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R4670 PySONIC (old)
nbls.py
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# -*- coding: utf-8 -*-
# @Author: Theo Lemaire
# @Email: theo.lemaire@epfl.ch
# @Date: 2016-09-29 16:16:19
# @Last Modified by: Theo Lemaire
# @Last Modified time: 2019-06-17 21:42:00
from
copy
import
deepcopy
import
logging
import
numpy
as
np
import
pandas
as
pd
from
scipy.interpolate
import
interp1d
from
scipy.integrate
import
solve_ivp
from
.simulators
import
PWSimulator
,
HybridSimulator
,
PeriodicSimulator
from
.bls
import
BilayerSonophore
from
.pneuron
import
PointNeuron
from
.model
import
Model
from
.batches
import
createQueue
from
..neurons
import
getLookups2D
,
getLookupsDCavg
from
..utils
import
*
from
..constants
import
*
from
..postpro
import
getFixedPoints
class
NeuronalBilayerSonophore
(
BilayerSonophore
):
''' This class inherits from the BilayerSonophore class and receives an PointNeuron instance
at initialization, to define the electro-mechanical NICE model and its SONIC variant. '''
tscale
=
'ms'
# relevant temporal scale of the model
simkey
=
'ASTIM'
# keyword used to characterize simulations made with this model
def
__init__
(
self
,
a
,
pneuron
,
Fdrive
=
None
,
embedding_depth
=
0.0
):
''' Constructor of the class.
:param a: in-plane radius of the sonophore structure within the membrane (m)
:param pneuron: point-neuron model
:param Fdrive: frequency of acoustic perturbation (Hz)
:param embedding_depth: depth of the embedding tissue around the membrane (m)
'''
# Check validity of input parameters
if
not
isinstance
(
pneuron
,
PointNeuron
):
raise
ValueError
(
'Invalid neuron type: "{}" (must inherit from PointNeuron class)'
.
format
(
pneuron
.
name
))
self
.
pneuron
=
pneuron
# Initialize BilayerSonophore parent object
BilayerSonophore
.
__init__
(
self
,
a
,
pneuron
.
Cm0
,
pneuron
.
Qm0
,
embedding_depth
)
def
__repr__
(
self
):
s
=
'{}({:.1f} nm, {}'
.
format
(
self
.
__class__
.
__name__
,
self
.
a
*
1e9
,
self
.
pneuron
)
if
self
.
d
>
0.
:
s
+=
', d={}m'
.
format
(
si_format
(
self
.
d
,
precision
=
1
,
space
=
' '
))
return
s
+
')'
def
params
(
self
):
params
=
super
()
.
params
()
params
.
update
(
self
.
pneuron
.
params
())
return
params
def
getPltVars
(
self
,
wrapleft
=
'df["'
,
wrapright
=
'"]'
):
pltvars
=
super
()
.
getPltVars
(
wrapleft
,
wrapright
)
pltvars
.
update
(
self
.
pneuron
.
getPltVars
(
wrapleft
,
wrapright
))
return
pltvars
def
getPltScheme
(
self
):
return
self
.
pneuron
.
getPltScheme
()
def
filecode
(
self
,
*
args
):
return
Model
.
filecode
(
self
,
*
args
)
def
inputVars
(
self
):
# Get parent input vars and supress irrelevant entries
bls_vars
=
super
()
.
inputVars
()
pneuron_vars
=
self
.
pneuron
.
inputVars
()
del
bls_vars
[
'Qm'
]
del
pneuron_vars
[
'Astim'
]
# Fill in current input vars in appropriate order
inputvars
=
bls_vars
inputvars
.
update
(
pneuron_vars
)
inputvars
[
'method'
]
=
None
return
inputvars
def
filecodes
(
self
,
Fdrive
,
Adrive
,
tstim
,
toffset
,
PRF
,
DC
,
method
=
'sonic'
):
# Get parent codes and supress irrelevant entries
bls_codes
=
super
()
.
filecodes
(
Fdrive
,
Adrive
,
0.0
)
pneuron_codes
=
self
.
pneuron
.
filecodes
(
0.0
,
tstim
,
toffset
,
PRF
,
DC
)
for
x
in
[
bls_codes
,
pneuron_codes
]:
del
x
[
'simkey'
]
del
bls_codes
[
'Qm'
]
del
pneuron_codes
[
'Astim'
]
# Fill in current codes in appropriate order
codes
=
{
'simkey'
:
self
.
simkey
,
'neuron'
:
pneuron_codes
.
pop
(
'neuron'
),
'nature'
:
pneuron_codes
.
pop
(
'nature'
)
}
codes
.
update
(
bls_codes
)
codes
.
update
(
pneuron_codes
)
codes
[
'method'
]
=
method
return
codes
def
fullDerivatives
(
self
,
t
,
y
,
Adrive
,
Fdrive
,
phi
):
''' Compute the derivatives of the (n+3) ODE full NBLS system variables.
:param t: specific instant in time (s)
:param y: vector of state variables
:param Adrive: acoustic drive amplitude (Pa)
:param Fdrive: acoustic drive frequency (Hz)
:param phi: acoustic drive phase (rad)
:return: vector of derivatives
'''
dydt_mech
=
BilayerSonophore
.
derivatives
(
self
,
t
,
y
[:
3
],
Adrive
,
Fdrive
,
y
[
3
],
phi
)
dydt_elec
=
self
.
pneuron
.
Qderivatives
(
t
,
y
[
3
:],
self
.
Capct
(
y
[
1
]))
return
dydt_mech
+
dydt_elec
def
effDerivatives
(
self
,
t
,
y
,
lkp
):
''' Compute the derivatives of the n-ODE effective HH system variables,
based on 1-dimensional linear interpolation of "effective" coefficients
that summarize the system's behaviour over an acoustic cycle.
:param t: specific instant in time (s)
:param y: vector of HH system variables at time t
:param lkp: dictionary of 1D data points of "effective" coefficients
over the charge domain, for specific frequency and amplitude values.
:return: vector of effective system derivatives at time t
'''
# Split input vector explicitly
Qm
,
*
states
=
y
# Compute charge and channel states variation
Vmeff
=
self
.
pneuron
.
interpVmeff
(
Qm
,
lkp
)
dQmdt
=
-
self
.
pneuron
.
iNet
(
Vmeff
,
states
)
*
1e-3
dstates
=
self
.
pneuron
.
derEffStates
(
Qm
,
states
,
lkp
)
# Return derivatives vector
return
[
dQmdt
,
*
[
dstates
[
k
]
for
k
in
self
.
pneuron
.
states
]]
def
interpEffVariable
(
self
,
key
,
Qm
,
stim
,
lkps1D
):
''' Interpolate Q-dependent effective variable along solution.
:param key: lookup variable key
:param Qm: charge density solution vector
:param stim: stimulation state solution vector
:param lkps1D: dictionary of lookups for ON and OFF states
:return: interpolated effective variable vector
'''
x
=
np
.
zeros
(
stim
.
size
)
x
[
stim
==
0
]
=
np
.
interp
(
Qm
[
stim
==
0
],
lkps1D
[
'OFF'
][
'Q'
],
lkps1D
[
'OFF'
][
key
],
left
=
np
.
nan
,
right
=
np
.
nan
)
x
[
stim
==
1
]
=
np
.
interp
(
Qm
[
stim
==
1
],
lkps1D
[
'ON'
][
'Q'
],
lkps1D
[
'ON'
][
key
],
left
=
np
.
nan
,
right
=
np
.
nan
)
return
x
def
runFull
(
self
,
Fdrive
,
Adrive
,
tstim
,
toffset
,
PRF
,
DC
,
phi
=
np
.
pi
):
''' Compute solutions of the full electro-mechanical system for a specific set of
US stimulation parameters, using a classic integration scheme.
The first iteration uses the quasi-steady simplification to compute
the initiation of motion from a flat leaflet configuration. Afterwards,
the ODE system is solved iteratively until completion.
:param Fdrive: acoustic drive frequency (Hz)
:param Adrive: acoustic drive amplitude (Pa)
:param tstim: duration of US stimulation (s)
:param toffset: duration of the offset (s)
:param PRF: pulse repetition frequency (Hz)
:param DC: pulse duty cycle (-)
:param phi: acoustic drive phase (rad)
:return: 2-tuple with the output dataframe and computation time.
'''
# Determine time step
dt
=
1
/
(
NPC_DENSE
*
Fdrive
)
# Compute non-zero deflection value for a small perturbation (solving quasi-steady equation)
Pac
=
self
.
Pacoustic
(
dt
,
Adrive
,
Fdrive
,
phi
)
Z0
=
self
.
balancedefQS
(
self
.
ng0
,
self
.
Qm0
,
Pac
)
# Set initial conditions
steady_states
=
self
.
pneuron
.
steadyStates
(
self
.
pneuron
.
Vm0
)
y0
=
np
.
concatenate
((
[
0.
,
Z0
,
self
.
ng0
,
self
.
Qm0
],
[
steady_states
[
k
]
for
k
in
self
.
pneuron
.
states
]))
# Initialize simulator and compute solution
logger
.
debug
(
'Computing detailed solution'
)
simulator
=
PWSimulator
(
lambda
t
,
y
:
self
.
fullDerivatives
(
t
,
y
,
Adrive
,
Fdrive
,
phi
),
lambda
t
,
y
:
self
.
fullDerivatives
(
t
,
y
,
0.
,
0.
,
0.
))
(
t
,
y
,
stim
),
tcomp
=
simulator
(
y0
,
dt
,
tstim
,
toffset
,
PRF
,
DC
,
print_progress
=
logger
.
getEffectiveLevel
()
<=
logging
.
INFO
,
target_dt
=
CLASSIC_TARGET_DT
,
monitor_time
=
True
)
logger
.
debug
(
'completed in
%s
s'
,
si_format
(
tcomp
,
1
))
# Store output in dataframe
data
=
pd
.
DataFrame
({
't'
:
t
,
'stimstate'
:
stim
,
'Z'
:
y
[:,
1
],
'ng'
:
y
[:,
2
],
'Qm'
:
y
[:,
3
]
})
data
[
'Vm'
]
=
data
[
'Qm'
]
.
values
/
self
.
v_Capct
(
data
[
'Z'
]
.
values
)
*
1e3
# mV
for
i
in
range
(
len
(
self
.
pneuron
.
states
)):
data
[
self
.
pneuron
.
states
[
i
]]
=
y
[:,
i
+
4
]
# Return dataframe and computation time
return
data
,
tcomp
def
runHybrid
(
self
,
Fdrive
,
Adrive
,
tstim
,
toffset
,
PRF
,
DC
,
phi
=
np
.
pi
):
''' Compute solutions of the system for a specific set of
US stimulation parameters, using a hybrid integration scheme.
:param Fdrive: acoustic drive frequency (Hz)
:param Adrive: acoustic drive amplitude (Pa)
:param tstim: duration of US stimulation (s)
:param toffset: duration of the offset (s)
:param phi: acoustic drive phase (rad)
:return: 3-tuple with the time profile, the solution matrix and a state vector
'''
# Determine time steps
dt_dense
,
dt_sparse
=
[
1.
/
(
n
*
Fdrive
)
for
n
in
[
NPC_DENSE
,
NPC_SPARSE
]]
# Compute non-zero deflection value for a small perturbation (solving quasi-steady equation)
Pac
=
self
.
Pacoustic
(
dt_dense
,
Adrive
,
Fdrive
,
phi
)
Z0
=
self
.
balancedefQS
(
self
.
ng0
,
self
.
Qm0
,
Pac
)
# Set initial conditions
steady_states
=
self
.
pneuron
.
steadyStates
(
self
.
pneuron
.
Vm0
)
y0
=
np
.
concatenate
((
[
0.
,
Z0
,
self
.
ng0
,
self
.
Qm0
],
[
steady_states
[
k
]
for
k
in
self
.
pneuron
.
states
],
))
is_dense_var
=
np
.
array
([
True
]
*
3
+
[
False
]
*
(
len
(
self
.
pneuron
.
states
)
+
1
))
# Initialize simulator and compute solution
logger
.
debug
(
'Computing hybrid solution'
)
simulator
=
HybridSimulator
(
lambda
t
,
y
:
self
.
fullDerivatives
(
t
,
y
,
Adrive
,
Fdrive
,
phi
),
lambda
t
,
y
:
self
.
fullDerivatives
(
t
,
y
,
0.
,
0.
,
0.
),
lambda
t
,
y
,
Cm
:
self
.
pneuron
.
Qderivatives
(
t
,
y
,
Cm
),
lambda
yref
:
self
.
Capct
(
yref
[
1
]),
is_dense_var
,
ivars_to_check
=
[
1
,
2
])
(
t
,
y
,
stim
),
tcomp
=
simulator
(
y0
,
dt_dense
,
dt_sparse
,
1.
/
Fdrive
,
tstim
,
toffset
,
PRF
,
DC
,
monitor_time
=
True
)
logger
.
debug
(
'completed in
%s
s'
,
si_format
(
tcomp
,
1
))
# Store output in dataframe
data
=
pd
.
DataFrame
({
't'
:
t
,
'stimstate'
:
stim
,
'Z'
:
y
[:,
1
],
'ng'
:
y
[:,
2
],
'Qm'
:
y
[:,
3
]
})
data
[
'Vm'
]
=
data
[
'Qm'
]
.
values
/
self
.
v_Capct
(
data
[
'Z'
]
.
values
)
*
1e3
# mV
for
i
in
range
(
len
(
self
.
pneuron
.
states
)):
data
[
self
.
pneuron
.
states
[
i
]]
=
y
[:,
i
+
4
]
# Return dataframe and computation time
return
data
,
tcomp
def
computeEffVars
(
self
,
Fdrive
,
Adrive
,
Qm
,
fs
):
''' Compute "effective" coefficients of the HH system for a specific
combination of stimulus frequency, stimulus amplitude and charge density.
A short mechanical simulation is run while imposing the specific charge density,
until periodic stabilization. The HH coefficients are then averaged over the last
acoustic cycle to yield "effective" coefficients.
:param Fdrive: acoustic drive frequency (Hz)
:param Adrive: acoustic drive amplitude (Pa)
:param Qm: imposed charge density (C/m2)
:param fs: list of sonophore membrane coverage fractions
:return: list with computation time and a list of dictionaries of effective variables
'''
# Run simulation and retrieve deflection and gas content vectors from last cycle
data
,
tcomp
=
BilayerSonophore
.
simulate
(
self
,
Fdrive
,
Adrive
,
Qm
)
Z_last
=
data
.
loc
[
-
NPC_DENSE
:,
'Z'
]
.
values
# m
Cm_last
=
self
.
v_Capct
(
Z_last
)
# F/m2
# For each coverage fraction
effvars
=
[]
for
x
in
fs
:
# Compute membrane capacitance and membrane potential vectors
Cm
=
x
*
Cm_last
+
(
1
-
x
)
*
self
.
Cm0
# F/m2
Vm
=
Qm
/
Cm
*
1e3
# mV
# Compute average cycle value for membrane potential and rate constants
effvars
.
append
({
'V'
:
np
.
mean
(
Vm
)})
effvars
[
-
1
]
.
update
(
self
.
pneuron
.
computeEffRates
(
Vm
))
# Log process
log
=
'{}: lookups @ {}Hz, {}Pa, {:.2f} nC/cm2'
.
format
(
self
,
*
si_format
([
Fdrive
,
Adrive
],
precision
=
1
,
space
=
' '
),
Qm
*
1e5
)
if
len
(
fs
)
>
1
:
log
+=
', fs = {:.0f} - {:.0f}%'
.
format
(
fs
.
min
()
*
1e2
,
fs
.
max
()
*
1e2
)
log
+=
', tcomp = {:.3f} s'
.
format
(
tcomp
)
logger
.
info
(
log
)
# Return effective coefficients
return
[
tcomp
,
effvars
]
def
runSONIC
(
self
,
Fdrive
,
Adrive
,
tstim
,
toffset
,
PRF
,
DC
):
''' Compute solutions of the system for a specific set of
US stimulation parameters, using charge-predicted "effective"
coefficients to solve the HH equations at each step.
:param Fdrive: acoustic drive frequency (Hz)
:param Adrive: acoustic drive amplitude (Pa)
:param tstim: duration of US stimulation (s)
:param toffset: duration of the offset (s)
:param PRF: pulse repetition frequency (Hz)
:param DC: pulse duty cycle (-)
:return: 3-tuple with the time profile, the effective solution matrix and a state vector
'''
# Load appropriate 2D lookups
Aref
,
Qref
,
lkps2D
,
_
=
getLookups2D
(
self
.
pneuron
.
name
,
a
=
self
.
a
,
Fdrive
=
Fdrive
)
# Check that acoustic amplitude is within lookup range
Adrive
=
isWithin
(
'amplitude'
,
Adrive
,
(
Aref
.
min
(),
Aref
.
max
()))
# Interpolate 2D lookups at zero and US amplitude
logger
.
debug
(
'Interpolating lookups at A =
%.2f
kPa and A = 0'
,
Adrive
*
1e-3
)
lkps1D
=
{
state
:
{
key
:
interp1d
(
Aref
,
y2D
,
axis
=
0
)(
val
)
for
key
,
y2D
in
lkps2D
.
items
()}
for
state
,
val
in
{
'ON'
:
Adrive
,
'OFF'
:
0.
}
.
items
()}
# Add reference charge vector to 1D lookup dictionaries
for
state
in
lkps1D
.
keys
():
lkps1D
[
state
][
'Q'
]
=
Qref
# Set initial conditions
steady_states
=
self
.
pneuron
.
steadyStates
(
self
.
pneuron
.
Vm0
)
y0
=
np
.
insert
(
np
.
array
([
steady_states
[
k
]
for
k
in
self
.
pneuron
.
states
]),
0
,
self
.
Qm0
)
# Initialize simulator and compute solution
logger
.
debug
(
'Computing effective solution'
)
simulator
=
PWSimulator
(
lambda
t
,
y
:
self
.
effDerivatives
(
t
,
y
,
lkps1D
[
'ON'
]),
lambda
t
,
y
:
self
.
effDerivatives
(
t
,
y
,
lkps1D
[
'OFF'
]))
(
t
,
y
,
stim
),
tcomp
=
simulator
(
y0
,
DT_EFFECTIVE
,
tstim
,
toffset
,
PRF
,
DC
,
monitor_time
=
True
)
logger
.
debug
(
'completed in
%s
s'
,
si_format
(
tcomp
,
1
))
# Store output in dataframe
data
=
pd
.
DataFrame
({
't'
:
t
,
'stimstate'
:
stim
,
'Qm'
:
y
[:,
0
]
})
data
[
'Vm'
]
=
self
.
interpEffVariable
(
'V'
,
data
[
'Qm'
]
.
values
,
stim
,
lkps1D
)
for
key
in
[
'Z'
,
'ng'
]:
data
[
key
]
=
np
.
full
(
t
.
size
,
np
.
nan
)
for
i
in
range
(
len
(
self
.
pneuron
.
states
)):
data
[
self
.
pneuron
.
states
[
i
]]
=
y
[:,
i
+
1
]
# Return dataframe and computation time
return
data
,
tcomp
def
meta
(
self
,
Fdrive
,
Adrive
,
tstim
,
toffset
,
PRF
,
DC
,
method
):
''' Return information about object and simulation parameters.
:param Fdrive: US frequency (Hz)
:param Adrive: acoustic drive amplitude (Pa)
:param tstim: stimulus duration (s)
:param toffset: stimulus offset (s)
:param PRF: pulse repetition frequency (Hz)
:param DC: stimulus duty cycle (-)
:param method: integration method
:return: meta-data dictionary
'''
return
{
'simkey'
:
self
.
simkey
,
'neuron'
:
self
.
pneuron
.
name
,
'a'
:
self
.
a
,
'd'
:
self
.
d
,
'Fdrive'
:
Fdrive
,
'Adrive'
:
Adrive
,
'tstim'
:
tstim
,
'toffset'
:
toffset
,
'PRF'
:
PRF
,
'DC'
:
DC
,
'method'
:
method
}
def
simulate
(
self
,
Fdrive
,
Adrive
,
tstim
,
toffset
,
PRF
=
100.
,
DC
=
1.0
,
method
=
'sonic'
):
''' Simulate the electro-mechanical model for a specific set of US stimulation parameters,
and return output data in a dataframe.
:param Fdrive: acoustic drive frequency (Hz)
:param Adrive: acoustic drive amplitude (Pa)
:param tstim: duration of US stimulation (s)
:param toffset: duration of the offset (s)
:param PRF: pulse repetition frequency (Hz)
:param DC: pulse duty cycle (-)
:param method: selected integration method
:return: 2-tuple with the output dataframe and computation time.
'''
logger
.
info
(
'
%s
: simulation @ f =
%s
Hz, A =
%s
Pa, t =
%s
s (
%s
s offset)
%s
'
,
self
,
si_format
(
Fdrive
,
0
,
space
=
' '
),
si_format
(
Adrive
,
2
,
space
=
' '
),
*
si_format
([
tstim
,
toffset
],
1
,
space
=
' '
),
(
', PRF = {}Hz, DC = {:.2f}%'
.
format
(
si_format
(
PRF
,
2
,
space
=
' '
),
DC
*
1e2
)
if
DC
<
1.0
else
''
))
# Check validity of stimulation parameters
BilayerSonophore
.
checkInputs
(
self
,
Fdrive
,
Adrive
,
0.0
,
0.0
)
self
.
pneuron
.
checkInputs
(
Adrive
,
tstim
,
toffset
,
PRF
,
DC
)
# Call appropriate simulation function
try
:
simfunc
=
{
'full'
:
self
.
runFull
,
'hybrid'
:
self
.
runHybrid
,
'sonic'
:
self
.
runSONIC
}[
method
]
except
KeyError
:
raise
ValueError
(
'Invalid integration method: "{}"'
.
format
(
method
))
data
,
tcomp
=
simfunc
(
Fdrive
,
Adrive
,
tstim
,
toffset
,
PRF
,
DC
)
# Log number of detected spikes
nspikes
=
self
.
pneuron
.
getNSpikes
(
data
)
logger
.
debug
(
'{} spike{} detected'
.
format
(
nspikes
,
plural
(
nspikes
)))
# Return dataframe and computation time
return
data
,
tcomp
@logCache
(
os
.
path
.
join
(
os
.
path
.
split
(
__file__
)[
0
],
'astim_titrations.log'
))
def
titrate
(
self
,
Fdrive
,
tstim
,
toffset
,
PRF
=
100.
,
DC
=
1.
,
method
=
'sonic'
,
xfunc
=
None
,
Arange
=
None
):
''' Use a binary search to determine the threshold amplitude needed to obtain
neural excitation for a given frequency, duration, PRF and duty cycle.
:param Fdrive: US frequency (Hz)
:param tstim: duration of US stimulation (s)
:param toffset: duration of the offset (s)
:param PRF: pulse repetition frequency (Hz)
:param DC: pulse duty cycle (-)
:param method: integration method
:param xfunc: function determining whether condition is reached from simulation output
:param Arange: search interval for Adrive, iteratively refined
:return: determined threshold amplitude (Pa)
'''
# Default output function
if
xfunc
is
None
:
xfunc
=
self
.
pneuron
.
titrationFunc
# Default amplitude interval
if
Arange
is
None
:
Arange
=
[
0.
,
getLookups2D
(
self
.
pneuron
.
name
,
a
=
self
.
a
,
Fdrive
=
Fdrive
)[
0
]
.
max
()]
return
binarySearch
(
lambda
x
:
xfunc
(
self
.
simulate
(
*
x
)[
0
]),
[
Fdrive
,
tstim
,
toffset
,
PRF
,
DC
,
method
],
1
,
Arange
,
THRESHOLD_CONV_RANGE_ASTIM
)
def
simQueue
(
self
,
freqs
,
amps
,
durations
,
offsets
,
PRFs
,
DCs
,
methods
,
outputdir
=
None
):
''' Create a serialized 2D array of all parameter combinations for a series of individual
parameter sweeps, while avoiding repetition of CW protocols for a given PRF sweep.
:param freqs: list (or 1D-array) of US frequencies
:param amps: list (or 1D-array) of acoustic amplitudes
:param durations: list (or 1D-array) of stimulus durations
:param offsets: list (or 1D-array) of stimulus offsets (paired with durations array)
:param PRFs: list (or 1D-array) of pulse-repetition frequencies
:param DCs: list (or 1D-array) of duty cycle values
:params methods: integration methods
:return: list of parameters (list) for each simulation
'''
method_ids
=
list
(
range
(
len
(
methods
)))
if
amps
is
None
:
amps
=
[
np
.
nan
]
DCs
=
np
.
array
(
DCs
)
queue
=
[]
if
1.0
in
DCs
:
queue
+=
createQueue
(
freqs
,
amps
,
durations
,
offsets
,
min
(
PRFs
),
1.0
,
method_ids
)
if
np
.
any
(
DCs
!=
1.0
):
queue
+=
createQueue
(
freqs
,
amps
,
durations
,
offsets
,
PRFs
,
DCs
[
DCs
!=
1.0
],
method_ids
)
for
item
in
queue
:
if
np
.
isnan
(
item
[
1
]):
item
[
1
]
=
None
item
[
-
1
]
=
methods
[
int
(
item
[
-
1
])]
if
outputdir
is
not
None
:
for
item
in
queue
:
item
.
insert
(
0
,
outputdir
)
return
queue
def
quasiSteadyStates
(
self
,
Fdrive
,
amps
=
None
,
charges
=
None
,
DCs
=
1.0
,
squeeze_output
=
False
):
''' Compute the quasi-steady state values of the neuron's gating variables
for a combination of US amplitudes, charge densities and duty cycles,
at a specific US frequency.
:param Fdrive: US frequency (Hz)
:param amps: US amplitudes (Pa)
:param charges: membrane charge densities (C/m2)
:param DCs: duty cycle value(s)
:return: 4-tuple with reference values of US amplitude and charge density,
as well as interpolated Vmeff and QSS gating variables
'''
# Get DC-averaged lookups interpolated at the appropriate amplitudes and charges
amps
,
charges
,
lookups
=
getLookupsDCavg
(
self
.
pneuron
.
name
,
self
.
a
,
Fdrive
,
amps
,
charges
,
DCs
)
# Compute QSS states using these lookups
nA
,
nQ
,
nDC
=
lookups
[
'V'
]
.
shape
QSS
=
{
k
:
np
.
empty
((
nA
,
nQ
,
nDC
))
for
k
in
self
.
pneuron
.
states
}
for
iA
in
range
(
nA
):
for
iDC
in
range
(
nDC
):
QSS_1D
=
self
.
pneuron
.
quasiSteadyStates
(
{
k
:
v
[
iA
,
:,
iDC
]
for
k
,
v
in
lookups
.
items
()})
for
k
in
QSS
.
keys
():
QSS
[
k
][
iA
,
:,
iDC
]
=
QSS_1D
[
k
]
# Compress outputs if needed
if
squeeze_output
:
QSS
=
{
k
:
v
.
squeeze
()
for
k
,
v
in
QSS
.
items
()}
lookups
=
{
k
:
v
.
squeeze
()
for
k
,
v
in
lookups
.
items
()}
# Return reference inputs and outputs
return
amps
,
charges
,
lookups
,
QSS
def
iNetQSS
(
self
,
Qm
,
Fdrive
,
Adrive
,
DC
):
''' Compute quasi-steady state net membrane current for a given combination
of US parameters and a given membrane charge density.
:param Qm: membrane charge density (C/m2)
:param Fdrive: US frequency (Hz)
:param Adrive: US amplitude (Pa)
:param DC: duty cycle (-)
:return: net membrane current (mA/m2)
'''
_
,
_
,
lookups
,
QSS
=
self
.
quasiSteadyStates
(
Fdrive
,
amps
=
Adrive
,
charges
=
Qm
,
DCs
=
DC
,
squeeze_output
=
True
)
return
self
.
pneuron
.
iNet
(
lookups
[
'V'
],
np
.
array
(
list
(
QSS
.
values
())))
# mA/m2
def
evaluateStability
(
self
,
Qm0
,
states0
,
lkp
):
''' Integrate the effective differential system from a given starting point,
until clear convergence or clear divergence is found.
:param Qm0: initial membrane charge density (C/m2)
:param states0: dictionary of initial states values
:param lkp: dictionary of 1D data points of "effective" coefficients
over the charge domain, for specific frequency and amplitude values.
:return: boolean indicating convergence state
'''
# Initialize y0 vector
t0
=
0.
y0
=
np
.
array
([
Qm0
]
+
list
(
states0
.
values
()))
# Initialize simulator and compute solution
# simulator = PeriodicSimulator(
# lambda t, y: self.effDerivatives(t, y, lkp),
# ivars_to_check=[0])
# simulator.stopfunc = simulator.stopFuncTmp
# simulator.refs = [Qm0]
# simulator.conv_thr = [QSS_Q_CONV_THR]
# simulator.div_thr = [QSS_Q_DIV_THR]
# simulator.t_history = QSS_HISTORY_INTERVAL
# t, y, stim = simulator.compute(
# y0,
# QSS_INTEGRATION_INTERVAL,
# QSS_INTEGRATION_INTERVAL,
# nmax=int(QSS_MAX_INTEGRATION_DURATION // QSS_INTEGRATION_INTERVAL)
# )
# conv = simulator.isAsymptoticallyStable(t, y, QSS_INTEGRATION_INTERVAL) != -1
# tf = t[-1]
# dQ = [y[-1, 0]]
# Initializing empty list to record evolution of charge deviation
n
=
int
(
QSS_HISTORY_INTERVAL
//
QSS_INTEGRATION_INTERVAL
)
# size of history
dQ
=
[]
# As long as there is no clear charge convergence or divergence
conv
,
div
=
False
,
False
tf
,
yf
=
t0
,
y0
while
not
conv
and
not
div
:
# Integrate system for small interval and retrieve final charge deviation
t0
,
y0
=
tf
,
yf
sol
=
solve_ivp
(
lambda
t
,
y
:
self
.
effDerivatives
(
t
,
y
,
lkp
),
[
t0
,
t0
+
QSS_INTEGRATION_INTERVAL
],
y0
,
method
=
'LSODA'
)
tf
,
yf
=
sol
.
t
[
-
1
],
sol
.
y
[:,
-
1
]
dQ
.
append
(
yf
[
0
]
-
Qm0
)
# logger.debug('{:.0f} ms: dQ = {:.5f} nC/cm2, avg dQ = {:.5f} nC/cm2'.format(
# tf * 1e3, dQ[-1] * 1e5, np.mean(dQ[-n:]) * 1e5))
# If last charge deviation is too large -> divergence
if
np
.
abs
(
dQ
[
-
1
])
>
QSS_Q_DIV_THR
:
div
=
True
# If last charge deviation or average deviation in recent history
# is small enough -> convergence
for
x
in
[
dQ
[
-
1
],
np
.
mean
(
dQ
[
-
n
:])]:
if
np
.
abs
(
x
)
<
QSS_Q_CONV_THR
:
conv
=
True
# If max integration duration is been reached -> error
if
tf
>
QSS_MAX_INTEGRATION_DURATION
:
logger
.
warning
(
'too many iterations (dQ = {:.5f} nC/cm2)'
.
format
(
dQ
[
-
1
]
*
1e5
))
conv
=
True
logger
.
debug
(
'{}vergence after {:.0f} ms: dQ = {:.5f} nC/cm2'
.
format
(
{
True
:
'con'
,
False
:
'di'
}[
conv
],
tf
*
1e3
,
dQ
[
-
1
]
*
1e5
))
return
conv
def
fixedPointsQSS
(
self
,
Fdrive
,
Adrive
,
DC
,
lkp
,
dQdt
):
''' Compute QSS fixed points along the charge dimension for a given combination
of US parameters, and determine their stability.
:param Fdrive: US frequency (Hz)
:param Adrive: US amplitude (Pa)
:param DC: duty cycle (-)
:param lkp: lookup dictionary for effective variables along charge dimension
:param dQdt: charge derivative profile along charge dimension
:return: 2-tuple with values of stable and unstable fixed points
'''
logger
.
debug
(
'A = {:.2f} kPa, DC = {:.0f}%'
.
format
(
Adrive
*
1e-3
,
DC
*
1e2
))
# Extract stable and unstable fixed points from QSS charge variation profile
def
dfunc
(
Qm
):
return
-
self
.
iNetQSS
(
Qm
,
Fdrive
,
Adrive
,
DC
)
SFP_candidates
=
getFixedPoints
(
lkp
[
'Q'
],
dQdt
,
filter
=
'stable'
,
der_func
=
dfunc
)
.
tolist
()
UFPs
=
getFixedPoints
(
lkp
[
'Q'
],
dQdt
,
filter
=
'unstable'
,
der_func
=
dfunc
)
.
tolist
()
SFPs
=
[]
pltvars
=
self
.
getPltVars
()
# For each candidate SFP
for
i
,
Qm
in
enumerate
(
SFP_candidates
):
logger
.
debug
(
'Q-SFP = {:.2f} nC/cm2'
.
format
(
Qm
*
1e5
))
# Re-compute QSS
*
_
,
QSS_FP
=
self
.
quasiSteadyStates
(
Fdrive
,
amps
=
Adrive
,
charges
=
Qm
,
DCs
=
DC
,
squeeze_output
=
True
)
# Simulate from unperturbed QSS and evaluate stability
if
not
self
.
evaluateStability
(
Qm
,
QSS_FP
,
lkp
):
logger
.
warning
(
'diverging system at ({:.2f} kPa, {:.2f} nC/cm2)'
.
format
(
Adrive
*
1e-3
,
Qm
*
1e5
))
UFPs
.
append
(
Qm
)
else
:
# For each state
unstable_states
=
[]
for
x
in
self
.
pneuron
.
states
:
pltvar
=
pltvars
[
x
]
unit_str
=
pltvar
.
get
(
'unit'
,
''
)
factor
=
pltvar
.
get
(
'factor'
,
1
)
is_stable_direction
=
[]
for
sign
in
[
-
1
,
+
1
]:
# Perturb state with small offset
QSS_perturbed
=
deepcopy
(
QSS_FP
)
QSS_perturbed
[
x
]
*=
(
1
+
sign
*
QSS_REL_OFFSET
)
# If gating state, bound within [0., 1.]
if
self
.
pneuron
.
isVoltageGated
(
x
):
QSS_perturbed
[
x
]
=
np
.
clip
(
QSS_perturbed
[
x
],
0.
,
1.
)
logger
.
debug
(
'{}: {:.5f} -> {:.5f} {}'
.
format
(
x
,
QSS_FP
[
x
]
*
factor
,
QSS_perturbed
[
x
]
*
factor
,
unit_str
))
# Simulate from perturbed QSS and evaluate stability
is_stable_direction
.
append
(
self
.
evaluateStability
(
Qm
,
QSS_perturbed
,
lkp
))
# Check if system shows stability upon x-state perturbation
# in both directions
if
not
np
.
all
(
is_stable_direction
):
unstable_states
.
append
(
x
)
# Classify fixed point as stable only if all states show stability
is_stable_FP
=
len
(
unstable_states
)
==
0
{
True
:
SFPs
,
False
:
UFPs
}[
is_stable_FP
]
.
append
(
Qm
)
logger
.
info
(
'{}stable fixed-point at ({:.2f} kPa, {:.2f} nC/cm2){}'
.
format
(
''
if
is_stable_FP
else
'un'
,
Adrive
*
1e-3
,
Qm
*
1e5
,
''
if
is_stable_FP
else
', caused by {} states'
.
format
(
unstable_states
)))
return
SFPs
,
UFPs
def
isStableQSS
(
self
,
Fdrive
,
Adrive
,
DC
):
_
,
Qref
,
lookups
,
QSS
=
self
.
quasiSteadyStates
(
Fdrive
,
amps
=
Adrive
,
DCs
=
DC
,
squeeze_output
=
True
)
lookups
[
'Q'
]
=
Qref
dQdt
=
-
self
.
pneuron
.
iNet
(
lookups
[
'V'
],
np
.
array
([
QSS
[
k
]
for
k
in
self
.
pneuron
.
states
]))
# mA/m2
SFPs
,
_
=
self
.
fixedPointsQSS
(
Fdrive
,
Adrive
,
DC
,
lookups
,
dQdt
)
return
len
(
SFPs
)
>
0
def
titrateQSS
(
self
,
Fdrive
,
DC
=
1.
,
Arange
=
None
):
# Default amplitude interval
if
Arange
is
None
:
Arange
=
[
0.
,
getLookups2D
(
self
.
pneuron
.
name
,
a
=
self
.
a
,
Fdrive
=
Fdrive
)[
0
]
.
max
()]
# Titration function
def
xfunc
(
x
):
if
self
.
pneuron
.
name
==
'STN'
:
return
self
.
isStableQSS
(
*
x
)
else
:
return
not
self
.
isStableQSS
(
*
x
)
return
binarySearch
(
xfunc
,
[
Fdrive
,
DC
],
1
,
Arange
,
THRESHOLD_CONV_RANGE_ASTIM
)
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