""" Compartmental models. This module defines the `SpatialNeuron` class, which defines multicompartmental models. """ import copy import weakref import numpy as np import sympy as sp from brian2.core.variables import Variables from brian2.equations.codestrings import Expression from brian2.equations.equations import ( DIFFERENTIAL_EQUATION, PARAMETER, SUBEXPRESSION, Equations, SingleEquation, extract_constant_subexpressions, ) from brian2.groups.group import CodeRunner, Group from brian2.groups.neurongroup import NeuronGroup, SubexpressionUpdater, to_start_stop from brian2.groups.subgroup import Subgroup from brian2.parsing.sympytools import str_to_sympy, sympy_to_str from brian2.units.allunits import amp, meter, ohm, siemens, volt from brian2.units.fundamentalunits import ( DimensionMismatchError, Quantity, fail_for_dimension_mismatch, have_same_dimensions, ) from brian2.units.stdunits import cm, uF from brian2.utils.logger import get_logger __all__ = ["SpatialNeuron"] logger = get_logger(__name__) class FlatMorphology: """ Container object to store the flattened representation of a morphology. Note that all values are stored as numpy arrays without unit information (i.e. in base units). """ def __init__(self, morphology): self.n = n = morphology.total_compartments # Total number of compartments # Per-compartment attributes self.length = np.zeros(n) self.distance = np.zeros(n) self.area = np.zeros(n) self.diameter = np.zeros(n) self.volume = np.zeros(n) self.r_length_1 = np.zeros(n) self.r_length_2 = np.zeros(n) self.start_x = np.zeros(n) self.start_y = np.zeros(n) self.start_z = np.zeros(n) self.x = np.zeros(n) self.y = np.zeros(n) self.z = np.zeros(n) self.end_x = np.zeros(n) self.end_y = np.zeros(n) self.end_z = np.zeros(n) self.depth = np.zeros(n, dtype=np.int32) self.sections = sections = morphology.total_sections self.end_distance = np.zeros(sections) # Index of the parent for each section (-1 for the root) self.morph_parent_i = np.zeros(sections, dtype=np.int32) # The children indices for each section (list of lists, will be later # transformed into an array representation) self.morph_children = [] # each section is child of exactly one parent, this stores the index in # the parents list of children self.morph_idxchild = np.zeros(sections, dtype=np.int32) self.starts = np.zeros(sections, dtype=np.int32) self.ends = np.zeros(sections, dtype=np.int32) # recursively fill the data structures self._sections_without_coordinates = False self.has_coordinates = False self._offset = 0 self._section_counter = 0 self._insert_data(morphology) if self.has_coordinates and self._sections_without_coordinates: logger.info( "The morphology has a mix of sections with and " "without coordinates. The SpatialNeuron object " "will store NaN values for the coordinates of " "the sections that do not specify coordinates. " "Call generate_coordinates on the morphology " "before creating the SpatialNeuron object to fill " "in the missing coordinates." ) # Do not store coordinates for morphologies that don't define them if not self.has_coordinates: self.start_x = self.start_y = self.start_z = None self.x = self.y = self.z = None self.end_x = self.end_y = self.end_z = None # Transform the list of list of children into a 2D array (stored as # 1D) -- note that this wastes space if the number of children per # section is very different. In practice, this should not be much of a # problem since most sections have 0, 1, or 2 children (e.g. SWC files # on neuromorpho.org are all binary trees) self.morph_children_num = np.array([len(c) for c in self.morph_children] + [0]) max_children = max(self.morph_children_num) morph_children = np.zeros((sections + 1, max_children), dtype=np.int32) for idx, section_children in enumerate(self.morph_children): morph_children[idx, : len(section_children)] = section_children self.morph_children = morph_children.reshape(-1) def _insert_data(self, section, parent_idx=-1, depth=0): n = section.n start = self._offset end = self._offset + n # Compartment attributes self.depth[start:end] = depth self.length[start:end] = np.asarray(section.length) self.distance[start:end] = np.asarray(section.distance) self.area[start:end] = np.asarray(section.area) self.diameter[start:end] = np.asarray(section.diameter) self.volume[start:end] = np.asarray(section.volume) self.r_length_1[start:end] = np.asarray(section.r_length_1) self.r_length_2[start:end] = np.asarray(section.r_length_2) if section.x is None: self._sections_without_coordinates = True self.start_x[start:end] = np.ones(n) * np.nan self.start_y[start:end] = np.ones(n) * np.nan self.start_z[start:end] = np.ones(n) * np.nan self.x[start:end] = np.ones(n) * np.nan self.y[start:end] = np.ones(n) * np.nan self.z[start:end] = np.ones(n) * np.nan self.end_x[start:end] = np.ones(n) * np.nan self.end_y[start:end] = np.ones(n) * np.nan self.end_z[start:end] = np.ones(n) * np.nan else: self.has_coordinates = True self.start_x[start:end] = np.asarray(section.start_x) self.start_y[start:end] = np.asarray(section.start_y) self.start_z[start:end] = np.asarray(section.start_z) self.x[start:end] = np.asarray(section.x) self.y[start:end] = np.asarray(section.y) self.z[start:end] = np.asarray(section.z) self.end_x[start:end] = np.asarray(section.end_x) self.end_y[start:end] = np.asarray(section.end_y) self.end_z[start:end] = np.asarray(section.end_z) # Section attributes idx = self._section_counter # We start counting from 1 for the parent indices, since the index 0 # is used for the (virtual) root compartment self.morph_parent_i[idx] = parent_idx + 1 self.morph_children.append([]) self.starts[idx] = start self.ends[idx] = end # Append ourselves to the children list of our parent self.morph_idxchild[idx] = len(self.morph_children[parent_idx + 1]) self.morph_children[parent_idx + 1].append(idx + 1) self.end_distance[idx] = section.end_distance # Recurse down the tree self._offset += n self._section_counter += 1 for child in section.children: self._insert_data(child, parent_idx=idx, depth=depth + 1) class SpatialNeuron(NeuronGroup): """ A single neuron with a morphology and possibly many compartments. Parameters ---------- morphology : `Morphology` The morphology of the neuron. model : str, `Equations` The equations defining the group. method : str, function, optional The numerical integration method. Either a string with the name of a registered method (e.g. "euler") or a function that receives an `Equations` object and returns the corresponding abstract code. If no method is specified, a suitable method will be chosen automatically. threshold : str, optional The condition which produces spikes. Should be a single line boolean expression. threshold_location : (int, `Morphology`), optional Compartment where the threshold condition applies, specified as an integer (compartment index) or a `Morphology` object corresponding to the compartment (e.g. ``morpho.axon[10*um]``). If unspecified, the threshold condition applies at all compartments. Cm : `Quantity`, optional Specific capacitance in uF/cm**2 (default 0.9). It can be accessed and modified later as a state variable. In particular, its value can differ in different compartments. Ri : `Quantity`, optional Intracellular resistivity in ohm.cm (default 150). It can be accessed as a shared state variable, but modified only before the first run. It is uniform across the neuron. reset : str, optional The (possibly multi-line) string with the code to execute on reset. events : dict, optional User-defined events in addition to the "spike" event defined by the ``threshold``. Has to be a mapping of strings (the event name) to strings (the condition) that will be checked. refractory : {str, `Quantity`}, optional Either the length of the refractory period (e.g. ``2*ms``), a string expression that evaluates to the length of the refractory period after each spike (e.g. ``'(1 + rand())*ms'``), or a string expression evaluating to a boolean value, given the condition under which the neuron stays refractory after a spike (e.g. ``'v > -20*mV'``) namespace : dict, optional A dictionary mapping identifier names to objects. If not given, the namespace will be filled in at the time of the call of `Network.run`, with either the values from the ``namespace`` argument of the `Network.run` method or from the local context, if no such argument is given. dtype : (`dtype`, `dict`), optional The `numpy.dtype` that will be used to store the values, or a dictionary specifying the type for variable names. If a value is not provided for a variable (or no value is provided at all), the preference setting `core.default_float_dtype` is used. dt : `Quantity`, optional The time step to be used for the simulation. Cannot be combined with the `clock` argument. clock : `Clock`, optional The update clock to be used. If neither a clock, nor the `dt` argument is specified, the `defaultclock` will be used. order : int, optional The priority of of this group for operations occurring at the same time step and in the same scheduling slot. Defaults to 0. name : str, optional A unique name for the group, otherwise use ``spatialneuron_0``, etc. """ def __init__( self, morphology=None, model=None, threshold=None, refractory=False, reset=None, events=None, threshold_location=None, dt=None, clock=None, order=0, Cm=0.9 * uF / cm**2, Ri=150 * ohm * cm, name="spatialneuron*", dtype=None, namespace=None, method=("exact", "exponential_euler", "rk2", "heun"), method_options=None, ): # #### Prepare and validate equations if isinstance(model, str): model = Equations(model) if not isinstance(model, Equations): raise TypeError( "model has to be a string or an Equations " f"object, is '{type(model)}' instead." ) # Insert the threshold mechanism at the specified location if threshold_location is not None: if hasattr(threshold_location, "_indices"): # assuming this is a method threshold_location = threshold_location._indices() # for now, only a single compartment allowed try: int(threshold_location) except TypeError: raise AttributeError( "Threshold can only be applied on a single location" ) threshold = f"({threshold}) and (i == {str(threshold_location)})" # Check flags (we have point currents) model.check_flags( { DIFFERENTIAL_EQUATION: ("point current",), PARAMETER: ("constant", "shared", "linked", "point current"), SUBEXPRESSION: ("shared", "point current", "constant over dt"), } ) #: The original equations as specified by the user (i.e. before #: inserting point-currents into the membrane equation, before adding #: all the internally used variables and constants, etc.). self.user_equations = model # Separate subexpressions depending whether they are considered to be # constant over a time step or not (this would also be done by the # NeuronGroup initializer later, but this would give incorrect results # for the linearity check) model, constant_over_dt = extract_constant_subexpressions(model) # Extract membrane equation if "Im" in model: if len(model["Im"].flags): raise TypeError( "Cannot specify any flags for the transmembrane current 'Im'." ) membrane_expr = model["Im"].expr # the membrane equation else: raise TypeError("The transmembrane current 'Im' must be defined") model_equations = [] # Insert point currents in the membrane equation for eq in model.values(): if eq.varname == "Im": continue # ignore -- handled separately if "point current" in eq.flags: fail_for_dimension_mismatch( eq.dim, amp, f"Point current {eq.varname} should be in amp" ) membrane_expr = Expression( f"{str(membrane_expr.code)}+{eq.varname}/area" ) eq = SingleEquation( eq.type, eq.varname, eq.dim, expr=eq.expr, flags=list(set(eq.flags) - {"point current"}), ) model_equations.append(eq) model_equations.append( SingleEquation( SUBEXPRESSION, "Im", dimensions=(amp / meter**2).dim, expr=membrane_expr, ) ) model_equations.append(SingleEquation(PARAMETER, "v", volt.dim)) model = Equations(model_equations) ###### Process model equations (Im) to extract total conductance and the remaining current # Expand expressions in the membrane equation for var, expr in model.get_substituted_expressions(include_subexpressions=True): if var == "Im": Im_expr = expr break else: raise AssertionError("Model equations did not contain Im!") # Differentiate Im with respect to v Im_sympy_exp = str_to_sympy(Im_expr.code) v_sympy = sp.Symbol("v", real=True) diffed = sp.diff(Im_sympy_exp, v_sympy) unevaled_derivatives = diffed.atoms(sp.Derivative) if len(unevaled_derivatives): raise TypeError( f"Cannot take the derivative of '{Im_expr.code}' with respect to v." ) gtot_str = sympy_to_str(sp.simplify(-diffed)) I0_str = sympy_to_str(sp.simplify(Im_sympy_exp - diffed * v_sympy)) if gtot_str == "0": gtot_str += "*siemens/meter**2" if I0_str == "0": I0_str += "*amp/meter**2" gtot_str = f"gtot__private={gtot_str}: siemens/meter**2" I0_str = f"I0__private={I0_str}: amp/meter**2" model += Equations(f"{gtot_str}\n{I0_str}") # Insert morphology (store a copy) self.morphology = copy.deepcopy(morphology) # Flatten the morphology self.flat_morphology = FlatMorphology(morphology) # Equations for morphology # TODO: check whether Cm and Ri are already in the equations # no: should be shared instead of constant # yes: should be constant (check) eqs_constants = Equations( """ length : meter (constant) distance : meter (constant) area : meter**2 (constant) volume : meter**3 Ic : amp/meter**2 diameter : meter (constant) Cm : farad/meter**2 (constant) Ri : ohm*meter (constant, shared) r_length_1 : meter (constant) r_length_2 : meter (constant) time_constant = Cm/gtot__private : second space_constant = (2/pi)**(1.0/3.0) * (area/(1/r_length_1 + 1/r_length_2))**(1.0/6.0) / (2*(Ri*gtot__private)**(1.0/2.0)) : meter """ ) if self.flat_morphology.has_coordinates: eqs_constants += Equations( """ x : meter (constant) y : meter (constant) z : meter (constant) """ ) NeuronGroup.__init__( self, morphology.total_compartments, model=model + eqs_constants, method_options=method_options, threshold=threshold, refractory=refractory, reset=reset, events=events, method=method, dt=dt, clock=clock, order=order, namespace=namespace, dtype=dtype, name=name, ) # Parameters and intermediate variables for solving the cable equations # Note that some of these variables could have meaningful physical # units (e.g. _v_star is in volt, _I0_all is in amp/meter**2 etc.) but # since these variables should never be used in user code, we don't # assign them any units self.variables.add_arrays( [ "_ab_star0", "_ab_star1", "_ab_star2", "_b_plus", "_b_minus", "_v_star", "_u_plus", "_u_minus", "_v_previous", "_c", # The following two are only necessary for # C code where we cannot deal with scalars # and arrays interchangeably: "_I0_all", "_gtot_all", ], size=self.N, read_only=True, ) self.Cm = Cm self.Ri = Ri # These explict assignments will load the morphology values from disk # in standalone mode self.distance_ = self.flat_morphology.distance self.length_ = self.flat_morphology.length self.area_ = self.flat_morphology.area self.diameter_ = self.flat_morphology.diameter self.volume_ = self.flat_morphology.volume self.r_length_1_ = self.flat_morphology.r_length_1 self.r_length_2_ = self.flat_morphology.r_length_2 if self.flat_morphology.has_coordinates: self.x_ = self.flat_morphology.x self.y_ = self.flat_morphology.y self.z_ = self.flat_morphology.z # Performs numerical integration step self.add_attribute("diffusion_state_updater") self.diffusion_state_updater = SpatialStateUpdater( self, method, clock=self.clock, order=order ) # Update v after the gating variables to obtain consistent Ic and Im self.diffusion_state_updater.order = 1 # Creation of contained_objects that do the work self.contained_objects.extend([self.diffusion_state_updater]) if len(constant_over_dt): self.subexpression_updater = SubexpressionUpdater(self, constant_over_dt) self.contained_objects.append(self.subexpression_updater) def __getattr__(self, name): """ Subtrees are accessed by attribute, e.g. neuron.axon. """ return self.spatialneuron_attribute(self, name) def __getitem__(self, item): """ Selects a segment, where x is a slice of either compartment indexes or distances. Note a: segment is not a SpatialNeuron, only a Group. """ return self.spatialneuron_segment(self, item) @staticmethod def _find_subtree_end(morpho): """ Go down a morphology recursively to find the (absolute) index of the "final" compartment (i.e. the one with the highest index) of the subtree. Parameters ---------- morpho : `Morphology` The morphology for which to find the index. Returns ------- index : int The highest index within the subtree. """ indices = [morpho.indices[-1]] for child in morpho.children: indices.append(SpatialNeuron._find_subtree_end(child)) return max(indices) @staticmethod def spatialneuron_attribute(neuron, name): """ Selects a subtree from `SpatialNeuron` neuron and returns a `SpatialSubgroup`. If it does not exist, returns the `Group` attribute. """ if name == "main": # Main section, without the subtrees indices = neuron.morphology.indices[:] start, stop = indices[0], indices[-1] return SpatialSubgroup( neuron, start, stop + 1, morphology=neuron.morphology ) elif (name != "morphology") and ( (name in getattr(neuron.morphology, "children", [])) or all([c in "LR123456789" for c in name]) ): # subtree morpho = neuron.morphology[name] start = morpho.indices[0] stop = SpatialNeuron._find_subtree_end(morpho) return SpatialSubgroup(neuron, start, stop + 1, morphology=morpho) else: return Group.__getattr__(neuron, name) @staticmethod def spatialneuron_segment(neuron, item): """ Selects a segment from `SpatialNeuron` neuron, where item is a slice of either compartment indexes or distances. Note a: segment is not a `SpatialNeuron`, only a `Group`. """ if isinstance(item, slice) and isinstance(item.start, Quantity): if item.step is not None: raise ValueError( "Cannot specify a step size for slicing basedon length." ) start, stop = item.start, item.stop if not have_same_dimensions(start, meter) or not have_same_dimensions( stop, meter ): raise DimensionMismatchError( "Start and stop should have units of meter", start, stop ) # Convert to integers (compartment numbers) indices = neuron.morphology.indices[item] start, stop = indices[0], indices[-1] + 1 elif not isinstance(item, slice) and hasattr(item, "indices"): start, stop = to_start_stop(item.indices[:], neuron._N) else: start, stop = to_start_stop(item, neuron._N) if isinstance(neuron, SpatialSubgroup): start += neuron.start stop += neuron.start if start >= stop: raise IndexError( f"Illegal start/end values for subgroup, {int(start)}>={int(stop)}" ) if isinstance(neuron, SpatialSubgroup): # Note that the start/stop values calculated above are always # absolute values, even for subgroups neuron = neuron.source return Subgroup(neuron, start, stop) class SpatialSubgroup(Subgroup): """ A subgroup of a `SpatialNeuron`. Parameters ---------- source : int First compartment. stop : int Ending compartment, not included (as in slices). morphology : `Morphology` Morphology corresponding to the subgroup (not the full morphology). name : str, optional Name of the subgroup. """ def __init__(self, source, start, stop, morphology, name=None): self.morphology = morphology if isinstance(source, SpatialSubgroup): source = source.source start += source.start stop += source.start Subgroup.__init__(self, source, start, stop, name) def __getattr__(self, name): return SpatialNeuron.spatialneuron_attribute(self, name) def __getitem__(self, item): return SpatialNeuron.spatialneuron_segment(self, item) class SpatialStateUpdater(CodeRunner, Group): """ The `CodeRunner` that updates the state variables of a `SpatialNeuron` at every timestep. """ def __init__(self, group, method, clock, order=0): # group is the neuron (a group of compartments) self.method_choice = method self.group = weakref.proxy(group) compartments = group.flat_morphology.n sections = group.flat_morphology.sections CodeRunner.__init__( self, group, "spatialstateupdate", code="""_gtot = gtot__private _I0 = I0__private""", clock=clock, when="groups", order=order, name=f"{group.name}_spatialstateupdater*", check_units=False, template_kwds={"number_sections": sections}, ) self.variables = Variables(self, default_index="_section_idx") self.variables.add_reference("N", group) # One value per compartment self.variables.add_arange("_compartment_idx", size=compartments) self.variables.add_array( "_invr", dimensions=siemens.dim, size=compartments, constant=True, index="_compartment_idx", ) # one value per section self.variables.add_arange("_section_idx", size=sections) self.variables.add_array( "_P_parent", size=sections, constant=True ) # elements below diagonal self.variables.add_arrays( ["_morph_idxchild", "_morph_parent_i", "_starts", "_ends"], size=sections, dtype=np.int32, constant=True, ) self.variables.add_arrays( ["_invr0", "_invrn"], dimensions=siemens.dim, size=sections, constant=True ) # one value per section + 1 value for the root self.variables.add_arange("_section_root_idx", size=sections + 1) self.variables.add_array( "_P_diag", size=sections + 1, constant=True, index="_section_root_idx" ) self.variables.add_array( "_B", size=sections + 1, constant=True, index="_section_root_idx" ) self.variables.add_array( "_morph_children_num", size=sections + 1, dtype=np.int32, constant=True, index="_section_root_idx", ) # 2D matrices of size (sections + 1) x max children per section self.variables.add_arange( "_morph_children_idx", size=len(group.flat_morphology.morph_children) ) self.variables.add_array( "_P_children", size=len(group.flat_morphology.morph_children), index="_morph_children_idx", constant=True, ) # elements above diagonal self.variables.add_array( "_morph_children", size=len(group.flat_morphology.morph_children), dtype=np.int32, constant=True, index="_morph_children_idx", ) self._enable_group_attributes() self._morph_parent_i = group.flat_morphology.morph_parent_i self._morph_children_num = group.flat_morphology.morph_children_num self._morph_children = group.flat_morphology.morph_children self._morph_idxchild = group.flat_morphology.morph_idxchild self._starts = group.flat_morphology.starts self._ends = group.flat_morphology.ends