"""Computation of apparent Young's modulus for RT-DC measurements"""
from __future__ import annotations
import numbers
import pathlib
from typing import Literal
import warnings
import numpy as np
import scipy.interpolate as spint
from ...warn import PipelineWarning
from .load import load_lut, load_mtext, register_lut # noqa: F401
from .pxcorr import get_pixelation_delta
from .pxcorr import get_pixelation_delta_pair # noqa: F401
# TODO: remove deprecated `convert`
from .scale_linear import convert # noqa: F401
from .scale_linear import scale_emodulus, scale_feature
from .viscosity import get_viscosity
#: Set this to True to globally enable spline extrapolation when the
#: `area_um`/`deform` data are outside the LUT. This is discouraged and
#: a :class:`KnowWhatYouAreDoingWarning` warning will be issued.
INACCURATE_SPLINE_EXTRAPOLATION = False
[docs]class KnowWhatYouAreDoingWarning(PipelineWarning):
pass
[docs]class YoungsModulusLookupTableExceededWarning(PipelineWarning):
pass
[docs]def get_emodulus(deform: float | np.array,
area_um: float | np.array | None = None,
volume: float | np.array | None = None,
medium: float | str = "0.49% MC-PBS",
channel_width: float = 20.0,
flow_rate: float = 0.16,
px_um: float = 0.34,
temperature: float | np.ndarray | None = 23.0,
lut_data: str | pathlib.Path | np.ndarray = "LE-2D-FEM-19",
visc_model: Literal['herold-2017',
'herold-2017-fallback',
'buyukurganci-2022',
'kestin-1978',
None] = "herold-2017-fallback",
extrapolate: bool = INACCURATE_SPLINE_EXTRAPOLATION,
copy: bool = True):
"""Compute apparent Young's modulus using a look-up table
Parameters
----------
area_um: float or ndarray
Apparent (2D image) area [µm²] of the event(s)
deform: float or ndarray
Deformation (1-circularity) of the event(s)
volume: float or ndarray
Apparent volume of the event(s). It is not possible to define
`volume` and `area_um` at the same time (makes no sense).
.. versionadded:: 0.25.0
medium: str or float
The medium to compute the viscosity for. If a string
is given, the viscosity is computed. If a float is given,
this value is used as the viscosity in mPa*s (Note that
`temperature` and `visc_model` must be set to None in this case).
channel_width: float
The channel width [µm]
flow_rate: float
Flow rate [µL/s]
px_um: float
The detector pixel size [µm] used for pixelation correction.
Set to zero to disable.
temperature: float, ndarray, or None
Temperature [°C] of the event(s)
lut_data: path, str, or tuple of (np.ndarray of shape (N, 3), dict)
The LUT data to use. If it is a key in :const:`INTERNAL_LUTS`,
then the respective LUT will be used. Otherwise, a path to a
file on disk or a tuple (LUT array, metadata) is possible.
The LUT metadata is used to check whether the given features
(e.g. `area_um` and `deform`) are valid interpolation choices.
.. versionadded:: 0.25.0
visc_model: str
The viscosity model to use,
see :func:`dclab.features.emodulus.viscosity.get_viscosity`
extrapolate: bool
Perform extrapolation using :func:`extrapolate_emodulus`. This
is discouraged!
copy: bool
Copy input arrays. If set to false, input arrays are
overridden.
Returns
-------
elasticity: float or ndarray
Apparent Young's modulus in kPa
Notes
-----
- The look-up table used was computed with finite elements methods
according to :cite:`Mokbel2017` and complemented with analytical
isoelastics from :cite:`Mietke2015`. The original simulation
results are available on figshare :cite:`FigshareWittwer2020`.
- The computation of the Young's modulus takes into account
a correction for the viscosity (medium, channel width, flow rate,
and temperature) :cite:`Mietke2015` and a correction for
pixelation for the deformation which were derived
from a (pixelated) image :cite:`Herold2017`.
- Note that while deformation is pixelation-corrected, area_um and
volume are scaled to match the LUT data. This is somewhat
fortunate, because we don't have to worry about the order of
applying pixelation correction and scale conversion.
- By using external LUTs, it is possible to interpolate on the
volume-deformation plane. This feature was added in version
0.25.0.
See Also
--------
dclab.features.emodulus.viscosity.get_viscosity: compute viscosity
for known media
"""
# Get lut data
lut, lut_meta = load_lut(lut_data)
# Get the correct features (sanity checks)
featx, featy, _ = lut_meta["column features"]
if featx == "area_um" and featy == "deform":
assert volume is None, "Don't define area_um and volume at same time!"
datax = np.array(area_um, dtype=float, copy=copy)
elif featx == "volume" and featy == "deform":
assert area_um is None, "Don't define area_um and volume at same time!"
datax = np.array(volume, dtype=float, copy=copy)
else:
raise KeyError("No recipe for '{}' and '{}'!".format(featx, featy))
# copy deform so we can use in-place pixel correction
deform = np.array(deform, dtype=float, copy=copy)
if px_um:
# Correct deformation for pixelation effect (subtract ddelt).
# It is important to do this before scaling datax (area_um/volume).
deform -= get_pixelation_delta(feat_corr=featy,
feat_absc=featx,
data_absc=datax,
px_um=px_um)
# Compute viscosity
if isinstance(medium, numbers.Number):
visco = medium
if temperature is not None:
raise ValueError("If `medium` is given in Pa*s, then "
+ "`temperature` must be set to None!")
if visc_model is not None:
warnings.warn("If `medium` is given in Pa*s, then `visc_model` "
"must be set to None. An exception will be raised "
"in future versions of dclab.",
DeprecationWarning)
else:
visco = get_viscosity(medium=medium, channel_width=channel_width,
flow_rate=flow_rate, temperature=temperature,
model=visc_model)
if isinstance(visco, np.ndarray):
# New in dclab 0.20.0: Computation for viscosities array
# Convert the input area_um to that of the LUT (deform does not change)
scale_kw = {"channel_width_in": channel_width,
"channel_width_out": lut_meta["channel_width"],
"inplace": False}
datax_4lut = scale_feature(feat=featx, data=datax, **scale_kw)
deform_4lut = np.array(deform, dtype=float, copy=copy)
# Normalize interpolation data such that the spacing for
# area and deformation is about the same during interpolation.
featx_norm = lut[:, 0].max()
normalize(lut[:, 0], featx_norm)
normalize(datax_4lut, featx_norm)
defo_norm = lut[:, 1].max()
normalize(lut[:, 1], defo_norm)
normalize(deform_4lut, defo_norm)
# Perform interpolation
emod = spint.griddata((lut[:, 0], lut[:, 1]), lut[:, 2],
(datax_4lut, deform_4lut),
method='linear')
if extrapolate:
# New in dclab 0.23.0: Perform extrapolation outside of the LUT
# This is not well-tested and thus discouraged!
extrapolate_emodulus(lut=lut,
datax=datax_4lut,
deform=deform_4lut,
emod=emod,
deform_norm=defo_norm,
inplace=True)
# Convert the LUT-interpolated emodulus back
backscale_kw = {"channel_width_in": lut_meta["channel_width"],
"channel_width_out": channel_width,
"flow_rate_in": lut_meta["flow_rate"],
"flow_rate_out": flow_rate,
"viscosity_in": lut_meta["fluid_viscosity"],
"viscosity_out": visco,
"inplace": True}
# deformation is not scaled (no units)
scale_feature(feat=featx, data=datax_4lut, **backscale_kw)
scale_emodulus(emod, **backscale_kw)
else:
# Corrections
# We correct the LUT, because it contains less points than
# the event data. Furthermore, the lut could be cached
# in the future, if this takes up a lot of time.
scale_kw = {"channel_width_in": lut_meta["channel_width"],
"channel_width_out": channel_width,
"flow_rate_in": lut_meta["flow_rate"],
"flow_rate_out": flow_rate,
"viscosity_in": lut_meta["fluid_viscosity"],
"viscosity_out": visco,
"inplace": True}
# deformation is not scaled (no units)
scale_feature(feat=featx, data=lut[:, 0], **scale_kw)
scale_emodulus(lut[:, 2], **scale_kw)
# Normalize interpolation data such that the spacing for
# area and deformation is about the same during interpolation.
featx_norm = lut[:, 0].max()
normalize(lut[:, 0], featx_norm)
normalize(datax, featx_norm)
defo_norm = lut[:, 1].max()
normalize(lut[:, 1], defo_norm)
normalize(deform, defo_norm)
# Perform interpolation
emod = spint.griddata((lut[:, 0], lut[:, 1]), lut[:, 2],
(datax, deform),
method='linear')
if extrapolate:
# New in dclab 0.23.0: Perform extrapolation outside of the LUT
# This is not well-tested and thus discouraged!
extrapolate_emodulus(lut=lut,
datax=datax,
deform=deform,
emod=emod,
deform_norm=defo_norm,
inplace=True)
# Let the user know when the emodulus contains too many nan values
nans = np.sum(np.isnan(emod))
if nans / emod.size > 0.1:
warnings.warn("The Young's modulus could not be computed for "
+ "{:.0f}% of the data. ".format(nans/emod.size*100)
+ "This is because they are not covered by the "
+ "look-up table '{}'.".format(lut_data),
YoungsModulusLookupTableExceededWarning)
return emod
[docs]def normalize(data, dmax):
"""Perform normalization in-place for interpolation
Note that :func:`scipy.interpolate.griddata` has a `rescale`
option which rescales the data onto the unit cube. For some
reason this does not work well with LUT data, so we
just normalize it by dividing by the maximum value.
"""
assert isinstance(data, np.ndarray)
data /= dmax
return data