def damage_hyphae(self, n_det, n_kill, time, health, grid, fungus: FungusCellList, iron):
for i in self.alive(self.cell_data['granule_count'] > 0):
cell = self[i]
vox = grid.get_voxel(cell['point'])
# Moore neighborhood, but order partially randomized. Closest to furthest order, but
# the order of any set of points of equal distance is random
neighborhood = list(itertools.product(tuple(range(-1 * n_det, n_det + 1)), repeat=3))
shuffle(neighborhood)
neighborhood = sorted(neighborhood, key=lambda v: v[0] ** 2 + v[1] ** 2 + v[2] ** 2)
for dx, dy, dz in neighborhood:
zi = vox.z + dz
yj = vox.y + dy
xk = vox.x + dx
if grid.is_valid_voxel(Voxel(x=xk, y=yj, z=zi)):
index_arr = fungus.get_cells_in_voxel(Voxel(x=xk, y=yj, z=zi))
if len(index_arr) > 0:
iron[zi, yj, xk] = 0
for index in index_arr:
if (
fungus[index]['form'] == FungusCellData.Form.HYPHAE
and cell['granule_count'] > 0
):
fungus[index]['health'] -= health * (time / n_kill)
cell['granule_count'] -= 1
cell['status'] = NeutrophilCellData.Status.GRANULATING
elif cell['granule_count'] == 0:
cell['status'] = NeutrophilCellData.Status.NONGRANULATING
break
def produce_cytokines(self, m_det, m_n, grid, fungus: FungusCellList,
cyto):
for i in self.alive():
vox = grid.get_voxel(self[i]['point'])
hyphae_count = 0
# Moore neighborhood
neighborhood = tuple(
itertools.product(tuple(range(-1 * m_det, m_det + 1)),
repeat=3))
for dx, dy, dz in neighborhood:
zi = vox.z + dz
yj = vox.y + dy
xk = vox.x + dx
if grid.is_valid_voxel(Voxel(x=xk, y=yj, z=zi)):
index_arr = fungus.get_cells_in_voxel(
Voxel(x=xk, y=yj, z=zi))
for index in index_arr:
if fungus[index]['form'] == FungusCellData.Form.HYPHAE:
hyphae_count += 1
cyto[vox.z, vox.y,
vox.x] = cyto[vox.z, vox.y, vox.x] + m_n * hyphae_count
def internalize_conidia(self, m_det, max_spores, p_in, grid,
fungus: FungusCellList):
for i in self.alive():
cell = self[i]
vox = grid.get_voxel(cell['point'])
# Moore neighborhood, but order partially randomized. Closest to furthest order, but
# the order of any set of points of equal distance is random
neighborhood = list(
itertools.product(tuple(range(-1 * m_det, m_det + 1)),
repeat=3))
shuffle(neighborhood)
neighborhood = sorted(neighborhood,
key=lambda v: v[0]**2 + v[1]**2 + v[2]**2)
for dx, dy, dz in neighborhood:
zi = vox.z + dz
yj = vox.y + dy
xk = vox.x + dx
if grid.is_valid_voxel(Voxel(x=xk, y=yj, z=zi)):
index_arr = fungus.get_cells_in_voxel(
Voxel(x=xk, y=yj, z=zi))
for index in index_arr:
if (fungus[index]['form']
== FungusCellData.Form.CONIDIA
and not fungus[index]['internalized']
and p_in > rg.random()):
fungus[index]['internalized'] = True
self.append_to_phagosome(i, index, max_spores)
def cytokine_update(self, s_det, h_det, cyto_rate, m_cyto, n_cyto, fungus,
grid):
for i in self.alive():
vox = grid.get_voxel(self[i]['point'])
# spores
spore_count = 0
# Moore neighborhood
neighborhood = tuple(
itertools.product(tuple(range(-1 * s_det, s_det + 1)),
repeat=3))
for dx, dy, dz in neighborhood:
zi = vox.z + dz
yj = vox.y + dy
xk = vox.x + dx
if grid.is_valid_voxel(Voxel(x=xk, y=yj, z=zi)):
index_arr = fungus.get_cells_in_voxel(
Voxel(x=xk, y=yj, z=zi))
for index in index_arr:
if fungus[index][
'form'] == FungusCellData.Form.CONIDIA and fungus[
index]['status'] in [
FungusCellData.Status.SWOLLEN,
FungusCellData.Status.GERMINATED,
]:
spore_count += 1
# hyphae_count
hyphae_count = 0
# Moore neighborhood
neighborhood = tuple(
itertools.product(tuple(range(-1 * h_det, h_det + 1)),
repeat=3))
for dx, dy, dz in neighborhood:
zi = vox.z + dz
yj = vox.y + dy
xk = vox.x + dx
if grid.is_valid_voxel(Voxel(x=xk, y=yj, z=zi)):
index_arr = fungus.get_cells_in_voxel(
Voxel(x=xk, y=yj, z=zi))
for index in index_arr:
if fungus[index]['form'] == FungusCellData.Form.HYPHAE:
hyphae_count += 1
m_cyto[vox.z, vox.y, vox.x] += cyto_rate * spore_count
n_cyto[vox.z, vox.y,
vox.x] += cyto_rate * (spore_count + hyphae_count)
def periodic_discrete_laplacian(
grid: RectangularGrid,
mask: np.ndarray,
dtype: np.dtype = _dtype_float64) -> csr_matrix:
"""Return a laplacian operator with periodic boundary conditions.
This computes a standard laplacian operator as a scipy linear operator, except it is
restricted to a grid mask. The use case for this is to compute surface diffusion
on a gridded variable. The mask is generated from a category on the lung_tissue
variable.
"""
graph_shape = len(grid), len(grid)
z_extent, y_extent, x_extent = grid.shape
laplacian = dok_matrix(graph_shape, dtype=dtype)
delta_z = grid.delta(0)
delta_y = grid.delta(1)
delta_x = grid.delta(2)
for k, j, i in zip(*(mask).nonzero()):
voxel = Voxel(x=i, y=j, z=k)
voxel_index = grid.get_flattened_index(voxel)
for offset in [(-1, 0, 0), (1, 0, 0), (0, -1, 0), (0, 1, 0),
(0, 0, -1), (0, 0, 1)]:
# voxel coordinate displacements
dk, dj, di = offset
# find the neighbor for periodic boundary conditions
neighbor: Voxel = Voxel(x=(i + di) % x_extent,
y=(j + dj) % y_extent,
z=(k + dk) % z_extent)
# but maybe it isn't in the mask (i.e. air)
if not mask[neighbor.z, neighbor.y, neighbor.x]:
continue
neighbor_index = grid.get_flattened_index(neighbor)
# continuous space displacements
dx = delta_x[k, j, i] * di
dy = delta_y[k, j, i] * dj
dz = delta_z[k, j, i] * dk
inverse_distance2 = 1 / (dx * dx + dy * dy + dz * dz
) # units: 1/(µm^2)
laplacian[voxel_index, voxel_index] -= inverse_distance2
laplacian[voxel_index, neighbor_index] += inverse_distance2
return laplacian.tocsr()
def get_adjacent_voxels(self,
voxel: Voxel,
corners: bool = False) -> Iterator[Voxel]:
"""Return an iterator over all neighbors of a given voxel.
Parameters
----------
voxel : simulation.coordinates.Voxel
The target voxel
corners : bool
Include voxels sharing corners and edges in addition to those sharing sides.
"""
dirs: Iterable[Tuple[int, int, int]]
if corners:
dirs = filter(lambda x: x != (0, 0, 0),
product([-1, 0, 1], [-1, 0, 1], [-1, 0, 1]))
else:
dirs = [(-1, 0, 0), (1, 0, 0), (0, -1, 0), (0, 1, 0), (0, 0, -1),
(0, 0, 1)]
for di, dj, dk in dirs:
i = voxel.x + di
j = voxel.y + dj
k = voxel.z + dk
neighbor = Voxel(x=i, y=j, z=k)
if self.is_valid_voxel(neighbor):
yield neighbor
def voxel_from_flattened_index(self, index: int) -> 'Voxel':
"""Create a Voxel from flattened index of the grid.
This is a convenience method that wraps numpy.unravel_index.
"""
z, y, x = np.unravel_index(index, self.shape)
return Voxel(x=float(x), y=float(y), z=float(z))
def iron_uptake(self, iron: np.ndarray, iron_max: float, iron_min: float,
iron_absorb: float):
"""Absorb iron from external environment."""
cells = self.cell_data
for vox_index in np.argwhere(iron > iron_min):
vox = Voxel(x=vox_index[2], y=vox_index[1], z=vox_index[0])
cells_here = self.get_cells_in_voxel(vox)
indices = []
for index in cells_here:
if (cells[index]['form'] == FungusCellData.Form.HYPHAE.value
and np.invert(cells[index]['internalized'])
and cells[index]['iron'] < iron_max):
indices.append(index)
if len(indices) > 0:
iron_split = iron_absorb * (iron[vox.z, vox.y, vox.x] /
len(indices))
for cell_index in indices:
cells[cell_index]['iron'] += iron_split
if cells[cell_index]['iron'] > iron_max:
cells[cell_index]['iron'] = iron_max
iron[vox.z, vox.y,
vox.x] = (1 - iron_absorb) * iron[vox.z, vox.y, vox.x]
def advance(self, state: State, previous_time: float) -> State:
"""Advance the state by a single time step."""
from nlisim.modules.macrophage import MacrophageState
hepcidin: HepcidinState = state.hepcidin
macrophage: MacrophageState = state.macrophage
voxel_volume: float = state.voxel_volume
# interaction with macrophages
activated_voxels = zip(*np.where(
activation_function(
x=hepcidin.grid,
k_d=hepcidin.k_d,
h=self.time_step / 60, # units: (min/step) / (min/hour)
volume=voxel_volume,
b=1,
) > rg.random(size=hepcidin.grid.shape)))
for z, y, x in activated_voxels:
for macrophage_cell_index in macrophage.cells.get_cells_in_voxel(
Voxel(x=x, y=y, z=z)):
macrophage_cell = macrophage.cells[macrophage_cell_index]
macrophage_cell['fpn'] = False
macrophage_cell['fpn_iteration'] = 0
# Degrading Hepcidin is done by the "liver"
# hepcidin does not diffuse
return state
def move(self, rec_r, grid, cyto, tissue, fungus: FungusCellList):
for cell_index in self.alive():
cell = self[cell_index]
cell_voxel = grid.get_voxel(cell['point'])
valid_voxel_offsets = []
above_threshold_voxel_offsets = []
# iterate over nearby voxels, recording the cytokine levels
for dx, dy, dz in itertools.product((-1, 0, 1), repeat=3):
zi = cell_voxel.z + dz
yj = cell_voxel.y + dy
xk = cell_voxel.x + dx
if grid.is_valid_voxel(Voxel(x=xk, y=yj, z=zi)):
if tissue[zi, yj, xk] != TissueType.AIR.value:
valid_voxel_offsets.append((dx, dy, dz))
if cyto[zi, yj, xk] >= rec_r:
above_threshold_voxel_offsets.append(
(cyto[zi, yj, xk], (dx, dy, dz)))
# pick a target for the move
if len(above_threshold_voxel_offsets) > 0:
# shuffle + sort (with _only_ 0-key, not lexicographic as tuples) ensures
# randomization when there are equal top cytokine levels
# note that numpy's shuffle will complain about ragged arrays
shuffle(above_threshold_voxel_offsets)
above_threshold_voxel_offsets = sorted(
above_threshold_voxel_offsets,
key=lambda x: x[0],
reverse=True)
_, target_voxel_offset = above_threshold_voxel_offsets[0]
elif len(valid_voxel_offsets) > 0:
target_voxel_offset = choice(valid_voxel_offsets)
else:
raise AssertionError(
'This cell has no valid voxel to move to, including the one that it is in!'
)
# Some nonsense here, b/c jump is happening at the voxel level, not the point level
starting_cell_point = Point(x=cell['point'][2],
y=cell['point'][1],
z=cell['point'][0])
starting_cell_voxel = grid.get_voxel(starting_cell_point)
ending_cell_voxel = grid.get_voxel(
Point(
x=grid.x[cell_voxel.x + target_voxel_offset[0]],
y=grid.y[cell_voxel.y + target_voxel_offset[1]],
z=grid.z[cell_voxel.z + target_voxel_offset[2]],
))
ending_cell_point = (starting_cell_point +
grid.get_voxel_center(ending_cell_voxel) -
grid.get_voxel_center(starting_cell_voxel))
cell['point'] = ending_cell_point
self.update_voxel_index([cell_index])
for i in range(0, self.len_phagosome(cell_index)):
f_index = cell['phagosome'][i]
fungus[f_index]['point'] = ending_cell_point
fungus.update_voxel_index([f_index])
def move(self, rec_r, grid, cyto, tissue):
for cell_index in self.alive(
self.cell_data['status'] == NeutrophilCellData.Status.NONGRANULATING
):
# TODO: Algorithm S3.17 says "if degranulating nearby hyphae, do not move" but do
# we have the "nearby hyphae" part of this condition?
cell = self[cell_index]
cell_voxel = grid.get_voxel(cell['point'])
valid_voxel_offsets = []
above_threshold_voxel_offsets = []
# iterate over nearby voxels, recording the cytokine levels
for dx, dy, dz in itertools.product((-1, 0, 1), repeat=3):
zi = cell_voxel.z + dz
yj = cell_voxel.y + dy
xk = cell_voxel.x + dx
if grid.is_valid_voxel(Voxel(x=xk, y=yj, z=zi)):
if tissue[zi, yj, xk] != TissueType.AIR.value:
valid_voxel_offsets.append((dx, dy, dz))
if cyto[zi, yj, xk] >= rec_r:
above_threshold_voxel_offsets.append((cyto[zi, yj, xk], (dx, dy, dz)))
# pick a target for the move
if len(above_threshold_voxel_offsets) > 0:
# shuffle + sort (with _only_ 0-key, not lexicographic as tuples) ensures
# randomization when there are equal top cytokine levels
# note that numpy's shuffle will complain about ragged arrays
shuffle(above_threshold_voxel_offsets)
above_threshold_voxel_offsets = sorted(
above_threshold_voxel_offsets, key=lambda x: x[0], reverse=True
)
_, target_voxel_offset = above_threshold_voxel_offsets[0]
elif len(valid_voxel_offsets) > 0:
target_voxel_offset = choice(valid_voxel_offsets)
else:
raise AssertionError(
'This cell has no valid voxel to move to, including the one that it is in!'
)
# Some nonsense here, b/c jump is happening at the voxel level, not the point level
starting_cell_point = Point(x=cell['point'][2], y=cell['point'][1], z=cell['point'][0])
starting_cell_voxel = grid.get_voxel(starting_cell_point)
ending_cell_voxel = grid.get_voxel(
Point(
x=grid.x[cell_voxel.x + target_voxel_offset[0]],
y=grid.y[cell_voxel.y + target_voxel_offset[1]],
z=grid.z[cell_voxel.z + target_voxel_offset[2]],
)
)
ending_cell_point = (
starting_cell_point
+ grid.get_voxel_center(ending_cell_voxel)
- grid.get_voxel_center(starting_cell_voxel)
)
cell['point'] = ending_cell_point
self.update_voxel_index([cell_index])
def get_voxels_in_range(self, point: Point,
distance: float) -> Iterator[Tuple[Voxel, float]]:
"""Return an iterator of voxels within a given distance of a point.
The values returned by the iterator are tuples of `(Voxel, distance)`
pairs. For example,
voxel, distance = next(self.get_voxels_in_range(point, 1))
where `distance` is the distance from `point` to the center of `voxel`.
Note: no guarantee is given to the order over which the voxels are
iterated.
Parameters
----------
point : simulation.coordinates.Point
The center point
distance : float
Return all voxels with centers less than the distance from the center point
"""
# Get a hyper-square containing a superset of what we want. This
# restricts the set of points that we need to explicitly compute.
dp = Point(x=distance, y=distance, z=distance)
z0, y0, x0 = point - dp
z1, y1, x1 = point + dp
x0 = max(x0, self.x[0])
x1 = min(x1, self.x[-1])
y0 = max(y0, self.y[0])
y1 = min(y1, self.y[-1])
z0 = max(z0, self.z[0])
z1 = min(z1, self.z[-1])
# get voxel indices of the lower left and upper right corners
k0, j0, i0 = self.get_voxel(Point(x=x0, y=y0, z=z0))
k1, j1, i1 = self.get_voxel(Point(x=x1, y=y1, z=z1))
# get a distance matrix over all voxels in the candidate range
z, y, x = self.meshgrid
dx = x[k0:k1 + 1, j0:j1 + 1, i0:i1 + 1] - point.x
dy = y[k0:k1 + 1, j0:j1 + 1, i0:i1 + 1] - point.y
dz = z[k0:k1 + 1, j0:j1 + 1, i0:i1 + 1] - point.z
distances = np.sqrt(dx * dx + dy * dy + dz * dz)
# iterate over all voxels and yield those in range
for k in range(distances.shape[0]):
for j in range(distances.shape[1]):
for i in range(distances.shape[2]):
d = distances[k, j, i]
if d <= distance:
yield Voxel(x=(i + i0), y=(j + j0), z=(k + k0)), d
def test_get_neighboring_cells(grid: RectangularGrid):
point = Point(x=4.5, y=4.5, z=4.5)
raw_cells = [CellData.create_cell(point=point) for _ in range(5)]
raw_cells[1]['point'] = Point(x=-1, y=4.5, z=4.5)
raw_cells[4]['point'] = Point(x=4.5, y=4.5, z=-1)
cells = CellList(grid=grid)
cells.extend(raw_cells)
assert_array_equal(cells.get_neighboring_cells(cells[0]), [0, 2, 3])
assert_array_equal(cells.get_cells_in_voxel(Voxel(x=0, y=0, z=0)),
[0, 2, 3])
def get_voxel(self, point: Point) -> Voxel:
"""Return the voxel containing the given point.
For points outside of the grid, this method will return invalid
indices. For example, given vertex coordinates `[1.5, 2.7, 6.5]` and point
`-1.5` or `7.1`, this method will return `-1` and `3`, respectively. Call the
the `is_valid_voxel` method to determine if the voxel is valid.
"""
# For some reason, extracting fields from a recordarray results in a
# transposed point object (shape (1,3) rather than (3,)). This code
# ensures the representation is as expected.
point = point.ravel().view(Point)
assert len(point) == 3, 'This method does not handle arrays of points'
ix = self._find_dimension_index(self.xv, point.x)
iy = self._find_dimension_index(self.yv, point.y)
iz = self._find_dimension_index(self.zv, point.z)
return Voxel(x=ix, y=iy, z=iz)
def discrete_laplacian(grid: RectangularGrid,
mask: np.ndarray,
dtype: np.dtype = np.float64) -> csr_matrix:
"""Return a discrete laplacian operator for the given restricted grid.
This computes a standard laplacian operator as a scipy linear operator, except it is
restricted to a grid mask. The use case for this is to compute surface diffusion
on a gridded variable. The mask is generated from a category on the lung_tissue
variable.
"""
graph_shape = len(grid), len(grid)
laplacian = dok_matrix(graph_shape)
delta_z = grid.delta(0)
delta_y = grid.delta(1)
delta_x = grid.delta(2)
for k, j, i in zip(*(mask).nonzero()):
voxel = Voxel(x=i, y=j, z=k)
voxel_index = grid.get_flattened_index(voxel)
normalization = 0
for neighbor in grid.get_adjecent_voxels(voxel, corners=False):
ni = neighbor.x
nj = neighbor.y
nk = neighbor.z
if not mask[nk, nj, ni]:
continue
neighbor_index = grid.get_flattened_index(neighbor)
dx = delta_x[k, j, i] * (i - ni)
dy = delta_y[k, j, i] * (j - nj)
dz = delta_z[k, j, i] * (k - nk)
distance2 = 1 / (dx * dx + dy * dy + dz * dz)
normalization -= distance2
laplacian[voxel_index, neighbor_index] = distance2
laplacian[voxel_index, voxel_index] = normalization
return laplacian.tocsr()
def chemotaxis(
self,
molecule,
drift_lambda,
drift_bias,
tissue,
grid: RectangularGrid,
):
# 'molecule' = state.'molecule'.concentration
# prob = 0-1 random number to determine which voxel is chosen to move
# 1. Get cells that are alive
for index in self.alive():
prob = rg.random()
# 2. Get voxel for each cell to get molecule in that voxel
cell = self[index]
vox = grid.get_voxel(cell['point'])
# 3. Set prob for neighboring voxels
p = []
vox_list = []
p_tot = 0.0
i = -1
# calculate individual probability
for x in [0, 1, -1]:
for y in [0, 1, -1]:
for z in [0, 1, -1]:
p.append(0.0)
vox_list.append([x, y, z])
i += 1
zk = vox.z + z
yj = vox.y + y
xi = vox.x + x
if grid.is_valid_voxel(Voxel(x=xi, y=yj, z=zk)):
if tissue[zk, yj, xi] in [
TissueType.SURFACTANT.value,
TissueType.BLOOD.value,
TissueType.EPITHELIUM.value,
TissueType.PORE.value,
]:
p[i] = logistic(molecule[zk, yj, xi],
drift_lambda, drift_bias)
p_tot += p[i]
# scale to sum of probabilities
if p_tot:
for i in range(len(p)):
p[i] = p[i] / p_tot
# chose vox from neighbors
cum_p = 0.0
for i in range(len(p)):
cum_p += p[i]
if prob <= cum_p:
cell['point'] = Point(
x=random.uniform(grid.xv[vox.x + vox_list[i][0]],
grid.xv[vox.x + vox_list[i][0] + 1]),
y=random.uniform(grid.yv[vox.y + vox_list[i][1]],
grid.yv[vox.y + vox_list[i][1] + 1]),
z=random.uniform(grid.zv[vox.z + vox_list[i][2]],
grid.zv[vox.z + vox_list[i][2] + 1]),
)
self.update_voxel_index([index])
break
def advance(self, state: State, previous_time: float):
erythrocyte: ErythrocyteState = state.erythrocyte
molecules: MoleculesState = state.molecules
hemoglobin: HemoglobinState = state.hemoglobin
hemolysin: HemolysinState = state.hemolysin
macrophage: MacrophageState = state.macrophage
afumigatus: AfumigatusState = state.afumigatus
grid: RectangularGrid = state.grid
voxel_volume: float = state.voxel_volume
shape = erythrocyte.cells['count'].shape
# erythrocytes replenish themselves
avg_number_of_new_erythrocytes = (1 - molecules.turnover_rate) * (
1 - erythrocyte.cells['count'] / erythrocyte.max_erythrocyte_voxel)
mask = avg_number_of_new_erythrocytes > 0
erythrocyte.cells['count'][mask] += np.random.poisson(
avg_number_of_new_erythrocytes[mask],
avg_number_of_new_erythrocytes[mask].shape)
# ---------- interactions
# uptake hemoglobin
erythrocyte.cells['hemoglobin'] += hemoglobin.grid
hemoglobin.grid.fill(0.0)
# interact with hemolysin. pop goes the blood cell
# TODO: avg? variable name improvement?
avg_lysed_erythrocytes = erythrocyte.cells[
'count'] * activation_function(
x=hemolysin.grid,
k_d=erythrocyte.kd_hemo,
h=self.time_step / 60, # units: (min/step) / (min/hour)
volume=voxel_volume,
b=1,
)
number_lysed = np.minimum(
np.random.poisson(avg_lysed_erythrocytes, shape),
erythrocyte.cells['count'])
erythrocyte.cells[
'hemoglobin'] += number_lysed * erythrocyte.hemoglobin_quantity
erythrocyte.cells['count'] -= number_lysed
# interact with Macrophage
erythrocytes_to_hemorrhage = erythrocyte.cells[
'hemorrhage'] * np.random.poisson(
erythrocyte.pr_macrophage_phagocytize_erythrocyte *
erythrocyte.cells['count'], shape)
for z, y, x in zip(*np.where(erythrocytes_to_hemorrhage > 0)):
local_macrophages = macrophage.cells.get_cells_in_voxel(
Voxel(x=x, y=y, z=z))
num_local_macrophages = len(local_macrophages)
for macrophage_index in local_macrophages:
macrophage_cell = macrophage.cells[macrophage_index]
if macrophage_cell['dead']:
continue
macrophage_cell['iron_pool'] += (
4 # number of iron atoms in hemoglobin
* erythrocyte.hemoglobin_quantity *
erythrocytes_to_hemorrhage[z, y, x] /
num_local_macrophages)
erythrocyte.cells['count'] -= erythrocytes_to_hemorrhage
# interact with fungus
for fungal_cell_index in afumigatus.cells.alive():
fungal_cell = afumigatus.cells[fungal_cell_index]
if fungal_cell['status'] == AfumigatusCellStatus.HYPHAE:
fungal_voxel: Voxel = grid.get_voxel(fungal_cell['point'])
erythrocyte.cells['hemorrhage'][tuple(fungal_voxel)] = True
return state
def v(x: int, y: int, z: int) -> Voxel:
return Voxel(x=x, y=y, z=z)