et al (2006)] Oxygen diffusion and partial pressure in the fetus [Sa Couto, et al (2002)] Uterine contractions during labour [Rodbard, et al (1963), Fung, et al (1997)] Blood flow through the maternal and fetal circulatory systems Regulatory changes to the fetal heart rate in response to low [Metcalfe, et al (1967)] oxygen concentration Mark Freeman and Kimberly Stanke Fields August 26, 2014 4 / 10
THE BEATRIJS MODEL Mark Freeman and Kimberly Stanke Fields August 26, 2014 5 / 10
TESTING BEATRIJS: OVINE EXPERIMENTS Sheep umbilical cords fitted with devices designed to cause occlusions Occlusions of increasingly large magnitude induced in late- term sheep fetuses periodically, interspersed with rest periods Fetal biological parameters measured and compared with output of Beatrijs model Majority of graphs output from Beatrijs model deemed realistic by panel of gynaecologists Mark Freeman and Kimberly Stanke Fields August 26, 2014 6 / 10
TESTING BEATRIJS: OVINE EXPERIMENTS Mark Freeman and Kimberly Stanke Fields August 26, 2014 7 / 10
TESTING BEATRIJS: REPRODUCING THE MODEL Uterine contractions successfully reproduced Mark Freeman and Kimberly Stanke Fields August 26, 2014 8 / 10
TESTING BEATRIJS: REPRODUCING THE MODEL Difficulty reproducing the rest of the models results: Initial conditions used by Beatrijs not stated in paper Circuit diagram describing arrangement, properties of model components inaccurate Erroneously printed equations Discrepancies, implicit contradictions between published volume parameters Paper unclear on models treatment of retrograde blood flow during expansion phase of each heartbeat Authors known to have used Euler Method to numerically solve system; unclear whether they discretized the system in the process Mark Freeman and Kimberly Stanke Fields August 26, 2014 9 / 10
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