def plotPO2YProfile(simParams, x=150e-6, **kwargs):
kroghSol = KroghSolution2DCone(simParams)
kroghSol.intravascularResistanceLDHalf = kwargs.get(
'K0', kroghSol.intravascularResistanceLDHalf)
kroghSol.convO2Transport = kwargs.get('convO2Transport', True)
if 'K0' in kwargs:
print "plotPO2Profile: Using K0 = %g" % kwargs['K0']
style = kwargs.get('style', {'color': 'k'})
PO2AnalyticalStyle = {
'color': 'k',
'linestyle': '-',
'linewidth': 1,
'dashes': (1.2, 1.5)
}
# 'dashes': (5,2.5,1,2.5)}
nr = 300
rMax = kroghSol.geometry.tissueRadius(x)
rAnalytical = np.linspace(0, rMax, nr)
rTissue = np.linspace(kroghSol.geometry['radiusWall'], rMax, nr)
PO2Analytical = [kroghSol.PO2Analytical(x, r) for r in rAnalytical]
PO2Tissue = [kroghSol.PO2Tissue(x, r) for r in rTissue]
PO2RBCMean = kroghSol.PO2RBCMeanAtX(x)
plt.plot(1e6 * rAnalytical, PO2Analytical, **PO2AnalyticalStyle)
plt.plot(1e6 * rTissue, PO2Tissue, linewidth=1, **style)
plt.plot(1e6 * kroghSol.Rrbc / 2, PO2RBCMean, '.', color='k', markersize=4)
plt.xlim(0, 1e6 * rMax)
plt.ylim(rounded_bounds(PO2Analytical, 10))
labels.setXLabel('r', 'um')
labels.setYLabel('PO2', 'mmHg')
def plotPO2ProfileInterstitialSpace(simParams, radius=17.6e-6, **kwargs):
kroghSol = KroghSolution2DCone(simParams)
kroghSol.intravascularResistanceLDHalf = kwargs.get(
'K0', kroghSol.intravascularResistanceLDHalf)
if 'K0' in kwargs:
print "plotPO2Profile: Using K0 = %g" % kwargs['K0']
style = kwargs.get('style', {'color': 'k'})
L = simParams['domainLength']
nx = 100
xValues = np.linspace(0, L, nx)
PO2 = [kroghSol.PO2Tissue(x, radius) for x in xValues]
plt.plot(1e6 * xValues, PO2, linewidth=1, **style)
plt.ylim(rounded_bounds(PO2, 10))
interstitialLayerWidth = 0.35e-6
kroghSol.geometry['radiusWall'] += interstitialLayerWidth
kroghSol.intravascularResistanceLDHalf *= 1.1
PO2WithInterstitial = [kroghSol.PO2Tissue(x, radius) for x in xValues]
plt.plot(1e6 * xValues, PO2WithInterstitial, '--')
labels.setXLabel('x', 'um')
labels.setYLabel('PO2', 'mmHg')
print 'Difference: ', np.array(PO2) - np.array(PO2WithInterstitial)
def plot_compared_hb_distal_distribution_multipanel(self, bin_width=0.02,
panel_annotation=('A', 'B', 'C')):
"""
Plot a comparison between the simulated and the integrated hemoglobin distribution.
Args:
bin_width (float): bin width for histogram
panel_annotation (sequence): panel annotations
"""
f, axarr = plt.subplots(4, sharex=True)
hist_axes = axarr[0:3]
bp_ax = axarr[-1]
sim_hb = self.postprocessor.distal_hb()
# compute integrated distal hemoglobin distributions
self.postprocessor.integrator.use_topological_radii = True
self.postprocessor.integrator.compute()
int_topol_hb, topol_weights = self.postprocessor.integrator.distal_hb_distribution()
int_topol_hb_repeat = self.postprocessor.integrator.distal_hb_distribution_with_repeat()
int_topol_mean = self.postprocessor.integrator.average_distal_hb()
int_topol_std = self.postprocessor.integrator.std_distal_hb()
self.postprocessor.integrator.use_topological_radii = False
self.postprocessor.integrator.compute()
int_func_hb, func_weights = self.postprocessor.integrator.distal_hb_distribution()
int_func_hb_repeat = self.postprocessor.integrator.distal_hb_distribution_with_repeat()
int_func_mean = self.postprocessor.integrator.average_distal_hb()
int_func_std = self.postprocessor.integrator.std_distal_hb()
# plot histograms
bounds = rounded_bounds(np.hstack((sim_hb, int_topol_hb, int_func_hb)), bin_width)
bins = np.arange(bounds[0], bounds[1]+0.5*bin_width, bin_width)
simul_count, _ = np.histogram(sim_hb, bins=bins, normed=True)
int_topol_count, _ = np.histogram(int_topol_hb, weights=topol_weights,
bins=bins, normed=True)
int_func_count, _ = np.histogram(int_func_hb, weights=func_weights,
bins=bins, normed=True)
bar_fraction = 0.8
bar_width = bin_width*bar_fraction
x = 0.5*(bins[:-1] + bins[1:])
hist_axes[0].bar(x, simul_count, bar_width,
edgecolor=style_scheme['simul_radii_edge_color'],
facecolor=style_scheme['simul_radii_face_color'],
linewidth=0.3,
label='moving RBCs')
hist_axes[1].bar(x, int_func_count, bar_width,
edgecolor=style_scheme['int_func_radii_edge_color'],
facecolor=style_scheme['int_func_radii_face_color'],
linewidth=0.3,
label='ODE (functional)')
hist_axes[2].bar(x, int_topol_count, bar_width,
edgecolor=style_scheme['int_topol_radii_edge_color'],
facecolor=style_scheme['int_topol_radii_face_color'],
linewidth=0.3,
label='ODE (geometric)')
xlim = max(0.0, round_to_base(axarr[0].get_xlim()[0], 0.1, func=np.floor)), \
axarr[0].get_xlim()[1]
axarr[0].set_xlim(xlim)
# plot mean and standard deviation
y_max = np.max(np.hstack((simul_count, int_topol_count, int_func_count)))
sim_mean = np.mean(self.postprocessor.distal_hb())
sim_std = np.std(self.postprocessor.distal_hb())
y_error_bar = 1.05*y_max
hist_axes[0].errorbar(sim_mean, y_error_bar, xerr=sim_std,
fmt='o', markersize=2, linewidth=1,
elinewidth=0.5,
capsize=2, capthick=0.5,
color=style_scheme['simul_radii_face_color'])
hist_axes[1].errorbar(int_func_mean, y_error_bar, xerr=int_func_std,
fmt='o', markersize=2, linewidth=1,
elinewidth=0.5,
capsize=2, capthick=0.5,
color=style_scheme['int_func_radii_face_color'])
hist_axes[2].errorbar(int_topol_mean, y_error_bar, xerr=int_topol_std,
fmt='o', markersize=2, linewidth=1,
elinewidth=0.5,
capsize=2, capthick=0.5,
color=style_scheme['int_topol_radii_edge_color'])
setXLabel('\mathrm{outflow\;saturation}\;S_v', '')
axarr[0].xaxis.set_major_locator(MultipleLocator(0.1))
for ax, annotation in zip(hist_axes, panel_annotation):
styles.create_COSH_legend(ax, loc='upper left')
ax.yaxis.set_major_locator(MultipleLocator(5))
# ax.yaxis.set_major_locator(MultipleLocator(10))
setYLabel('f_{S_v}', '', ax=ax)
for ax, annotation in zip(axarr, panel_annotation):
annotate_axis_corner(ax, annotation, xy=(0.956, 0.79))
# if annotation != 'C':
# annotate_axis_corner(ax, annotation, xy=(0.956, 0.79))
# else:
# annotate_axis_corner(ax, annotation, xy=(0.956, 0.72))
# boxplot
data = [int_topol_hb_repeat, int_func_hb_repeat, sim_hb]
offset = len(panel_annotation) - len(data)
labels = panel_annotation[-1-offset::-1]
medianprops = {'color': 'w'}
flierprops = {'marker': '.', 'markersize': 2}
bp = bp_ax.boxplot(data, whis=[5, 95], vert=False, labels=labels,
patch_artist=True, medianprops=medianprops, flierprops=flierprops,
showfliers=False)
fill_colors = [style_scheme['int_topol_radii_edge_color'],
style_scheme['int_func_radii_face_color'],
style_scheme['simul_radii_face_color']]
for patch, color in zip(bp['boxes'], fill_colors):
patch.set_facecolor(color)
print "5th percentile of topological: ", np.percentile(int_topol_hb_repeat, 5)
print "First quartile of topological: ", np.percentile(int_topol_hb_repeat, 25)
print "Median of topological: ", np.percentile(int_topol_hb_repeat, 50)
print "Third quartile of topological: ", np.percentile(int_topol_hb_repeat, 75)
print "95th percentile of topological: ", np.percentile(int_topol_hb_repeat, 95)
# statistical testing
F = int_topol_std**2/sim_std**2
pvalue = scipy.stats.f.sf(F, np.size(int_topol_hb) - 1, np.size(sim_hb) - 1)
print "p-value for ODE model (topological radii) vs. moving RBC: {:g}".format(pvalue)
F = int_func_std**2/sim_std**2
pvalue = scipy.stats.f.sf(F, np.size(int_func_hb) - 1, np.size(sim_hb) - 1)
print "p-value for ODE model (functional radii) vs. moving RBC: {:g}".format(pvalue)
F = int_topol_std**2/int_func_std**2
pvalue = scipy.stats.f.sf(F, np.size(int_topol_hb) - 1, np.size(int_func_hb) - 1)
print "p-value for ODE model, topological vs. functional radii: {:g}".format(pvalue)
def plot_compared_hb_distal_distribution(self, bin_width=0.02):
"""
Plot a comparison between the simulated and the integrated hemoglobin distribution.
Args:
bin_width (float): bin width for histogram
"""
ax = plt.gca()
sim_hb = self.postprocessor.distal_hb()
# compute integrated distal hemoglobin distributions
self.postprocessor.integrator.use_topological_radii = True
self.postprocessor.integrator.compute()
int_topol_hb, topol_weights = self.postprocessor.integrator.distal_hb_distribution()
int_topol_mean = self.postprocessor.integrator.average_distal_hb()
int_topol_std = self.postprocessor.integrator.std_distal_hb()
self.postprocessor.integrator.use_topological_radii = False
self.postprocessor.integrator.compute()
int_func_hb, func_weights = self.postprocessor.integrator.distal_hb_distribution()
int_func_mean = self.postprocessor.integrator.average_distal_hb()
int_func_std = self.postprocessor.integrator.std_distal_hb()
# plot histograms
bounds = rounded_bounds(np.hstack((sim_hb, int_topol_hb, int_func_hb)), bin_width)
bins = np.arange(bounds[0], bounds[1]+0.5*bin_width, bin_width)
bar_fraction = 0.7
bar_width = 1./3.*bin_width*bar_fraction
simul_count, _ = np.histogram(sim_hb, bins=bins, normed=True)
int_topol_count, _ = np.histogram(int_topol_hb, weights=topol_weights,
bins=bins, normed=True)
int_func_count, _ = np.histogram(int_func_hb, weights=func_weights,
bins=bins, normed=True)
x1 = 0.5*(bins[:-1] + bins[1:]) - bar_width
x2 = 0.5*(bins[:-1] + bins[1:])
x3 = 0.5*(bins[:-1] + bins[1:]) + bar_width
ax.bar(x1, simul_count, bar_width,
edgecolor=style_scheme['simul_radii_edge_color'],
facecolor=style_scheme['simul_radii_face_color'],
linewidth=0.3,
label='moving RBCs')
ax.bar(x2, int_func_count, bar_width,
edgecolor=style_scheme['int_func_radii_edge_color'],
facecolor=style_scheme['int_func_radii_face_color'],
linewidth=0.3,
label='ODE (functional)')
ax.bar(x3, int_topol_count, bar_width,
edgecolor=style_scheme['int_topol_radii_edge_color'],
facecolor=style_scheme['int_topol_radii_face_color'],
linewidth=0.3,
label='ODE (geometric)')
xlim = max(0.0, round_to_base(ax.get_xlim()[0], 0.1, func=np.floor)), ax.get_xlim()[1]
ax.set_xlim(xlim)
# plot mean and standard deviation
y_max = np.max(np.hstack((simul_count, int_topol_count, int_func_count)))
sim_mean = np.mean(self.postprocessor.distal_hb())
sim_std = np.std(self.postprocessor.distal_hb())
ax.errorbar(sim_mean, 1.1*y_max, xerr=sim_std,
fmt='o', markersize=2, linewidth=1,
elinewidth=0.5,
capsize=2, capthick=0.5,
color=style_scheme['simul_radii_face_color'])
ax.errorbar(int_func_mean, 1.06*y_max, xerr=int_func_std,
fmt='o', markersize=2, linewidth=1,
elinewidth=0.5,
capsize=2, capthick=0.5,
color=style_scheme['int_func_radii_face_color'])
ax.errorbar(int_topol_mean, 1.02*y_max, xerr=int_topol_std,
fmt='o', markersize=2, linewidth=1,
elinewidth=0.5,
capsize=2, capthick=0.5,
color=style_scheme['int_topol_radii_edge_color'])
styles.create_COSH_legend(ax, bbox_to_anchor=(0.45, 0.95))
setXLabel('\mathrm{outflow\;saturation}\;S_v', '')
setYLabel('\mathrm{probability\;density}', '')
ax.xaxis.set_major_locator(MultipleLocator(0.1))
ax.yaxis.set_major_locator(MultipleLocator(5))
def plot_integrated_hb_distal_distribution(self, bin_width=0.01, **kwargs):
hb, weights = self.postprocessor.integrator.distal_hb_distribution()
bounds = rounded_bounds(hb, bin_width)
bins = np.arange(bounds[0], bounds[1]+0.5*bin_width, bin_width)
plt.hist(hb, bins=bins, histtype='bar', weights=weights, **kwargs)
setXLabel('\mathrm{outflow\;saturation}\;S_v', '')
def plot_simulated_hb_distal_distribution(self, bin_width=0.01, **kwargs):
values = self.postprocessor.distal_hb()
bounds = rounded_bounds(values, bin_width)
bins = np.arange(bounds[0], bounds[1]+0.5*bin_width, bin_width)
plt.hist(values, bins=bins, histtype='bar', **kwargs)
setXLabel('\mathrm{outflow\;saturation}\;S_v', '')