2.5.2 Curve Fitting
After collecting volume response data, one must determine the
parameters that cause the model to best-approximate the data.
With knowledge of V iso and V b from prior Boyle van ’t Hoff experiments, the initial mean cell water volume fraction can be estimated.
This parameter has direct implications to the 2p model because it is
related to the surface area to water volume ratio (SA:V) that
appears, implicitly, in Eq. 21 or as a lumped parameter b in
Eq. 25. With cell population level measurements as in impedance
based measurements or in most fluorescence based approaches, a
cell population estimate of this SA:V is sufficient. With individual
cells such as oocytes, the specific SA:V should be used if possible.
Impedance and fluorescence methods can capture data at very high
rates (e.g., 10
1 –10
3 samples/s), but these data are typically “noisy”
and must be smoothed by a moving average scheme (see ref. 27 or
85). In general is most important to capture data at a higher rate
during the initial shrink or swell portion of the experiment, and of
greatest importance is an accurate measure of the minimal or maximal volume achieved during the protocol (see Fig. 7, for example).
In fact, with a precise estimate of the time and volume of the
maxima or minima, exact solution techniques can be employed to
estimate the water and solute permeabilities [77]. In general,
0
5
10
15
20
0.75
0.80
0.85
0.90
0.95
1.00
1.05
Time (s)
W W
iso
Fig. 7 Fits of volume vs time data for hypothetical boar sperm response to 1 mol/kg DMSO. Data are
hypothetically collected every 1 s and indicated by solid dots. The best fit shown by a dashed line was used to
generate the data. Note that this number of points and distribution shows how the density of important early
time data is more important than later time data. An alternate fit is shown in solid line. For this fit, L p is 5 times
the actual, and P s is 0.85 times the actual P s . For this dataset it is clear that the best fit is “best,” but for other
datasets with some experimental noise it is clear how improper fits with aberrant values can be found (and
justified). Ideally, a number of points in the initial rapid volume change period are obtained
152
James D. Benson
After collecting volume response data, one must determine the
parameters that cause the model to best-approximate the data.
With knowledge of V iso and V b from prior Boyle van ’t Hoff experiments, the initial mean cell water volume fraction can be estimated.
This parameter has direct implications to the 2p model because it is
related to the surface area to water volume ratio (SA:V) that
appears, implicitly, in Eq. 21 or as a lumped parameter b in
Eq. 25. With cell population level measurements as in impedance
based measurements or in most fluorescence based approaches, a
cell population estimate of this SA:V is sufficient. With individual
cells such as oocytes, the specific SA:V should be used if possible.
Impedance and fluorescence methods can capture data at very high
rates (e.g., 10
1 –10
3 samples/s), but these data are typically “noisy”
and must be smoothed by a moving average scheme (see ref. 27 or
85). In general is most important to capture data at a higher rate
during the initial shrink or swell portion of the experiment, and of
greatest importance is an accurate measure of the minimal or maximal volume achieved during the protocol (see Fig. 7, for example).
In fact, with a precise estimate of the time and volume of the
maxima or minima, exact solution techniques can be employed to
estimate the water and solute permeabilities [77]. In general,
0
5
10
15
20
0.75
0.80
0.85
0.90
0.95
1.00
1.05
Time (s)
W W
iso
Fig. 7 Fits of volume vs time data for hypothetical boar sperm response to 1 mol/kg DMSO. Data are
hypothetically collected every 1 s and indicated by solid dots. The best fit shown by a dashed line was used to
generate the data. Note that this number of points and distribution shows how the density of important early
time data is more important than later time data. An alternate fit is shown in solid line. For this fit, L p is 5 times
the actual, and P s is 0.85 times the actual P s . For this dataset it is clear that the best fit is “best,” but for other
datasets with some experimental noise it is clear how improper fits with aberrant values can be found (and
justified). Ideally, a number of points in the initial rapid volume change period are obtained
152
James D. Benson