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Network.py
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Network.py
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#------------------------------------------------------------------------------
# The Network class contains the methods that require knowledge of the vascular network as a whole
#
# Lowell Taylor Edgar
# University of Edinburgh
# 2019
from math import pi
from math import acos
from math import cos
from math import sin
from numpy import sign
import random as rand
from Vessel import *
from Tensor3D import *
from Input import *
from ECell import *
#------------------------------------------------------------------------------
# Realign polarity vectors in cells based on weights
def realign_polarity(vessels):
for vess in vessels:
for cell in vess.cells:
# Original polarity vector
pol_old = cell.polarity.copy()
# Flow vector
flow_vect = -float(sign(vess.Q))*vess.unit.copy()
# Random walk component
rand_vect = Vect(rand.uniform(-1, 1), rand.uniform(-1, 1), 0.)
rand_vect.unit()
# if (flow_vect.length() == 0.):
# if (vessels[vess.n1-1].num_cells == 0):
# flow_vect = -vess.unit.copy()
#
# if (vessels[vess.n0-1].num_cells == 0):
# flow_vect = vess.unit.copy()
#
# if (vessels[vess.n1-1].num_cells == 0 and vessels[vess.n0-1].num_cells == 0):
# flow_vect = -vess.unit.copy()
# Phi1 - Realignment angle due to persistence
phi1 = 0.
# Phi2 - Realignment angle due to flow
phi2_dot = pol_old * flow_vect
if (phi2_dot > 1.):
phi2_dot = 1.
elif (phi2_dot < -1.):
phi2_dot = -1.
phi2 = acos(phi2_dot)
if (pol_old.cross(flow_vect).z < 0):
phi2 = -phi2
# Phi3 - Realignment angle due to random walk component
phi3_dot = pol_old * rand_vect
if (phi3_dot > 1.):
phi3_dot = 1.
elif (phi3_dot < -1.):
phi3_dot = -1.
phi3 = acos(phi3_dot)
if (pol_old.cross(rand_vect).z < 0):
phi3 = -phi3
# # If shear weighting of polarization is enabled
# if (yes_shear_polar):
# if (vess.tau <= tau_max):
# eta = vess.tau/tau_max
# else:
# eta = 1.0
#
# w2 = (1 - w1)*eta
# w3 = (1 - w1)*(1 - eta)
# Calculate new realignment angle from weighted average
theta = w1*phi1 + w2*phi2 + w3*phi3
# Calculate the new polarity vector by rotating the old vector by theta
Q = Tensor2O([cos(theta), -sin(theta), 0, sin(theta), cos(theta), 0, 0, 0, 0])
pol_new = Q*pol_old
pol_new.unit()
cell.polarity = pol_new.copy()
#------------------------------------------------------------------------------
# Perform cell migration
def cell_migration(vessels, bifur_nodes, bifur):
# Determine if a cell is migrating out of a vessel segment by checking the
# angle between polarity and the vessel's unit vector
for vess in vessels:
for cell in vess.cells:
dot_prod = vess.unit * cell.polarity
if (dot_prod > 1.):
dot_prod = 1.
elif (dot_prod < -1.):
dot_prod = -1.
pol_angle = acos(dot_prod)
cell.migrate = 0
if (0. <= pol_angle <= pi/3.):
cell.migrate = -1 # Migrate along the vessel's unit vector
elif ((2*pi)/3. <= pol_angle <= pi):
cell.migrate = 1 # Migrate against the vessel's unit vector
# Diffusion-based smoothing scheme
if (yes_smoothing == True):
vessel_smoothing(vessels)
# Move the cells that are migrating to their new vessel
for vess in vessels:
cells_that_migrated = []
for i in range(len(vess.cells)):
# If cell is migrating upstream, move to upstream neighbour
if (vess.cells[i].migrate == 1):
migrating_cell = vess.cells[i]
if (len(vess.neigh0) == 1):
migrating_cell.vessID = vess.neigh0[0]
vessels[vess.neigh0[0]-1].cells.append(migrating_cell)
# If more than one neighbour...
elif (len(vess.neigh0) == 2):
if (yes_new_branch == False):
handle_bifurcation(migrating_cell, vess, vess.n0, vessels[vess.neigh0[0]-1], vessels[vess.neigh0[1]-1])
else:
new_handle_bifurcation(migrating_cell, vess, vess.n0, vessels[vess.neigh0[0]-1], vessels[vess.neigh0[1]-1], bifur_nodes, bifur)
if (migrating_cell.migrate != 0):
cells_that_migrated.append(i)
migrating_cell.migrate = 0
# If cell is migrating downstream, move to downstream neighbour
if (vess.cells[i].migrate == -1):
migrating_cell = vess.cells[i]
if (len(vess.neigh1) == 1):
migrating_cell.vessID = vess.neigh1[0]
vessels[vess.neigh1[0]-1].cells.append(migrating_cell)
# If more than one neighbour...
elif (len(vess.neigh1) == 2):
if (yes_new_branch == False):
handle_bifurcation(migrating_cell, vess, vess.n1, vessels[vess.neigh1[0]-1], vessels[vess.neigh1[1]-1])
else:
new_handle_bifurcation(migrating_cell, vess, vess.n1, vessels[vess.neigh1[0]-1], vessels[vess.neigh1[1]-1], bifur_nodes, bifur)
if (migrating_cell.migrate != 0):
cells_that_migrated.append(i)
migrating_cell.migrate = 0
# Remove the cells that left the vessel (or rather, keep only the cells that didn't leave)
new_cells = []
for i in range(len(vess.cells)):
if i not in cells_that_migrated:
new_cells.append(vess.cells[i])
vess.cells = new_cells
# Update cell number in vessels after migration
for vess in vessels:
vess.num_cells = len(vess.cells)
# Apply Dirichlet boundary conditions
max_cell_num = 0
# Determine the max cell ID number for adding new cells
for vess in vessels:
for cell in vess.cells:
if (cell.ID > max_cell_num):
max_cell_num = cell.ID
for vess in vessels:
if (vess.dirichlet != 0 and vess.num_cells != vess.dirichlet):
# If cell number is less than dirichlet condition, add cells
if (vess.num_cells < vess.dirichlet):
while (vess.num_cells < vess.dirichlet):
max_cell_num += 1
vess.cells.append(ECell(max_cell_num, vess.ID, Vect(0, 0, 0)))
vess.num_cells = len(vess.cells)
pass
# If cell number is more than dirichlet condition, remove cells randomly
elif (vess.num_cells > vess.dirichlet):
while (vess.num_cells > vess.dirichlet):
vess.cells.pop(rand.randrange(len(vess.cells)))
vess.num_cells = len(vess.cells)
pass
# Update vessels after migration
for vess in vessels:
vess.num_cells = len(vess.cells)
vess.update_diameter()
vess.update_conductance()
#------------------------------------------------------------------------------
# Determine cell behavior at a bifurcation
def vessel_smoothing(vessels):
for vess in vessels:
# If flow in the vessel is positive, check downstream neighbour
if (vess.Q > 0.):
# If current vessel has only one downstream neighbour
if (len(vess.neigh1) == 1):
if (vessels[vess.neigh1[0]-1].num_cells < vess.num_cells) and (vessels[vess.neigh1[0]-1].num_cells != 0):
#if (vessels[vess.neigh1[0]-1].num_cells < vess.num_cells):
smoothed = False
while (smoothed == False):
rand_cell = rand.randint(0, vess.num_cells-1)
if (vess.cells[rand_cell].migrate != 0):
vess.cells[rand_cell].migrate = 0
smoothed = True
# # If current vessel has more than one downstream neighbour
# if (len(vess.neigh1) == 2):
# if ((vessels[vess.neigh1[0]-1].num_cells < vess.num_cells) and (vessels[vess.neigh1[0]-1].num_cells != 0)) or ((vessels[vess.neigh1[1]-1].num_cells < vess.num_cells) and (vessels[vess.neigh1[1]-1].num_cells != 0)):
#
# smoothed = False
#
# while (smoothed == False):
# rand_cell = rand.randint(0, vess.num_cells-1)
#
# if (vess.cells[rand_cell].migrate != 0):
# vess.cells[rand_cell].migrate = 0
# smoothed = True
# If flow in the vessel is negative, check upstream neighbour
if (vess.Q < 0.):
# If current vessel has only one upstream neighbour
if (len(vess.neigh0) == 1):
if (vessels[vess.neigh0[0]-1].num_cells < vess.num_cells) and (vessels[vess.neigh0[0]-1].num_cells != 0):
#if (vessels[vess.neigh0[0]-1].num_cells < vess.num_cells):
smoothed = False
while (smoothed == False):
rand_cell = rand.randint(0, vess.num_cells-1)
if (vess.cells[rand_cell].migrate != 0):
vess.cells[rand_cell].migrate = 0
smoothed = True
# # If current vessel has more than one upstream neighbour
# if (len(vess.neigh0) == 2):
# if ((vessels[vess.neigh0[0]-1].num_cells < vess.num_cells) and (vessels[vess.neigh0[0]-1].num_cells != 0)) or ((vessels[vess.neigh0[1]-1].num_cells < vess.num_cells) and (vessels[vess.neigh0[1]-1].num_cells != 0)):
#
# smoothed = False
#
# while (smoothed == False):
# rand_cell = rand.randint(0, vess.num_cells-1)
#
# if (vess.cells[rand_cell].migrate != 0):
# vess.cells[rand_cell].migrate = 0
# smoothed = True
#------------------------------------------------------------------------------
# Handle a bifurcation point while migrating
def handle_bifurcation(migrating_cell, parent_vess, bif_node, branch1, branch2):
# Determine if flow within branches are incoming or outgoing of the bifurcation
if (branch1.n1 == bif_node):
if (branch1.Q > 0):
branch1_status = "incoming"
else:
branch1_status = "outgoing"
if (branch1.n0 == bif_node):
if (branch1.Q > 0):
branch1_status = "outgoing"
else:
branch1_status = "incoming"
if (branch2.n1 == bif_node):
if (branch2.Q > 0):
branch2_status = "incoming"
else:
branch2_status = "outgoing"
if (branch2.n0 == bif_node):
if (branch2.Q > 0):
branch2_status = "outgoing"
else:
branch2_status = "incoming"
# If flow is only incoming in one branch, always choose that branch (ie, against flow)
if (branch1_status == "incoming" and branch2_status == "outgoing"):
migrating_cell.vessID = branch1.ID
branch1.cells.append(migrating_cell)
return
if (branch2_status == "incoming" and branch1_status == "outgoing"):
migrating_cell.vessID = branch2.ID
branch2.cells.append(migrating_cell)
return
# If a flow-converging, cell-diverging bifurcation, randomly pick one
if (branch1_status == "incoming" and branch2_status == "incoming"):
#bifurcation_rule(migrating_cell, parent_vess, branch1, branch2)
new_bifurcation_rule(migrating_cell, parent_vess, branch1, branch2)
return
#------------------------------------------------------------------------------
# Determine cell behavior using the specified bifurcation rule
def bifurcation_rule(migrating_cell, parent_vess, branch1, branch2):
# Bifurcation Rule 1 - Choose branch with the highest flow
if (branch_rule == 1):
if (abs(branch1.Q) > abs(branch2.Q)):
migrating_cell.vessID = branch1.ID
branch1.cells.append(migrating_cell)
return
else:
migrating_cell.vessID = branch2.ID
branch2.cells.append(migrating_cell)
return
# Bifurcation Rule 3 - Choose one branch at random, equal probability
if (branch_rule == 3):
if (rand.uniform(0, 1) > 0.5):
migrating_cell.vessID = branch1.ID
branch1.cells.append(migrating_cell)
return
else:
migrating_cell.vessID = branch2.ID
branch2.cells.append(migrating_cell)
return
# Bifurcation Rule 4 - Assign probability based on number of cells
if (branch_rule == 4):
if (branch1.num_cells < parent_vess.num_cells) and (branch2.num_cells < parent_vess.num_cells):
prob1 = (branch1.num_cells/parent_vess.num_cells)
else:
prob1 = (branch1.num_cells/(branch1.num_cells + branch2.num_cells))
if (rand.uniform(0, 1) < prob1):
migrating_cell.vessID = branch1.ID
branch1.cells.append(migrating_cell)
return
else:
migrating_cell.vessID = branch2.ID
branch2.cells.append(migrating_cell)
return
# Bifurcation Rule 6 - Weighted average of flow and cell number
if (branch_rule == 6):
Q_ratio = branch2.Q/(branch1.Q + branch2.Q)
cell_ratio = branch2.num_cells/(branch1.num_cells + branch2.num_cells)
prob2 = branch_alpha*Q_ratio + (1 - branch_alpha)*cell_ratio
if (rand.uniform(0, 1) > prob2):
migrating_cell.vessID = branch1.ID
branch1.cells.append(migrating_cell)
return
else:
migrating_cell.vessID = branch2.ID
branch2.cells.append(migrating_cell)
return
# Bifurcation Rule 7 - Weighted average of WSS and cell number
if (branch_rule == 7):
if ((branch1.tau + branch2.tau) != 0. and (branch1.num_cells + branch2.num_cells) != 0.):
tau_ratio = branch2.tau/(branch1.tau + branch2.tau)
cell_ratio = branch2.num_cells/(branch1.num_cells + branch2.num_cells)
tau1 = branch1.tau/(branch1.tau + branch2.tau)
cell1 = branch1.num_cells/(branch1.num_cells + branch2.num_cells)
tau2 = branch2.tau/(branch1.tau + branch2.tau)
cell2 = branch2.num_cells/(branch1.num_cells + branch2.num_cells)
#prob1 = branch_alpha*tau1 + (1 - branch_alpha)*cell1
#prob2 = branch_alpha*tau2 + (1 - branch_alpha)*cell2
prob1 = branch_alpha*tau1 + (1 - branch_alpha)*cell2
prob2 = branch_alpha*tau2 + (1 - branch_alpha)*cell1
assert (round(prob1, 8) == round((1 - prob2), 8)), "p1 = {0} does not match {1}".format(prob1, (1 - prob2))
if (rand.uniform(0, 1) > prob2):
migrating_cell.vessID = branch1.ID
branch1.cells.append(migrating_cell)
return
else:
migrating_cell.vessID = branch2.ID
branch2.cells.append(migrating_cell)
return
#------------------------------------------------------------------------------
# Handle a bifurcation point while migrating (new)
def new_handle_bifurcation(migrating_cell, parent_vess, bif_node, branch1, branch2, bifur_nodes, bifur):
# Set the minimum value of flow, less than this and cells won't consider entering that branch
flow_min = (1e-4)/(3.6e12)
# Determine if flow within branches are incoming or outgoing of the bifurcation
if (branch1.n0 == bif_node):
if (abs(branch1.Q) < flow_min):
branch1_status = "zero"
else:
if (branch1.Q > 0):
branch1_status = "outgoing"
else:
branch1_status = "incoming"
if (branch1.n1 == bif_node):
if (abs(branch1.Q) < flow_min):
branch1_status = "zero"
else:
if (branch1.Q > 0):
branch1_status = "incoming"
else:
branch1_status = "outgoing"
if (branch2.n0 == bif_node):
if (abs(branch2.Q) < flow_min):
branch2_status = "zero"
else:
if (branch2.Q > 0):
branch2_status = "outgoing"
else:
branch2_status = "incoming"
if (branch2.n1 == bif_node):
if (abs(branch2.Q) < flow_min):
branch2_status = "zero"
else:
if (branch2.Q > 0):
branch2_status = "incoming"
else:
branch2_status = "outgoing"
# If flow is zero in one of the branches, chose the other one
if (branch1_status != "zero" and branch2_status == "zero"):
migrating_cell.vessID = branch1.ID
branch1.cells.append(migrating_cell)
return
if (branch1_status == "zero" and branch2_status != "zero"):
migrating_cell.vessID = branch2.ID
branch2.cells.append(migrating_cell)
return
# If flow is only incoming in one branch, always choose that branch (ie, against flow)
if (branch1_status == "incoming" and branch2_status == "outgoing"):
migrating_cell.vessID = branch1.ID
branch1.cells.append(migrating_cell)
return
if (branch2_status == "incoming" and branch1_status == "outgoing"):
migrating_cell.vessID = branch2.ID
branch2.cells.append(migrating_cell)
return
# If a flow-converging, cell-diverging bifurcation, enact bifurcation rules
if (branch1_status == "incoming" and branch2_status == "incoming"):
new_bifurcation_rule(migrating_cell, parent_vess, branch1, branch2)
#------------------------------------------------------------------------------
# Determine cell behavior using the specified bifurcation rule (new)
def new_bifurcation_rule(migrating_cell, parent_vess, branch1, branch2):
# Handle the case of capillaries splitting off from the vein
if (parent_vess.type == "vein" and branch1.type == "vein") or (parent_vess.type == "vein" and branch2.type == "vein"):
# Vein bifurcation option 1 - Probabilty of splitting off vein given by initial capillary and vein size
if (vein_bf_option == 1):
if (branch1.type == "capillary"):
prob1 = num_cell_cap/num_cell_vein
if (rand.uniform(0,1) <= prob1):
migrating_cell.vessID = branch1.ID
branch1.cells.append(migrating_cell)
return
if (branch2.type == "capillary"):
prob2 = num_cell_cap/num_cell_vein
if (rand.uniform(0,1) <= prob2):
migrating_cell.vessID = branch2.ID
branch2.cells.append(migrating_cell)
return
# Vein bifurcation option 2 - Implement form of capillary bifurcation rules at vein
if (vein_bf_option == 2):
# Bifurcation Rule 3 - Choose a branch at random, equal chance
if (branch_rule == 3):
if (branch1.type == "capillary"):
if (rand.uniform(0, 1) <= 0.5):
migrating_cell.vessID = branch1.ID
branch1.cells.append(migrating_cell)
return
if (branch2.type == "capillary"):
if (rand.uniform(0, 1) <= 0.5):
migrating_cell.vessID = branch2.ID
branch2.cells.append(migrating_cell)
return
# Bifurcation Rule 7 - Weighted average of WSS and cell number
if (branch_rule == 7):
if (branch1.type == "capillary"):
tau_ratio = branch1.tau/parent_vess.tau
cell_ratio = branch1.num_cells/parent_vess.num_cells
prob1 = branch_alpha*tau_ratio + (1 - branch_alpha)*cell_ratio
if (rand.uniform(0,1) <= prob1):
migrating_cell.vessID = branch1.ID
branch1.cells.append(migrating_cell)
return
if (branch2.type == "capillary"):
tau_ratio = branch2.tau/parent_vess.tau
cell_ratio = branch2.num_cells/parent_vess.num_cells
prob2 = branch_alpha*tau_ratio + (1 - branch_alpha)*cell_ratio
if (rand.uniform(0,1) <= prob2):
migrating_cell.vessID = branch2.ID
branch2.cells.append(migrating_cell)
return
# If all vessels in question are capillaries, enact bifurcation rule
if (branch1.type == "capillary" and branch2.type == "capillary"):
# Bifurcation Rule 1 - Choose branch with the highest flow
if (branch_rule == 1):
if (abs(branch1.Q) > abs(branch2.Q)):
migrating_cell.vessID = branch1.ID
branch1.cells.append(migrating_cell)
return
else:
migrating_cell.vessID = branch2.ID
branch2.cells.append(migrating_cell)
return
# Bifurcation Rule 2 - Choose the branch with most similar polarity
if (branch_rule == 2):
if (migrating_cell.polarity*branch1.unit < migrating_cell.polarity*branch2.unit):
migrating_cell.vessID = branch1.ID
branch1.cells.append(migrating_cell)
return
else:
migrating_cell.vessID = branch2.ID
branch2.cells.append(migrating_cell)
return
# Bifurcation Rule 3 - Choose one branch at random, equal probability
if (branch_rule == 3):
if (rand.uniform(0, 1) > 0.5):
migrating_cell.vessID = branch1.ID
branch1.cells.append(migrating_cell)
return
else:
migrating_cell.vessID = branch2.ID
branch2.cells.append(migrating_cell)
return
# Bifurcation Rule 4 - Choose one branch at random, equal probability
if (branch_rule == 4):
if (rand.uniform(0, 1) > 0.3):
migrating_cell.vessID = branch1.ID
branch1.cells.append(migrating_cell)
return
else:
migrating_cell.vessID = branch2.ID
branch2.cells.append(migrating_cell)
return
# Bifurcation Rule 5 - Assign probability based on number of cells
if (branch_rule == 5):
if (branch1.num_cells < parent_vess.num_cells) and (branch2.num_cells < parent_vess.num_cells):
prob1 = (branch1.num_cells/parent_vess.num_cells)
else:
prob1 = (branch1.num_cells/(branch1.num_cells + branch2.num_cells))
if (rand.uniform(0, 1) < prob1):
migrating_cell.vessID = branch1.ID
branch1.cells.append(migrating_cell)
return
else:
migrating_cell.vessID = branch2.ID
branch2.cells.append(migrating_cell)
return
# Bifurcation Rule 6 - Weighted average of flow and cell number
if (branch_rule == 6):
Q_ratio = branch2.Q/(branch1.Q + branch2.Q)
cell_ratio = branch2.num_cells/(branch1.num_cells + branch2.num_cells)
prob2 = branch_alpha*Q_ratio + (1 - branch_alpha)*cell_ratio
if (rand.uniform(0, 1) > prob2):
migrating_cell.vessID = branch1.ID
branch1.cells.append(migrating_cell)
return
else:
migrating_cell.vessID = branch2.ID
branch2.cells.append(migrating_cell)
return
# Bifurcation Rule 7 - Weighted average of WSS and cell number
if (branch_rule == 7):
if ((branch1.tau + branch2.tau) != 0. and (branch1.num_cells + branch2.num_cells) != 0.):
tau_ratio = branch2.tau/(branch1.tau + branch2.tau)
cell_ratio = branch2.num_cells/(branch1.num_cells + branch2.num_cells)
tau1 = branch1.tau/(branch1.tau + branch2.tau)
cell1 = branch1.num_cells/(branch1.num_cells + branch2.num_cells)
tau2 = branch2.tau/(branch1.tau + branch2.tau)
cell2 = branch2.num_cells/(branch1.num_cells + branch2.num_cells)
prob1 = branch_alpha*tau1 + (1 - branch_alpha)*cell1
prob2 = branch_alpha*tau2 + (1 - branch_alpha)*cell2
if (branch1.first_bprob == True):
branch1.bprob = prob1
branch1.first_bprob = False
else:
prob1 = (bp_u*prob1 + bp_v*branch1.bprob)/(bp_u + bp_v)
branch1.bprob = prob1
if (branch2.first_bprob == True):
branch2.bprob = prob2
branch2.first_bprob = False
else:
prob2 = (bp_u*prob2 + bp_v*branch2.bprob)/(bp_u + bp_v)
branch2.bprob = prob2
#assert (round(prob1, 8) == round((1 - prob2), 8)), "p1 = {0} does not match {1}".format(prob1, (1 - prob2))
if (rand.uniform(0, 1) > prob2):
migrating_cell.vessID = branch1.ID
branch1.cells.append(migrating_cell)
return
else:
migrating_cell.vessID = branch2.ID
branch2.cells.append(migrating_cell)
return