def test_LineSourcePotential_02(self):
'''test LineSourcePotential implementation when assigning
a location inside cylindric volume'''
cell = get_cell(n_seg=1)
cell.z = cell.z * 10
lsp = lfp.LineSourcePotential(cell=cell,
x=np.array([.131441]),
y=np.array([0.]),
z=np.array([5.]),
sigma=0.3)
M = lsp.get_transformation_matrix()
imem = np.array([[0., 1., -1.]])
V_ex = M @ imem
Deltas_n = 10.
h_n = -5.
r_n = cell.d[0] / 2
l_n = Deltas_n + h_n
# Use Eq. C.13 case II (h<0, l>0) from Gary Holt's 1998 thesis
V_gt = imem / (4 * np.pi * lsp.sigma * Deltas_n) * np.log(
(np.sqrt(h_n**2 + r_n**2) - h_n) *
(np.sqrt(l_n**2 + r_n**2) + l_n) / r_n**2)
np.testing.assert_allclose(V_ex, V_gt)
def test_LineSourcePotential_03(self):
'''test LineSourcePotential implementation'''
cell = get_cell(n_seg=1)
cell.z = cell.z * 10
lsp = lfp.LineSourcePotential(cell=cell,
x=np.array([2.]),
y=np.array([0.]),
z=np.array([-1.]),
sigma=0.3)
M = lsp.get_transformation_matrix()
imem = np.array([[0., 1., -1.]])
V_ex = M @ imem
Deltas_n = 10.
h_n = 1.
r_n = 2.
l_n = Deltas_n + h_n
# Use Eq. C.13 case III (h>0, l>0) from Gary Holt's 1998 thesis
V_gt = imem / (4 * np.pi * lsp.sigma * Deltas_n) * np.log(
(np.sqrt(l_n**2 + r_n**2) + l_n) /
(np.sqrt(h_n**2 + r_n**2) + h_n))
np.testing.assert_allclose(V_ex, V_gt)
def test_RecExtElectrode_04(self):
"""test RecExcElectrode implementation,
method='root_as_point' and rootinds parameter"""
cell = get_cell(n_seg=4)
sigma = 0.3
r = np.array([1, 0, 2])
# all point sources
el0 = lfp.PointSourcePotential(cell=cell,
x=np.array([r[0]]),
y=np.array([r[1]]),
z=np.array([r[2]]),
sigma=sigma)
M0 = el0.get_transformation_matrix()
# all line sources
el1 = lfp.LineSourcePotential(cell=cell,
x=np.array([r[0]]),
y=np.array([r[1]]),
z=np.array([r[2]]),
sigma=sigma)
M1 = el1.get_transformation_matrix()
# vary which index is treated as point
ids = np.arange(cell.totnsegs)
for i in range(cell.totnsegs):
el = lfp.RecExtElectrode(cell=cell,
x=r[0],
y=r[1],
z=r[2],
sigma=sigma,
method='root_as_point',
rootinds=np.array([i]))
M = el.get_transformation_matrix()
np.testing.assert_almost_equal(M0[0, i], M[0, i])
np.testing.assert_equal(M1[0, ids != i], M[0, ids != i])
# multiple roots
for i in range(cell.totnsegs - 1):
rootinds = np.array([i, i + 1])
notroots = np.ones(cell.totnsegs, dtype=bool)
notroots[rootinds] = False
el = lfp.RecExtElectrode(cell=cell,
x=r[0],
y=r[1],
z=r[2],
sigma=sigma,
method='root_as_point',
rootinds=rootinds)
M = el.get_transformation_matrix()
np.testing.assert_allclose(M0[0, rootinds], M[0, rootinds])
np.testing.assert_equal(M1[0, notroots], M[0, notroots])
# locations where extracellular potential is predicted
dx = 1
dz = 1
axis = np.round([x.min() - 10, x.max() + 10, y.min() - 10, y.max() + 10])
# axis = np.round(axis)
X, Y = np.meshgrid(
np.linspace(axis[0], axis[1],
int(np.diff(axis[:2]) // dx) + 1),
np.linspace(axis[2], axis[3],
int(np.diff(axis[2:]) // dz) + 1))
Z = np.zeros_like(X)
# LineSourcePotential object, get mapping for all segments per CV
lsp = lfpykit.LineSourcePotential(cell=cell_geometry,
x=X.flatten(),
y=Y.flatten(),
z=Z.flatten())
M_tmp = lsp.get_transformation_matrix()
# Define response matrix from M with columns weighted by area of each frusta
M = np.zeros((lsp.x.size, I_m.shape[0]))
for i in range(I_m.shape[0]):
inds = CV_ind == i
M[:, i] = M_tmp[:, inds] @ (cell_geometry.area[inds] /
cell_geometry.area[inds].sum())
# Extracellular potential using segment information at last time step
# in x,y-plane coordinates
V_e = M @ cell_geometry.I_m[:, -1]