BOLD monitoring
BOLD monitoring utilities are provided in the module ANNarchy.extensions.bold, which must be explicitly imported:
from ANNarchy import *
from ANNarchy.extensions.bold import BoldMonitor
ANNarchy.extensions.bold.BoldMonitor
:copyright: Copyright 2013 - now, see AUTHORS.
:license: GPLv2, see LICENSE for details.
BoldMonitor
Bases: object
Monitors the BOLD signal for several populations using a computational model.
The BOLD monitor transforms one or two input population variables (such as the mean firing rate) into a recordable BOLD signal according to a computational model (for example a variation of the Balloon model).
Source code in ANNarchy/extensions/bold/BoldMonitor.py
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236 | class BoldMonitor(object):
"""
Monitors the BOLD signal for several populations using a computational model.
The BOLD monitor transforms one or two input population variables (such as the mean firing rate) into a recordable BOLD signal according to a computational model (for example a variation of the Balloon model).
"""
def __init__(self,
populations=None,
bold_model=balloon_RN,
mapping={'I_CBF': 'r'},
scale_factor=None,
normalize_input=None,
recorded_variables=None,
start=False,
net_id=0,
copied=False):
"""
:param populations: list of recorded populations.
:param bold_model: computational model for BOLD signal defined as a BoldModel class/object (see ANNarchy.extensions.bold.PredefinedModels for more predefined examples). Default is `balloon_RN`.
:param mapping: mapping dictionary between the inputs of the BOLD model (`I_CBF` for single inputs, `I_CBF` and `I_CMRO2` for double inputs in the provided examples) and the variables of the input populations. By default, `{'I_CBF': 'r'}` maps the firing rate `r` of the input population(s) to the variable `I_CBF` of the BOLD model.
:param scale_factor: list of float values to allow a weighting of signals between populations. By default, the input signal is weighted by the ratio of the population size to all populations within the recorded region.
:param normalize_input: list of integer values which represent a optional baseline per population. The input signals will require an additional normalization using a baseline value. A value different from 0 represents the time period for determing this baseline in milliseconds (biological time).
:param recorded_variables: which variables of the BOLD model should be recorded? (by default, the output variable of the BOLD model is added, e.g. ["BOLD"] for the provided examples).
"""
self.net_id = net_id
# instantiate if necessary, please note
# that population will make a deepcopy on this objects
if inspect.isclass(bold_model):
bold_model = bold_model()
# for reporting
bold_model._model_instantiated = True
# The usage of [] as default arguments in the __init__ call lead to strange side effects.
# We decided therefore to use None as default and create the lists locally.
if populations is None:
Global._error("Either a population or a list of populations must be provided to the BOLD monitor (populations=...)")
if scale_factor is None:
scale_factor = []
if normalize_input is None:
normalize_input = []
if recorded_variables is None:
recorded_variables = []
# argument check
if not(isinstance(populations, list)):
populations = [populations]
if not(isinstance(scale_factor, list)):
scale_factor = [scale_factor]*len(populations)
if not(isinstance(normalize_input, list)):
normalize_input = [normalize_input]*len(populations)
if isinstance(recorded_variables, str):
recorded_variables = [recorded_variables]
if len(scale_factor) > 0:
if len(populations) != len(scale_factor):
Global._error("BoldMonitor: Length of scale_factor must be equal to number of populations")
if len(normalize_input) > 0:
if len(populations) != len(normalize_input):
Global._error("BoldMonitor: Length of normalize_input must be equal to number of populations")
# Check mapping
for target, input_var in mapping.items():
if not target in bold_model._inputs:
Global._error("BoldMonitor: the key " + target + " of mapping is not part of the BOLD model.")
# Check recorded variables
if len(recorded_variables) == 0:
recorded_variables = bold_model._output
else:
# Add the output variables (and remove doublons)
l1 = bold_model._output
l2 = [recorded_variables] if isinstance(recorded_variables, str) else recorded_variables
recorded_variables = list(set(l2+l1))
recorded_variables.sort()
if not copied:
# Add the container to the object management
Global._network[0]['extensions'].append(self)
self.id = len(Global._network[self.net_id]['extensions'])
# create the population
self._bold_pop = Population(1, neuron=bold_model, name= bold_model.name )
self._bold_pop.enabled = start
# create the monitor
self._monitor = Monitor(self._bold_pop, recorded_variables, start=start)
# create the projection(s)
self._acc_proj = []
if len(scale_factor) == 0:
pop_overall_size = 0
for _, pop in enumerate(populations):
pop_overall_size += pop.size
# the conductance is normalized between [0 .. 1]. This scale factor
# should balance different population sizes
for _, pop in enumerate(populations):
scale_factor_conductance = float(pop.size)/float(pop_overall_size)
scale_factor.append(scale_factor_conductance)
if len(normalize_input) == 0:
normalize_input = [0] * len(populations)
# TODO: can we check if users used NormProjections? If not, this will crash ...
for target, input_var in mapping.items():
for pop, scale, normalize in zip(populations, scale_factor, normalize_input):
tmp_proj = AccProjection(pre = pop, post=self._bold_pop, target=target, variable=input_var, scale_factor=scale, normalize_input=normalize)
tmp_proj.connect_all_to_all(weights= 1.0)
self._acc_proj.append(tmp_proj)
else:
# Add the container to the object management
Global._network[net_id]['extensions'].append(self)
self.id = len(Global._network[self.net_id]['extensions'])
# instances are assigned by the copying instance
self._bold_pop = None
self._monitor = None
self._acc_proj = []
self.name = "bold_monitor"
# store arguments for copy
self._populations = populations
self._bold_model = bold_model
self._mapping = mapping
self._scale_factor = scale_factor
self._normalize_input = normalize_input
self._recorded_variables = recorded_variables
self._start = start
# Finalize initialization
self._initialized = True if not copied else False
#
# MONITOR functions
#
def start(self):
"""
Same as `ANNarchy.core.Monitor.start()`
"""
self._monitor.start()
# enable ODEs
self._bold_pop.cyInstance.activate(True)
# check if we have projections with baseline
for proj in self._acc_proj:
if proj._normalize_input > 0:
proj.cyInstance.start(proj._normalize_input/Global.config["dt"])
def stop(self):
"""
Same as `ANNarchy.core.Monitor.stop()`
"""
self._monitor.stop()
# enable ODEs
self._bold_pop.cyInstance.activate(False)
def get(self, variable):
"""
Same as `ANNarchy.core.Monitor.get()`
"""
return self._monitor.get(variable)
#
# POPULATION functions i. e. access to model parameter
#
# Method called when accessing an attribute.
# We overload the default to allow access to monitor variables.
def __getattr__(self, name):
if name == '_initialized' or not hasattr(self, '_initialized'): # Before the end of the constructor
return object.__getattribute__(self, name)
if self._initialized:
if self._bold_pop.initialized == False:
Global._error("BoldMonitor: attributes can not modified before compile()")
if name in self._bold_pop.attributes:
return getattr(self._bold_pop, name)
return object.__getattribute__(self, name)
# Method called when accessing an attribute.
# We overload the default to allow access to monitor variables.
def __setattr__(self, name, value):
if name == '_initialized' or not hasattr(self, '_initialized'): # Before the end of the constructor
return object.__setattr__(self, name, value)
if self._initialized:
if self._bold_pop.initialized == False:
Global._error("BoldMonitor: attributes can not modified before compile()")
if name in self._bold_pop.attributes:
setattr(self._bold_pop, name, value)
else:
raise AttributeError("the variable '"+str(name)+ "' is not an attribute of the bold model.")
else:
object.__setattr__(self, name, value)
#
# Destruction
def _clear(self):
pass
|
__init__(populations=None, bold_model=balloon_RN, mapping={'I_CBF': 'r'}, scale_factor=None, normalize_input=None, recorded_variables=None, start=False, net_id=0, copied=False)
Parameters:
-
populations
–
list of recorded populations.
-
bold_model
–
computational model for BOLD signal defined as a BoldModel class/object (see ANNarchy.extensions.bold.PredefinedModels for more predefined examples). Default is balloon_RN.
-
mapping
–
mapping dictionary between the inputs of the BOLD model (I_CBF for single inputs, I_CBF and I_CMRO2 for double inputs in the provided examples) and the variables of the input populations. By default, {'I_CBF': 'r'} maps the firing rate r of the input population(s) to the variable I_CBF of the BOLD model.
-
scale_factor
–
list of float values to allow a weighting of signals between populations. By default, the input signal is weighted by the ratio of the population size to all populations within the recorded region.
-
normalize_input
–
list of integer values which represent a optional baseline per population. The input signals will require an additional normalization using a baseline value. A value different from 0 represents the time period for determing this baseline in milliseconds (biological time).
-
recorded_variables
–
which variables of the BOLD model should be recorded? (by default, the output variable of the BOLD model is added, e.g. ["BOLD"] for the provided examples).
Source code in ANNarchy/extensions/bold/BoldMonitor.py
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159 | def __init__(self,
populations=None,
bold_model=balloon_RN,
mapping={'I_CBF': 'r'},
scale_factor=None,
normalize_input=None,
recorded_variables=None,
start=False,
net_id=0,
copied=False):
"""
:param populations: list of recorded populations.
:param bold_model: computational model for BOLD signal defined as a BoldModel class/object (see ANNarchy.extensions.bold.PredefinedModels for more predefined examples). Default is `balloon_RN`.
:param mapping: mapping dictionary between the inputs of the BOLD model (`I_CBF` for single inputs, `I_CBF` and `I_CMRO2` for double inputs in the provided examples) and the variables of the input populations. By default, `{'I_CBF': 'r'}` maps the firing rate `r` of the input population(s) to the variable `I_CBF` of the BOLD model.
:param scale_factor: list of float values to allow a weighting of signals between populations. By default, the input signal is weighted by the ratio of the population size to all populations within the recorded region.
:param normalize_input: list of integer values which represent a optional baseline per population. The input signals will require an additional normalization using a baseline value. A value different from 0 represents the time period for determing this baseline in milliseconds (biological time).
:param recorded_variables: which variables of the BOLD model should be recorded? (by default, the output variable of the BOLD model is added, e.g. ["BOLD"] for the provided examples).
"""
self.net_id = net_id
# instantiate if necessary, please note
# that population will make a deepcopy on this objects
if inspect.isclass(bold_model):
bold_model = bold_model()
# for reporting
bold_model._model_instantiated = True
# The usage of [] as default arguments in the __init__ call lead to strange side effects.
# We decided therefore to use None as default and create the lists locally.
if populations is None:
Global._error("Either a population or a list of populations must be provided to the BOLD monitor (populations=...)")
if scale_factor is None:
scale_factor = []
if normalize_input is None:
normalize_input = []
if recorded_variables is None:
recorded_variables = []
# argument check
if not(isinstance(populations, list)):
populations = [populations]
if not(isinstance(scale_factor, list)):
scale_factor = [scale_factor]*len(populations)
if not(isinstance(normalize_input, list)):
normalize_input = [normalize_input]*len(populations)
if isinstance(recorded_variables, str):
recorded_variables = [recorded_variables]
if len(scale_factor) > 0:
if len(populations) != len(scale_factor):
Global._error("BoldMonitor: Length of scale_factor must be equal to number of populations")
if len(normalize_input) > 0:
if len(populations) != len(normalize_input):
Global._error("BoldMonitor: Length of normalize_input must be equal to number of populations")
# Check mapping
for target, input_var in mapping.items():
if not target in bold_model._inputs:
Global._error("BoldMonitor: the key " + target + " of mapping is not part of the BOLD model.")
# Check recorded variables
if len(recorded_variables) == 0:
recorded_variables = bold_model._output
else:
# Add the output variables (and remove doublons)
l1 = bold_model._output
l2 = [recorded_variables] if isinstance(recorded_variables, str) else recorded_variables
recorded_variables = list(set(l2+l1))
recorded_variables.sort()
if not copied:
# Add the container to the object management
Global._network[0]['extensions'].append(self)
self.id = len(Global._network[self.net_id]['extensions'])
# create the population
self._bold_pop = Population(1, neuron=bold_model, name= bold_model.name )
self._bold_pop.enabled = start
# create the monitor
self._monitor = Monitor(self._bold_pop, recorded_variables, start=start)
# create the projection(s)
self._acc_proj = []
if len(scale_factor) == 0:
pop_overall_size = 0
for _, pop in enumerate(populations):
pop_overall_size += pop.size
# the conductance is normalized between [0 .. 1]. This scale factor
# should balance different population sizes
for _, pop in enumerate(populations):
scale_factor_conductance = float(pop.size)/float(pop_overall_size)
scale_factor.append(scale_factor_conductance)
if len(normalize_input) == 0:
normalize_input = [0] * len(populations)
# TODO: can we check if users used NormProjections? If not, this will crash ...
for target, input_var in mapping.items():
for pop, scale, normalize in zip(populations, scale_factor, normalize_input):
tmp_proj = AccProjection(pre = pop, post=self._bold_pop, target=target, variable=input_var, scale_factor=scale, normalize_input=normalize)
tmp_proj.connect_all_to_all(weights= 1.0)
self._acc_proj.append(tmp_proj)
else:
# Add the container to the object management
Global._network[net_id]['extensions'].append(self)
self.id = len(Global._network[self.net_id]['extensions'])
# instances are assigned by the copying instance
self._bold_pop = None
self._monitor = None
self._acc_proj = []
self.name = "bold_monitor"
# store arguments for copy
self._populations = populations
self._bold_model = bold_model
self._mapping = mapping
self._scale_factor = scale_factor
self._normalize_input = normalize_input
self._recorded_variables = recorded_variables
self._start = start
# Finalize initialization
self._initialized = True if not copied else False
|
get(variable)
Same as ANNarchy.core.Monitor.get()
Source code in ANNarchy/extensions/bold/BoldMonitor.py
| def get(self, variable):
"""
Same as `ANNarchy.core.Monitor.get()`
"""
return self._monitor.get(variable)
|
start()
Same as ANNarchy.core.Monitor.start()
Source code in ANNarchy/extensions/bold/BoldMonitor.py
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176 | def start(self):
"""
Same as `ANNarchy.core.Monitor.start()`
"""
self._monitor.start()
# enable ODEs
self._bold_pop.cyInstance.activate(True)
# check if we have projections with baseline
for proj in self._acc_proj:
if proj._normalize_input > 0:
proj.cyInstance.start(proj._normalize_input/Global.config["dt"])
|
stop()
Same as ANNarchy.core.Monitor.stop()
Source code in ANNarchy/extensions/bold/BoldMonitor.py
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185 | def stop(self):
"""
Same as `ANNarchy.core.Monitor.stop()`
"""
self._monitor.stop()
# enable ODEs
self._bold_pop.cyInstance.activate(False)
|
BOLD models
The provided BOLD models follow the Balloon model (Buxton et al., 1998) with the different variations studied in (Stephan et al., 2007). Those models all compute the vascular response to neural activity through a dampened oscillator:
\[
\frac{ds}{dt} = \phi \, I_\text{CBF} - \kappa \, s - \gamma \, (f_{in} - 1)
\]
\[
\frac{df_{in}}{dt} = s
\]
This allows to compute the oxygen extraction fraction:
\[
E = 1 - (1 - E_{0})^{ \frac{1}{f_{in}} }
\]
The (normalized) venous blood volume is computed as:
\[
\tau_0 \, \frac{dv}{dt} = (f_{in} - f_{out})
\]
\[
f_{out} = v^{\frac{1}{\alpha}}
\]
The level of deoxyhemoglobin into the venous compartment is computed by:
\[
\tau_0 \, \frac{dq}{dt} = f_{in} \, \frac{E}{E_0} - \frac{q}{v} \, f_{out}
\]
Using the two signals \(v\) and \(q\), there are two ways to compute the corresponding BOLD signal:
- N: Non-linear BOLD equation:
\[
BOLD = v_0 \, ( k_1 \, (1-q) + k_2 \, (1- \dfrac{q}{v}) + k_3 \, (1 - v) )
\]
\[
BOLD = v_0 \, ((k_1 + k_2) \, (1 - q) + (k_3 - k_2) \, (1 - v))
\]
Additionally, the three coefficients \(k_1\), \(k_2\), \(k_3\) can be computed in two different ways:
- C: classical coefficients from (Buxton et al., 1998):
\[k_1 = (1 - v_0) \, 4.3 \, v_0 \, E_0 \, \text{TE}\]
\[k_2 = 2 \, E_0\]
\[k_3 = 1 - \epsilon\]
- R: revised coefficients from (Obata et al., 2004):
\[k_1 = 4.3 \, v_0 \, E_0 \, \text{TE}\]
\[k_2 = \epsilon \, r_0 \, E_0 \, \text{TE}\]
\[k_3 = 1 - \epsilon\]
This makes a total of four different BOLD model (RN, RL, CN, CL) which are provided by the extension. The different parameters can be modified in the constructor. Additionally, we also provide the model that was used in (Maith et al., 2021) and the two-inputs model of (Maith et al, 2022).
ANNarchy.extensions.bold.BoldModel
:copyright: Copyright 2013 - now, see AUTHORS.
:license: GPLv2, see LICENSE for details.
BoldModel
Bases: Neuron
Base class to define a BOLD model to be used in a BOLD monitor.
A BOLD model is quite similar to a regular rate-coded neuron. It gets a weighted sum of inputs with a specific target (e.g. I_CBF) and compute a single output variable (called BOLD in the predefined models, but it could be anything).
The main difference is that a BOLD model should also declare which targets are used for the input signal:
bold_model = BoldModel(
parameters = '''
tau = 1000.
''',
equations = '''
I_CBF = sum(I_CBF)
# ...
tau * dBOLD/dt = I_CBF - BOLD
''',
inputs = "I_CBF"
)
Source code in ANNarchy/extensions/bold/BoldModel.py
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48 | class BoldModel(Neuron):
"""
Base class to define a BOLD model to be used in a BOLD monitor.
A BOLD model is quite similar to a regular rate-coded neuron. It gets a weighted sum of inputs with a specific target (e.g. I_CBF) and compute a single output variable (called `BOLD` in the predefined models, but it could be anything).
The main difference is that a BOLD model should also declare which targets are used for the input signal:
```python
bold_model = BoldModel(
parameters = '''
tau = 1000.
''',
equations = '''
I_CBF = sum(I_CBF)
# ...
tau * dBOLD/dt = I_CBF - BOLD
''',
inputs = "I_CBF"
)
```
"""
def __init__(self, parameters, equations, inputs, output=["BOLD"], name="Custom BOLD model", description=""):
"""
See ANNarchy.extensions.bold.PredefinedModels.py for some example models.
:param parameters: parameters of the model and their initial value.
:param equations: equations defining the temporal evolution of variables.
:param inputs: single variable or list of input signals (e.g. 'I_CBF' or ['I_CBF', 'I_CMRO2']).
:param output: output variable of the model (default is 'BOLD').
:param name: optional model name.
:param description: optional model description.
"""
# The processing in BoldMonitor expects lists, but the interface
# should allow also single strings (if only one variable is considered)
self._inputs = [inputs] if isinstance(inputs, str) else inputs
self._output = [output] if isinstance(output, str) else output
Neuron.__init__(self, parameters=parameters, equations=equations, name=name, description=description)
self._model_instantiated = False # activated by BoldMonitor
|
__init__(parameters, equations, inputs, output=['BOLD'], name='Custom BOLD model', description='')
See ANNarchy.extensions.bold.PredefinedModels.py for some example models.
Parameters:
-
parameters
–
parameters of the model and their initial value.
-
equations
–
equations defining the temporal evolution of variables.
-
inputs
–
single variable or list of input signals (e.g. 'I_CBF' or ['I_CBF', 'I_CMRO2']).
-
output
–
output variable of the model (default is 'BOLD').
-
name
–
-
description
–
optional model description.
Source code in ANNarchy/extensions/bold/BoldModel.py
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48 | def __init__(self, parameters, equations, inputs, output=["BOLD"], name="Custom BOLD model", description=""):
"""
See ANNarchy.extensions.bold.PredefinedModels.py for some example models.
:param parameters: parameters of the model and their initial value.
:param equations: equations defining the temporal evolution of variables.
:param inputs: single variable or list of input signals (e.g. 'I_CBF' or ['I_CBF', 'I_CMRO2']).
:param output: output variable of the model (default is 'BOLD').
:param name: optional model name.
:param description: optional model description.
"""
# The processing in BoldMonitor expects lists, but the interface
# should allow also single strings (if only one variable is considered)
self._inputs = [inputs] if isinstance(inputs, str) else inputs
self._output = [output] if isinstance(output, str) else output
Neuron.__init__(self, parameters=parameters, equations=equations, name=name, description=description)
self._model_instantiated = False # activated by BoldMonitor
|
ANNarchy.extensions.bold.balloon_RN
Bases: BoldModel
A balloon model with revised coefficients and non-linear BOLD equation derived from Stephan et al. (2007).
Equivalent code:
balloon_RN = BoldModel(
parameters = '''
second = 1000.0
phi = 1.0
kappa = 1/1.54
gamma = 1/2.46
E_0 = 0.34
tau = 0.98
alpha = 0.33
V_0 = 0.02
v_0 = 40.3
TE = 40/1000.
epsilon = 1.43
r_0 = 25.
''',
equations = '''
# Single input
I_CBF = sum(I_CBF) : init=0
ds/dt = (phi * I_CBF - kappa * s - gamma * (f_in - 1))/second : init=0
df_in/dt = s / second : init=1, min=0.01
E = 1 - (1 - E_0)**(1 / f_in) : init=0.3424
dq/dt = (f_in * E / E_0 - (q / v) * f_out)/(tau*second) : init=1, min=0.01
dv/dt = (f_in - f_out)/(tau*second) : init=1, min=0.01
f_out = v**(1 / alpha) : init=1, min=0.01
# Revised coefficients
k_1 = 4.3 * v_0 * E_0 * TE
k_2 = epsilon * r_0 * E_0 * TE
k_3 = 1.0 - epsilon
# Non-linear equation
BOLD = V_0 * (k_1 * (1 - q) + k_2 * (1 - (q / v)) + k_3 * (1 - v)) : init=0
''',
inputs="I_CBF",
)
Source code in ANNarchy/extensions/bold/PredefinedModels.py
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401 | class balloon_RN(BoldModel):
"""
A balloon model with revised coefficients and non-linear BOLD equation derived from Stephan et al. (2007).
Equivalent code:
```python
balloon_RN = BoldModel(
parameters = '''
second = 1000.0
phi = 1.0
kappa = 1/1.54
gamma = 1/2.46
E_0 = 0.34
tau = 0.98
alpha = 0.33
V_0 = 0.02
v_0 = 40.3
TE = 40/1000.
epsilon = 1.43
r_0 = 25.
''',
equations = '''
# Single input
I_CBF = sum(I_CBF) : init=0
ds/dt = (phi * I_CBF - kappa * s - gamma * (f_in - 1))/second : init=0
df_in/dt = s / second : init=1, min=0.01
E = 1 - (1 - E_0)**(1 / f_in) : init=0.3424
dq/dt = (f_in * E / E_0 - (q / v) * f_out)/(tau*second) : init=1, min=0.01
dv/dt = (f_in - f_out)/(tau*second) : init=1, min=0.01
f_out = v**(1 / alpha) : init=1, min=0.01
# Revised coefficients
k_1 = 4.3 * v_0 * E_0 * TE
k_2 = epsilon * r_0 * E_0 * TE
k_3 = 1.0 - epsilon
# Non-linear equation
BOLD = V_0 * (k_1 * (1 - q) + k_2 * (1 - (q / v)) + k_3 * (1 - v)) : init=0
''',
inputs="I_CBF",
)
```
"""
def __init__(self,
phi = 1.0,
kappa = 1/1.54,
gamma = 1/2.46,
E_0 = 0.34,
tau = 0.98,
alpha = 0.33,
V_0 = 0.02,
v_0 = 40.3,
TE = 40/1000.,
epsilon = 1.43,
r_0 = 25,
):
"""
:param phi: input coefficient
:param kappa: signal decay
:param gamma: feedback regulation
:param E_0: oxygen extraction fraction at rest
:param tau: time constant (in s!)
:param alpha: vessel stiffness
:param V_0: resting venous blood volume fraction
:param v_0: frequency offset at the outer surface of the magnetized vessel for fully deoxygenated blood at 1.5 T
:param TE: echo time
:param epsilon: ratio of intra- and extravascular signal
:param r_0: slope of the relation between the intravascular relaxation rate and oxygen saturation
"""
parameters = """
second = 1000.0 : population
phi = %(phi)s : population
kappa = %(kappa)s : population
gamma = %(gamma)s : population
E_0 = %(E_0)s : population
tau = %(tau)s : population
alpha = %(alpha)s : population
V_0 = %(V_0)s : population
v_0 = %(v_0)s : population
TE = %(TE)s : population
epsilon = %(epsilon)s : population
r_0 = %(r_0)s : population
""" % {
'phi': phi,
'kappa': kappa,
'gamma': gamma,
'E_0': E_0,
'tau': tau,
'alpha': alpha,
'V_0': V_0,
'v_0': v_0,
'TE': TE,
'epsilon': epsilon,
'r_0': r_0,
}
equations = """
# Single input
I_CBF = sum(I_CBF) : init=0
ds/dt = (phi * I_CBF - kappa * s - gamma * (f_in - 1))/second : init=0
df_in/dt = s / second : init=1, min=0.01
E = 1 - (1 - E_0)**(1 / f_in) : init=0.3424
dq/dt = (f_in * E / E_0 - (q / v) * f_out)/(tau*second) : init=1, min=0.01
dv/dt = (f_in - f_out)/(tau*second) : init=1, min=0.01
f_out = v**(1 / alpha) : init=1, min=0.01
# Revised coefficients
k_1 = 4.3 * v_0 * E_0 * TE
k_2 = epsilon * r_0 * E_0 * TE
k_3 = 1.0 - epsilon
# Non-linear equation
BOLD = V_0 * (k_1 * (1 - q) + k_2 * (1 - (q / v)) + k_3 * (1 - v)) : init=0
"""
name = "BOLD model RN"
description = "BOLD computation with revised coefficients and non-linear BOLD equation (Stephan et al., 2007)."
BoldModel.__init__(self,
parameters=parameters,
equations=equations,
inputs="I_CBF",
output="BOLD",
name=name, description=description
)
|
__init__(phi=1.0, kappa=1 / 1.54, gamma=1 / 2.46, E_0=0.34, tau=0.98, alpha=0.33, V_0=0.02, v_0=40.3, TE=40 / 1000.0, epsilon=1.43, r_0=25)
Parameters:
-
phi
–
-
kappa
–
-
gamma
–
-
E_0
–
oxygen extraction fraction at rest
-
tau
–
-
alpha
–
-
V_0
–
resting venous blood volume fraction
-
v_0
–
frequency offset at the outer surface of the magnetized vessel for fully deoxygenated blood at 1.5 T
-
TE
–
-
epsilon
–
ratio of intra- and extravascular signal
-
r_0
–
slope of the relation between the intravascular relaxation rate and oxygen saturation
Source code in ANNarchy/extensions/bold/PredefinedModels.py
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401 | def __init__(self,
phi = 1.0,
kappa = 1/1.54,
gamma = 1/2.46,
E_0 = 0.34,
tau = 0.98,
alpha = 0.33,
V_0 = 0.02,
v_0 = 40.3,
TE = 40/1000.,
epsilon = 1.43,
r_0 = 25,
):
"""
:param phi: input coefficient
:param kappa: signal decay
:param gamma: feedback regulation
:param E_0: oxygen extraction fraction at rest
:param tau: time constant (in s!)
:param alpha: vessel stiffness
:param V_0: resting venous blood volume fraction
:param v_0: frequency offset at the outer surface of the magnetized vessel for fully deoxygenated blood at 1.5 T
:param TE: echo time
:param epsilon: ratio of intra- and extravascular signal
:param r_0: slope of the relation between the intravascular relaxation rate and oxygen saturation
"""
parameters = """
second = 1000.0 : population
phi = %(phi)s : population
kappa = %(kappa)s : population
gamma = %(gamma)s : population
E_0 = %(E_0)s : population
tau = %(tau)s : population
alpha = %(alpha)s : population
V_0 = %(V_0)s : population
v_0 = %(v_0)s : population
TE = %(TE)s : population
epsilon = %(epsilon)s : population
r_0 = %(r_0)s : population
""" % {
'phi': phi,
'kappa': kappa,
'gamma': gamma,
'E_0': E_0,
'tau': tau,
'alpha': alpha,
'V_0': V_0,
'v_0': v_0,
'TE': TE,
'epsilon': epsilon,
'r_0': r_0,
}
equations = """
# Single input
I_CBF = sum(I_CBF) : init=0
ds/dt = (phi * I_CBF - kappa * s - gamma * (f_in - 1))/second : init=0
df_in/dt = s / second : init=1, min=0.01
E = 1 - (1 - E_0)**(1 / f_in) : init=0.3424
dq/dt = (f_in * E / E_0 - (q / v) * f_out)/(tau*second) : init=1, min=0.01
dv/dt = (f_in - f_out)/(tau*second) : init=1, min=0.01
f_out = v**(1 / alpha) : init=1, min=0.01
# Revised coefficients
k_1 = 4.3 * v_0 * E_0 * TE
k_2 = epsilon * r_0 * E_0 * TE
k_3 = 1.0 - epsilon
# Non-linear equation
BOLD = V_0 * (k_1 * (1 - q) + k_2 * (1 - (q / v)) + k_3 * (1 - v)) : init=0
"""
name = "BOLD model RN"
description = "BOLD computation with revised coefficients and non-linear BOLD equation (Stephan et al., 2007)."
BoldModel.__init__(self,
parameters=parameters,
equations=equations,
inputs="I_CBF",
output="BOLD",
name=name, description=description
)
|
ANNarchy.extensions.bold.balloon_RL
Bases: BoldModel
A balloon model with revised coefficients and linear BOLD equation derived from Stephan et al. (2007).
Equivalent code:
balloon_RL = BoldModel(
parameters = '''
second = 1000.0
phi = 1.0
kappa = 1/1.54
gamma = 1/2.46
E_0 = 0.34
tau = 0.98
alpha = 0.33
V_0 = 0.02
v_0 = 40.3
TE = 40/1000.
epsilon = 1.43
r_0 = 25.
''',
equations = '''
# Single input
I_CBF = sum(I_CBF) : init=0
ds/dt = (phi * I_CBF - kappa * s - gamma * (f_in - 1))/second : init=0
df_in/dt = s / second : init=1, min=0.01
E = 1 - (1 - E_0)**(1 / f_in) : init=0.3424
dq/dt = (f_in * E / E_0 - (q / v) * f_out)/(tau*second) : init=1, min=0.01
dv/dt = (f_in - f_out)/(tau*second) : init=1, min=0.01
f_out = v**(1 / alpha) : init=1, min=0.01
# Revised coefficients
k_1 = 4.3 * v_0 * E_0 * TE
k_2 = epsilon * r_0 * E_0 * TE
k_3 = 1.0 - epsilon
# Linear equation
BOLD = V_0 * ((k_1 + k_2) * (1 - q) + (k_3 - k_2) * (1 - v)) : init=0
''',
inputs="I_CBF",
)
Source code in ANNarchy/extensions/bold/PredefinedModels.py
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531 | class balloon_RL(BoldModel):
"""
A balloon model with revised coefficients and linear BOLD equation derived from Stephan et al. (2007).
Equivalent code:
```python
balloon_RL = BoldModel(
parameters = '''
second = 1000.0
phi = 1.0
kappa = 1/1.54
gamma = 1/2.46
E_0 = 0.34
tau = 0.98
alpha = 0.33
V_0 = 0.02
v_0 = 40.3
TE = 40/1000.
epsilon = 1.43
r_0 = 25.
''',
equations = '''
# Single input
I_CBF = sum(I_CBF) : init=0
ds/dt = (phi * I_CBF - kappa * s - gamma * (f_in - 1))/second : init=0
df_in/dt = s / second : init=1, min=0.01
E = 1 - (1 - E_0)**(1 / f_in) : init=0.3424
dq/dt = (f_in * E / E_0 - (q / v) * f_out)/(tau*second) : init=1, min=0.01
dv/dt = (f_in - f_out)/(tau*second) : init=1, min=0.01
f_out = v**(1 / alpha) : init=1, min=0.01
# Revised coefficients
k_1 = 4.3 * v_0 * E_0 * TE
k_2 = epsilon * r_0 * E_0 * TE
k_3 = 1.0 - epsilon
# Linear equation
BOLD = V_0 * ((k_1 + k_2) * (1 - q) + (k_3 - k_2) * (1 - v)) : init=0
''',
inputs="I_CBF",
)
```
"""
def __init__(self,
phi = 1.0,
kappa = 1/1.54,
gamma = 1/2.46,
E_0 = 0.34,
tau = 0.98,
alpha = 0.33,
V_0 = 0.02,
v_0 = 40.3,
TE = 40/1000.,
epsilon = 1.43,
r_0 = 25,
):
"""
:param phi: input coefficient
:param kappa: signal decay
:param gamma: feedback regulation
:param E_0: oxygen extraction fraction at rest
:param tau: time constant (in s!)
:param alpha: vessel stiffness
:param V_0: resting venous blood volume fraction
:param v_0: frequency offset at the outer surface of the magnetized vessel for fully deoxygenated blood at 1.5 T
:param TE: echo time
:param epsilon: ratio of intra- and extravascular signal
:param r_0: slope of the relation between the intravascular relaxation rate and oxygen saturation
"""
parameters = """
second = 1000.0 : population
phi = %(phi)s : population
kappa = %(kappa)s : population
gamma = %(gamma)s : population
E_0 = %(E_0)s : population
tau = %(tau)s : population
alpha = %(alpha)s : population
V_0 = %(V_0)s : population
v_0 = %(v_0)s : population
TE = %(TE)s : population
epsilon = %(epsilon)s : population
r_0 = %(r_0)s : population
""" % {
'phi': phi,
'kappa': kappa,
'gamma': gamma,
'E_0': E_0,
'tau': tau,
'alpha': alpha,
'V_0': V_0,
'v_0': v_0,
'TE': TE,
'epsilon': epsilon,
'r_0': r_0,
}
equations = """
# Single input
I_CBF = sum(I_CBF) : init=0
ds/dt = (phi * I_CBF - kappa * s - gamma * (f_in - 1))/second : init=0
df_in/dt = s / second : init=1, min=0.01
E = 1 - (1 - E_0)**(1 / f_in) : init=0.3424
tau*dq/dt = f_in * E / E_0 - (q / v) * f_out : init=1, min=0.01
tau*dv/dt = f_in - f_out : init=1, min=0.01
f_out = v**(1 / alpha) : init=1, min=0.01
# Revised coeeficients
k_1 = 4.3 * v_0 * E_0 * TE
k_2 = epsilon * r_0 * E_0 * TE
k_3 = 1 - epsilon
# Linear equation
BOLD = V_0 * ((k_1 + k_2) * (1 - q) + (k_3 - k_2) * (1 - v)) : init=0
"""
name = "BOLD model RL"
description = "BOLD computation with revised coefficients and linear BOLD equation (Stephan et al., 2007)."
BoldModel.__init__(self,
parameters=parameters,
equations=equations,
inputs="I_CBF",
output="BOLD",
name=name, description=description
)
|
__init__(phi=1.0, kappa=1 / 1.54, gamma=1 / 2.46, E_0=0.34, tau=0.98, alpha=0.33, V_0=0.02, v_0=40.3, TE=40 / 1000.0, epsilon=1.43, r_0=25)
Parameters:
-
phi
–
-
kappa
–
-
gamma
–
-
E_0
–
oxygen extraction fraction at rest
-
tau
–
-
alpha
–
-
V_0
–
resting venous blood volume fraction
-
v_0
–
frequency offset at the outer surface of the magnetized vessel for fully deoxygenated blood at 1.5 T
-
TE
–
-
epsilon
–
ratio of intra- and extravascular signal
-
r_0
–
slope of the relation between the intravascular relaxation rate and oxygen saturation
Source code in ANNarchy/extensions/bold/PredefinedModels.py
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531 | def __init__(self,
phi = 1.0,
kappa = 1/1.54,
gamma = 1/2.46,
E_0 = 0.34,
tau = 0.98,
alpha = 0.33,
V_0 = 0.02,
v_0 = 40.3,
TE = 40/1000.,
epsilon = 1.43,
r_0 = 25,
):
"""
:param phi: input coefficient
:param kappa: signal decay
:param gamma: feedback regulation
:param E_0: oxygen extraction fraction at rest
:param tau: time constant (in s!)
:param alpha: vessel stiffness
:param V_0: resting venous blood volume fraction
:param v_0: frequency offset at the outer surface of the magnetized vessel for fully deoxygenated blood at 1.5 T
:param TE: echo time
:param epsilon: ratio of intra- and extravascular signal
:param r_0: slope of the relation between the intravascular relaxation rate and oxygen saturation
"""
parameters = """
second = 1000.0 : population
phi = %(phi)s : population
kappa = %(kappa)s : population
gamma = %(gamma)s : population
E_0 = %(E_0)s : population
tau = %(tau)s : population
alpha = %(alpha)s : population
V_0 = %(V_0)s : population
v_0 = %(v_0)s : population
TE = %(TE)s : population
epsilon = %(epsilon)s : population
r_0 = %(r_0)s : population
""" % {
'phi': phi,
'kappa': kappa,
'gamma': gamma,
'E_0': E_0,
'tau': tau,
'alpha': alpha,
'V_0': V_0,
'v_0': v_0,
'TE': TE,
'epsilon': epsilon,
'r_0': r_0,
}
equations = """
# Single input
I_CBF = sum(I_CBF) : init=0
ds/dt = (phi * I_CBF - kappa * s - gamma * (f_in - 1))/second : init=0
df_in/dt = s / second : init=1, min=0.01
E = 1 - (1 - E_0)**(1 / f_in) : init=0.3424
tau*dq/dt = f_in * E / E_0 - (q / v) * f_out : init=1, min=0.01
tau*dv/dt = f_in - f_out : init=1, min=0.01
f_out = v**(1 / alpha) : init=1, min=0.01
# Revised coeeficients
k_1 = 4.3 * v_0 * E_0 * TE
k_2 = epsilon * r_0 * E_0 * TE
k_3 = 1 - epsilon
# Linear equation
BOLD = V_0 * ((k_1 + k_2) * (1 - q) + (k_3 - k_2) * (1 - v)) : init=0
"""
name = "BOLD model RL"
description = "BOLD computation with revised coefficients and linear BOLD equation (Stephan et al., 2007)."
BoldModel.__init__(self,
parameters=parameters,
equations=equations,
inputs="I_CBF",
output="BOLD",
name=name, description=description
)
|
ANNarchy.extensions.bold.balloon_CL
Bases: BoldModel
A balloon model with classical coefficients and linear BOLD equation derived from Stephan et al. (2007).
Equivalent code:
balloon_CL = BoldModel(
parameters = '''
second = 1000.0
phi = 1.0
kappa = 1/1.54
gamma = 1/2.46
E_0 = 0.34
tau = 0.98
alpha = 0.33
V_0 = 0.02
v_0 = 40.3
TE = 40/1000.
epsilon = 1.43
''',
equations = '''
# Single input
I_CBF = sum(I_CBF) : init=0
ds/dt = (phi * I_CBF - kappa * s - gamma * (f_in - 1))/second : init=0
df_in/dt = s / second : init=1, min=0.01
E = 1 - (1 - E_0)**(1 / f_in) : init=0.3424
dq/dt = (f_in * E / E_0 - (q / v) * f_out)/(tau*second) : init=1, min=0.01
dv/dt = (f_in - f_out)/(tau*second) : init=1, min=0.01
f_out = v**(1 / alpha) : init=1, min=0.01
# Classic coefficients
k_1 = (1 - V_0) * 4.3 * v_0 * E_0 * TE
k_2 = 2 * E_0
k_3 = 1 - epsilon
# Linear equation
BOLD = V_0 * ((k_1 + k_2) * (1 - q) + (k_3 - k_2) * (1 - v)) : init=0
''',
inputs="I_CBF",
)
Source code in ANNarchy/extensions/bold/PredefinedModels.py
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272 | class balloon_CL(BoldModel):
"""
A balloon model with classical coefficients and linear BOLD equation derived from Stephan et al. (2007).
Equivalent code:
```python
balloon_CL = BoldModel(
parameters = '''
second = 1000.0
phi = 1.0
kappa = 1/1.54
gamma = 1/2.46
E_0 = 0.34
tau = 0.98
alpha = 0.33
V_0 = 0.02
v_0 = 40.3
TE = 40/1000.
epsilon = 1.43
''',
equations = '''
# Single input
I_CBF = sum(I_CBF) : init=0
ds/dt = (phi * I_CBF - kappa * s - gamma * (f_in - 1))/second : init=0
df_in/dt = s / second : init=1, min=0.01
E = 1 - (1 - E_0)**(1 / f_in) : init=0.3424
dq/dt = (f_in * E / E_0 - (q / v) * f_out)/(tau*second) : init=1, min=0.01
dv/dt = (f_in - f_out)/(tau*second) : init=1, min=0.01
f_out = v**(1 / alpha) : init=1, min=0.01
# Classic coefficients
k_1 = (1 - V_0) * 4.3 * v_0 * E_0 * TE
k_2 = 2 * E_0
k_3 = 1 - epsilon
# Linear equation
BOLD = V_0 * ((k_1 + k_2) * (1 - q) + (k_3 - k_2) * (1 - v)) : init=0
''',
inputs="I_CBF",
)
```
"""
def __init__(self,
phi = 1.0,
kappa = 1/1.54,
gamma = 1/2.46,
E_0 = 0.34,
tau = 0.98,
alpha = 0.33,
V_0 = 0.02,
v_0 = 40.3,
TE = 40/1000.,
epsilon = 1.43,
):
"""
:param phi: input coefficient
:param kappa: signal decay
:param gamma: feedback regulation
:param E_0: oxygen extraction fraction at rest
:param tau: time constant (in s!)
:param alpha: vessel stiffness
:param V_0: resting venous blood volume fraction
:param v_0: frequency offset at the outer surface of the magnetized vessel for fully deoxygenated blood at 1.5 T
:param TE: echo time
:param epsilon: ratio of intra- and extravascular signal
"""
parameters = """
second = 1000.0 : population
phi = %(phi)s : population
kappa = %(kappa)s : population
gamma = %(gamma)s : population
E_0 = %(E_0)s : population
tau = %(tau)s : population
alpha = %(alpha)s : population
V_0 = %(V_0)s : population
v_0 = %(v_0)s : population
TE = %(TE)s : population
epsilon = %(epsilon)s : population
""" % {
'phi': phi,
'kappa': kappa,
'gamma': gamma,
'E_0': E_0,
'tau': tau,
'alpha': alpha,
'V_0': V_0,
'v_0': v_0,
'TE': TE,
'epsilon': epsilon,
}
equations = """
# Single input
I_CBF = sum(I_CBF) : init=0
ds/dt = (phi * I_CBF - kappa * s - gamma * (f_in - 1))/second : init=0
df_in/dt = s / second : init=1, min=0.01
E = 1 - (1 - E_0)**(1 / f_in) : init=0.3424
dq/dt = (f_in * E / E_0 - (q / v) * f_out)/(tau*second) : init=1, min=0.01
dv/dt = (f_in - f_out)/(tau*second) : init=1, min=0.01
f_out = v**(1 / alpha) : init=1, min=0.01
# Classic coefficients
k_1 = (1 - V_0) * 4.3 * v_0 * E_0 * TE
k_2 = 2 * E_0
k_3 = 1 - epsilon
# Linear equation
BOLD = V_0 * ((k_1 + k_2) * (1 - q) + (k_3 - k_2) * (1 - v)) : init=0
"""
name = "BoldNeuron CL"
description = "BOLD computation with classic coefficients and linear BOLD equation (Stephan et al., 2007)."
BoldModel.__init__(self,
parameters=parameters,
equations=equations,
inputs="I_CBF",
output="BOLD",
name=name, description=description
)
|
__init__(phi=1.0, kappa=1 / 1.54, gamma=1 / 2.46, E_0=0.34, tau=0.98, alpha=0.33, V_0=0.02, v_0=40.3, TE=40 / 1000.0, epsilon=1.43)
Parameters:
-
phi
–
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kappa
–
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gamma
–
-
E_0
–
oxygen extraction fraction at rest
-
tau
–
-
alpha
–
-
V_0
–
resting venous blood volume fraction
-
v_0
–
frequency offset at the outer surface of the magnetized vessel for fully deoxygenated blood at 1.5 T
-
TE
–
-
epsilon
–
ratio of intra- and extravascular signal
Source code in ANNarchy/extensions/bold/PredefinedModels.py
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272 | def __init__(self,
phi = 1.0,
kappa = 1/1.54,
gamma = 1/2.46,
E_0 = 0.34,
tau = 0.98,
alpha = 0.33,
V_0 = 0.02,
v_0 = 40.3,
TE = 40/1000.,
epsilon = 1.43,
):
"""
:param phi: input coefficient
:param kappa: signal decay
:param gamma: feedback regulation
:param E_0: oxygen extraction fraction at rest
:param tau: time constant (in s!)
:param alpha: vessel stiffness
:param V_0: resting venous blood volume fraction
:param v_0: frequency offset at the outer surface of the magnetized vessel for fully deoxygenated blood at 1.5 T
:param TE: echo time
:param epsilon: ratio of intra- and extravascular signal
"""
parameters = """
second = 1000.0 : population
phi = %(phi)s : population
kappa = %(kappa)s : population
gamma = %(gamma)s : population
E_0 = %(E_0)s : population
tau = %(tau)s : population
alpha = %(alpha)s : population
V_0 = %(V_0)s : population
v_0 = %(v_0)s : population
TE = %(TE)s : population
epsilon = %(epsilon)s : population
""" % {
'phi': phi,
'kappa': kappa,
'gamma': gamma,
'E_0': E_0,
'tau': tau,
'alpha': alpha,
'V_0': V_0,
'v_0': v_0,
'TE': TE,
'epsilon': epsilon,
}
equations = """
# Single input
I_CBF = sum(I_CBF) : init=0
ds/dt = (phi * I_CBF - kappa * s - gamma * (f_in - 1))/second : init=0
df_in/dt = s / second : init=1, min=0.01
E = 1 - (1 - E_0)**(1 / f_in) : init=0.3424
dq/dt = (f_in * E / E_0 - (q / v) * f_out)/(tau*second) : init=1, min=0.01
dv/dt = (f_in - f_out)/(tau*second) : init=1, min=0.01
f_out = v**(1 / alpha) : init=1, min=0.01
# Classic coefficients
k_1 = (1 - V_0) * 4.3 * v_0 * E_0 * TE
k_2 = 2 * E_0
k_3 = 1 - epsilon
# Linear equation
BOLD = V_0 * ((k_1 + k_2) * (1 - q) + (k_3 - k_2) * (1 - v)) : init=0
"""
name = "BoldNeuron CL"
description = "BOLD computation with classic coefficients and linear BOLD equation (Stephan et al., 2007)."
BoldModel.__init__(self,
parameters=parameters,
equations=equations,
inputs="I_CBF",
output="BOLD",
name=name, description=description
)
|
ANNarchy.extensions.bold.balloon_CN
Bases: BoldModel
A balloon model with classic coefficients and non-linear BOLD equation derived from Stephan et al. (2007).
Equivalent code:
balloon_CN = BoldModel(
parameters = '''
second = 1000.0
phi = 1.0
kappa = 1/1.54
gamma = 1/2.46
E_0 = 0.34
tau = 0.98
alpha = 0.33
V_0 = 0.02
v_0 = 40.3
TE = 40/1000.
epsilon = 1.43
''',
equations = '''
# Single input
I_CBF = sum(I_CBF) : init=0
ds/dt = (phi * I_CBF - kappa * s - gamma * (f_in - 1))/second : init=0
df_in/dt = s / second : init=1, min=0.01
E = 1 - (1 - E_0)**(1 / f_in) : init=0.3424
dq/dt = (f_in * E / E_0 - (q / v) * f_out)/(tau*second) : init=1, min=0.01
dv/dt = (f_in - f_out)/(tau*second) : init=1, min=0.01
f_out = v**(1 / alpha) : init=1, min=0.01
# Classic coefficients
k_1 = (1 - V_0) * 4.3 * v_0 * E_0 * TE
k_2 = 2 * E_0
k_3 = 1 - epsilon
# Non-linear equation
BOLD = V_0 * (k_1 * (1 - q) + k_2 * (1 - (q / v)) + k_3 * (1 - v)) : init=0
''',
inputs="I_CBF",
)
Source code in ANNarchy/extensions/bold/PredefinedModels.py
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147 | class balloon_CN(BoldModel):
"""
A balloon model with classic coefficients and non-linear BOLD equation derived from Stephan et al. (2007).
Equivalent code:
```python
balloon_CN = BoldModel(
parameters = '''
second = 1000.0
phi = 1.0
kappa = 1/1.54
gamma = 1/2.46
E_0 = 0.34
tau = 0.98
alpha = 0.33
V_0 = 0.02
v_0 = 40.3
TE = 40/1000.
epsilon = 1.43
''',
equations = '''
# Single input
I_CBF = sum(I_CBF) : init=0
ds/dt = (phi * I_CBF - kappa * s - gamma * (f_in - 1))/second : init=0
df_in/dt = s / second : init=1, min=0.01
E = 1 - (1 - E_0)**(1 / f_in) : init=0.3424
dq/dt = (f_in * E / E_0 - (q / v) * f_out)/(tau*second) : init=1, min=0.01
dv/dt = (f_in - f_out)/(tau*second) : init=1, min=0.01
f_out = v**(1 / alpha) : init=1, min=0.01
# Classic coefficients
k_1 = (1 - V_0) * 4.3 * v_0 * E_0 * TE
k_2 = 2 * E_0
k_3 = 1 - epsilon
# Non-linear equation
BOLD = V_0 * (k_1 * (1 - q) + k_2 * (1 - (q / v)) + k_3 * (1 - v)) : init=0
''',
inputs="I_CBF",
)
```
"""
def __init__(self,
phi = 1.0,
kappa = 1/1.54,
gamma = 1/2.46,
E_0 = 0.34,
tau = 0.98,
alpha = 0.33,
V_0 = 0.02,
v_0 = 40.3,
TE = 40/1000.,
epsilon = 1.43,
):
"""
:param phi: input coefficient
:param kappa: signal decay
:param gamma: feedback regulation
:param E_0: oxygen extraction fraction at rest
:param tau: time constant (in s!)
:param alpha: vessel stiffness
:param V_0: resting venous blood volume fraction
:param v_0: frequency offset at the outer surface of the magnetized vessel for fully deoxygenated blood at 1.5 T
:param TE: echo time
:param epsilon: ratio of intra- and extravascular signal
"""
parameters = """
second = 1000.0 : population
phi = %(phi)s : population
kappa = %(kappa)s : population
gamma = %(gamma)s : population
E_0 = %(E_0)s : population
tau = %(tau)s : population
alpha = %(alpha)s : population
V_0 = %(V_0)s : population
v_0 = %(v_0)s : population
TE = %(TE)s : population
epsilon = %(epsilon)s : population
""" % {
'phi': phi,
'kappa': kappa,
'gamma': gamma,
'E_0': E_0,
'tau': tau,
'alpha': alpha,
'V_0': V_0,
'v_0': v_0,
'TE': TE,
'epsilon': epsilon,
}
equations = """
# Single input
I_CBF = sum(I_CBF) : init=0
ds/dt = (phi * I_CBF - kappa * s - gamma * (f_in - 1))/second : init=0
df_in/dt = s / second : init=1, min=0.01
E = 1 - (1 - E_0)**(1 / f_in) : init=0.3424
dq/dt = (f_in * E / E_0 - (q / v) * f_out)/(tau*second) : init=1, min=0.01
dv/dt = (f_in - f_out)/(tau*second) : init=1, min=0.01
f_out = v**(1 / alpha) : init=1, min=0.01
# Classic coefficients
k_1 = (1 - V_0) * 4.3 * v_0 * E_0 * TE
k_2 = 2 * E_0
k_3 = 1 - epsilon
# Non-linear equation
BOLD = V_0 * (k_1 * (1 - q) + k_2 * (1 - (q / v)) + k_3 * (1 - v)) : init=0
"""
name = "BoldNeuron CN",
description = "BOLD computation with classic coefficients and non-linear BOLD equation (Stephan et al., 2007)."
BoldModel.__init__(self,
parameters=parameters,
equations=equations,
inputs="I_CBF",
output="BOLD",
name=name, description=description
)
|
__init__(phi=1.0, kappa=1 / 1.54, gamma=1 / 2.46, E_0=0.34, tau=0.98, alpha=0.33, V_0=0.02, v_0=40.3, TE=40 / 1000.0, epsilon=1.43)
Parameters:
-
phi
–
-
kappa
–
-
gamma
–
-
E_0
–
oxygen extraction fraction at rest
-
tau
–
-
alpha
–
-
V_0
–
resting venous blood volume fraction
-
v_0
–
frequency offset at the outer surface of the magnetized vessel for fully deoxygenated blood at 1.5 T
-
TE
–
-
epsilon
–
ratio of intra- and extravascular signal
Source code in ANNarchy/extensions/bold/PredefinedModels.py
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147 | def __init__(self,
phi = 1.0,
kappa = 1/1.54,
gamma = 1/2.46,
E_0 = 0.34,
tau = 0.98,
alpha = 0.33,
V_0 = 0.02,
v_0 = 40.3,
TE = 40/1000.,
epsilon = 1.43,
):
"""
:param phi: input coefficient
:param kappa: signal decay
:param gamma: feedback regulation
:param E_0: oxygen extraction fraction at rest
:param tau: time constant (in s!)
:param alpha: vessel stiffness
:param V_0: resting venous blood volume fraction
:param v_0: frequency offset at the outer surface of the magnetized vessel for fully deoxygenated blood at 1.5 T
:param TE: echo time
:param epsilon: ratio of intra- and extravascular signal
"""
parameters = """
second = 1000.0 : population
phi = %(phi)s : population
kappa = %(kappa)s : population
gamma = %(gamma)s : population
E_0 = %(E_0)s : population
tau = %(tau)s : population
alpha = %(alpha)s : population
V_0 = %(V_0)s : population
v_0 = %(v_0)s : population
TE = %(TE)s : population
epsilon = %(epsilon)s : population
""" % {
'phi': phi,
'kappa': kappa,
'gamma': gamma,
'E_0': E_0,
'tau': tau,
'alpha': alpha,
'V_0': V_0,
'v_0': v_0,
'TE': TE,
'epsilon': epsilon,
}
equations = """
# Single input
I_CBF = sum(I_CBF) : init=0
ds/dt = (phi * I_CBF - kappa * s - gamma * (f_in - 1))/second : init=0
df_in/dt = s / second : init=1, min=0.01
E = 1 - (1 - E_0)**(1 / f_in) : init=0.3424
dq/dt = (f_in * E / E_0 - (q / v) * f_out)/(tau*second) : init=1, min=0.01
dv/dt = (f_in - f_out)/(tau*second) : init=1, min=0.01
f_out = v**(1 / alpha) : init=1, min=0.01
# Classic coefficients
k_1 = (1 - V_0) * 4.3 * v_0 * E_0 * TE
k_2 = 2 * E_0
k_3 = 1 - epsilon
# Non-linear equation
BOLD = V_0 * (k_1 * (1 - q) + k_2 * (1 - (q / v)) + k_3 * (1 - v)) : init=0
"""
name = "BoldNeuron CN",
description = "BOLD computation with classic coefficients and non-linear BOLD equation (Stephan et al., 2007)."
BoldModel.__init__(self,
parameters=parameters,
equations=equations,
inputs="I_CBF",
output="BOLD",
name=name, description=description
)
|
ANNarchy.extensions.bold.balloon_maith2021
Bases: BoldModel
The balloon model as used in Maith et al. (2021).
Source code in ANNarchy/extensions/bold/PredefinedModels.py
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653 | class balloon_maith2021(BoldModel):
"""
The balloon model as used in Maith et al. (2021).
"""
def __init__(self):
"Constructor"
parameters = """
second = 1000.0
phi = 1.0
kappa = 0.665
gamma = 0.412
E_0 = 0.3424
tau = 1.0368
alpha = 0.3215
V_0 = 0.02
"""
equations = """
I_CBF = sum(I_CBF) : init=0
ds/dt = (phi * I_CBF - kappa * s - gamma * (f_in - 1))/second : init=0
df_in/dt = s / second : init=1, min=0.01
E = 1 - (1 - E_0)**(1 / f_in) : init=0.3424
dq/dt = (f_in * E / E_0 - (q / v) * f_out)/(tau*second) : init=1, min=0.01
dv/dt = (f_in - f_out)/(tau*second) : init=1, min=0.01
f_out = v**(1 / alpha) : init=1, min=0.01
k_1 = 7 * E_0
k_2 = 2
k_3 = 2 * E_0 - 0.2
BOLD = V_0 * (k_1 * (1 - q) + k_2 * (1 - (q / v)) + k_3 * (1 - v)) : init=0
"""
name = "Maith2021 BOLD model"
description = "BOLD computation from Maith et al. (2021)."
BoldModel.__init__(self,
parameters=parameters,
equations=equations,
inputs="I_CBF",
output="BOLD",
name=name, description=description
)
|
__init__()
Constructor
Source code in ANNarchy/extensions/bold/PredefinedModels.py
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653 | def __init__(self):
"Constructor"
parameters = """
second = 1000.0
phi = 1.0
kappa = 0.665
gamma = 0.412
E_0 = 0.3424
tau = 1.0368
alpha = 0.3215
V_0 = 0.02
"""
equations = """
I_CBF = sum(I_CBF) : init=0
ds/dt = (phi * I_CBF - kappa * s - gamma * (f_in - 1))/second : init=0
df_in/dt = s / second : init=1, min=0.01
E = 1 - (1 - E_0)**(1 / f_in) : init=0.3424
dq/dt = (f_in * E / E_0 - (q / v) * f_out)/(tau*second) : init=1, min=0.01
dv/dt = (f_in - f_out)/(tau*second) : init=1, min=0.01
f_out = v**(1 / alpha) : init=1, min=0.01
k_1 = 7 * E_0
k_2 = 2
k_3 = 2 * E_0 - 0.2
BOLD = V_0 * (k_1 * (1 - q) + k_2 * (1 - (q / v)) + k_3 * (1 - v)) : init=0
"""
name = "Maith2021 BOLD model"
description = "BOLD computation from Maith et al. (2021)."
BoldModel.__init__(self,
parameters=parameters,
equations=equations,
inputs="I_CBF",
output="BOLD",
name=name, description=description
)
|
Bases: BoldModel
BOLD model with two input signals (CBF-driving and CMRO2-driving) for the ballon model and non-linear BOLD equation with revised coefficients based on Buxton et al. (2004), Friston et al. (2000) and Stephan et al. (2007).
Source code in ANNarchy/extensions/bold/PredefinedModels.py
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605 | class balloon_two_inputs(BoldModel):
"""
BOLD model with two input signals (CBF-driving and CMRO2-driving) for the ballon model and non-linear BOLD equation with revised coefficients based on Buxton et al. (2004), Friston et al. (2000) and Stephan et al. (2007).
"""
def __init__(self):
"Constructor"
# damped harmonic oscillators, gamma->spring coefficient, kappa->damping coefficient
# CBF --> gamma from Friston
# CMRO2 --> faster --> gamma=gamma_CBF*10 (therefore scaling of I_CMRO2 by (gamma_CMRO2 / gamma_CBF) --> if same input (I_CBF==I_CMRO2) CMRO2 and CBF same steady-state)
# critical kappa --> kappa**2-4*gamma = 0 --> kappa=sqrt(4*gamma)
# CBF underdamped for undershoot --> kappa = 0.6*sqrt(4*gamma)
# CMRO2 critical --> kappa = sqrt(4*gamma)
# after CBF and CMRO2 standard balloon model with revised coefficients, parameter values = Friston et al. (2000)
parameters = """
kappa_CBF = 0.7650920556760059
gamma_CBF = 1/2.46
kappa_CMRO2 = 4.032389192727559
gamma_CMRO2 = 10/2.46
phi_CBF = 1.0
phi_CMRO2 = 1.0
E_0 = 0.34
tau = 0.98
alpha = 0.33
V_0 = 0.02
v_0 = 40.3
TE = 40/1000.
epsilon = 1
r_0 = 25
tau_out1 = 0
tau_out2 = 20
second = 1000
"""
equations = """
# CBF input
I_CBF = sum(I_CBF) : init=0
second*ds_CBF/dt = phi_CBF * I_CBF - kappa_CBF * s_CBF - gamma_CBF * (f_in - 1) : init=0
second*df_in/dt = s_CBF : init=1, min=0.01
# CMRO2 input
I_CMRO2 = sum(I_CMRO2) : init=0
second*ds_CMRO2/dt = phi_CMRO2 * I_CMRO2 * (gamma_CMRO2 / gamma_CBF) - kappa_CMRO2 * s_CMRO2 - gamma_CMRO2 * (r - 1) : init=0
second*dr/dt = s_CMRO2 : init=1, min=0.01
dv = f_in - v**(1 / alpha)
tau_out = if dv>0: tau_out1 else: tau_out2
f_out = v**(1/alpha) + tau_out * dv / (tau + tau_out) : init=1, min=0.01
dq/dt = (r - (q / v) * f_out) / (second*tau) : init=1, min=0.01
dv/dt = dv / (tau + tau_out) / second : init=1, min=0.01
# Revised coefficients
k_1 = 4.3 * v_0 * E_0 * TE
k_2 = epsilon * r_0 * E_0 * TE
k_3 = 1 - epsilon
# Non-linear equation
BOLD = V_0 * (k_1 * (1 - q) + k_2 * (1 - (q / v)) + k_3 * (1 - v)) : init=0
"""
name = "BOLD model with two inputs"
description = "BOLD model with two inputs (CBF-driving and CMRO2-driving). Combination of neurovascular coupling of Friston et al. (2000) and non-linear Balloon model with revised coefficients (Buxton et al, 1998, Stephan et al, 2007)"
BoldModel.__init__(self,
parameters=parameters,
equations=equations,
inputs=['I_CBF', 'I_CMRO2'],
output="BOLD",
name=name,
description=description
)
|
Constructor
Source code in ANNarchy/extensions/bold/PredefinedModels.py
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605 | def __init__(self):
"Constructor"
# damped harmonic oscillators, gamma->spring coefficient, kappa->damping coefficient
# CBF --> gamma from Friston
# CMRO2 --> faster --> gamma=gamma_CBF*10 (therefore scaling of I_CMRO2 by (gamma_CMRO2 / gamma_CBF) --> if same input (I_CBF==I_CMRO2) CMRO2 and CBF same steady-state)
# critical kappa --> kappa**2-4*gamma = 0 --> kappa=sqrt(4*gamma)
# CBF underdamped for undershoot --> kappa = 0.6*sqrt(4*gamma)
# CMRO2 critical --> kappa = sqrt(4*gamma)
# after CBF and CMRO2 standard balloon model with revised coefficients, parameter values = Friston et al. (2000)
parameters = """
kappa_CBF = 0.7650920556760059
gamma_CBF = 1/2.46
kappa_CMRO2 = 4.032389192727559
gamma_CMRO2 = 10/2.46
phi_CBF = 1.0
phi_CMRO2 = 1.0
E_0 = 0.34
tau = 0.98
alpha = 0.33
V_0 = 0.02
v_0 = 40.3
TE = 40/1000.
epsilon = 1
r_0 = 25
tau_out1 = 0
tau_out2 = 20
second = 1000
"""
equations = """
# CBF input
I_CBF = sum(I_CBF) : init=0
second*ds_CBF/dt = phi_CBF * I_CBF - kappa_CBF * s_CBF - gamma_CBF * (f_in - 1) : init=0
second*df_in/dt = s_CBF : init=1, min=0.01
# CMRO2 input
I_CMRO2 = sum(I_CMRO2) : init=0
second*ds_CMRO2/dt = phi_CMRO2 * I_CMRO2 * (gamma_CMRO2 / gamma_CBF) - kappa_CMRO2 * s_CMRO2 - gamma_CMRO2 * (r - 1) : init=0
second*dr/dt = s_CMRO2 : init=1, min=0.01
dv = f_in - v**(1 / alpha)
tau_out = if dv>0: tau_out1 else: tau_out2
f_out = v**(1/alpha) + tau_out * dv / (tau + tau_out) : init=1, min=0.01
dq/dt = (r - (q / v) * f_out) / (second*tau) : init=1, min=0.01
dv/dt = dv / (tau + tau_out) / second : init=1, min=0.01
# Revised coefficients
k_1 = 4.3 * v_0 * E_0 * TE
k_2 = epsilon * r_0 * E_0 * TE
k_3 = 1 - epsilon
# Non-linear equation
BOLD = V_0 * (k_1 * (1 - q) + k_2 * (1 - (q / v)) + k_3 * (1 - v)) : init=0
"""
name = "BOLD model with two inputs"
description = "BOLD model with two inputs (CBF-driving and CMRO2-driving). Combination of neurovascular coupling of Friston et al. (2000) and non-linear Balloon model with revised coefficients (Buxton et al, 1998, Stephan et al, 2007)"
BoldModel.__init__(self,
parameters=parameters,
equations=equations,
inputs=['I_CBF', 'I_CMRO2'],
output="BOLD",
name=name,
description=description
)
|
References
Buxton, R. B., Wong, E. C., and Frank, L. R. (1998). Dynamics of blood flow and oxygenation changes during brain activation: the balloon model. Magnetic resonance in medicine 39, 855–864. doi:10.1002/mrm.1910390602
Friston et al. (2000). Nonlinear responses in fMRI: the balloon model, volterra kernels, and other hemodynamics. NeuroImage 12, 466–477
Buxton et al. (2004). Modeling the hemodynamic response to brain activation. Neuroimage 23, S220–S233. doi:10.1016/j.neuroimage.2004.07.013
Stephan et al. (2007). Comparing hemodynamic models with DCM. Neuroimage 38, 387–401. doi:10.1016/j.neuroimage.2007.07.040
Maith et al. (2021) A computational model-based analysis of basal ganglia pathway changes in Parkinson’s disease inferred from resting-state fMRI. European Journal of Neuroscience. 2021; 53: 2278– 2295. doi:10.1111/ejn.14868
Maith et al. (2022) BOLD monitoring in the neural simulator ANNarchy. Frontiers in Neuroinformatics 16. doi:10.3389/fninf.2022.790966.