«Novel Biophotonic Imaging Techniques for Assessing Women’s Reproductive Health by Tyler Kaine Drake Department of Biomedical Engineering Duke ...»
5.2 Study design A complete description of the dual- modality instrument as used in this study is provided in Section 3.2.2 of this document.
Measurements were made using a custom calibration socket made of black anodized aluminum.
The socket features 5 grooves of various depths (36, 75, 183, 271, and 375 µ;m) which are consitent with gel thicknesses that have been measured in in vivo studies.27, 76 A diagram of the measurement geometry is shown below.
The test gel used for measurement was a FACTS- 001 hydroxyl- ethyl cellulose, or HEC, gel.
The gel was diluted using a vaginal fluid simulant (VFS) to concentrations of whole gel to 10%, 20%, 33%, and 50% VFS by volume.78 First, an experiment was performed on an unlabeled gel in order to determine the index of refraction, n, of the gel at each dilution, and to characterize light leakage of the fluorimetry device.
The grooves of the calibration socket were filled using a syringe with unlabeled FACTS- 001 gel, the socket was secured to the tube of the probe, and 82 measurements were captured with the dual- modality instrument.
Index of refraction for the dilutions was calculated using the mLCI dataset and OPL = nt, where t is the depth of the groove of each socket and n is the index of refraction.
Fluorimetric light leakage could lead to an overestimate of depth, so light leakage was characterized as well.
The fluorimetric signal was recorded for each groove during the scan process of the unlabeled gel, and this intensity value was subtracted from the fluorescein- labeled signal in the remaining experiments.
Fluorescein- labeled FACTS- 001 gel (0.1% w/w;
Akorn AK- Fluor, Lake Forest, IL) was then inserted into the calibration socket, and the five wells were again imaged.
The labeled test gel was then diluted 10% by volume with VFS, placed into the socket, and measured simultaneously by both modalities.
This procedure was repeated for 20%, 33%, and 50% VFS dilutions of FACTS- 001, and measurements were captured for each.
Fluorimetry measurements were taken at the central coordinate of each groove in the calibration socket, with a field of view of approximately 1 cm.
The mLCI field of view consisted of six measurements spots aligned perpendicularly across the axial direction of the calibration socket, covering about 3.5 mm azimuthally.
mLCI data were sampled every 1 mm axially, and 10 consecutive axial measurements were averaged at each depth groove of the calibration socket for data comparison between the modalities.
5.3 Results Optical path length measurements from mLCI were initially used to calculate index of refraction, n, for each of the gel dilutions with VFS.
The equation OPL = nt was simply solved for n, and the results are provided below in Table 5.1.
The calculated index values were used to calibrate the mLCI device for thickness measurements of the fluorescein- labeled FACTS- 001 test gel.
Calculated index of refraction values for FACTS- 001 gel diluted with VFS.
Thickness measurements of an example dataset are provided below in Figure 5.2.
Measured thickness values for the 33% dilution with VFS of FACTS- 001 gel are plotted with mLCI measurements on the x- axis and fluorimetry values on the y- axis.
mLCI errorbars (x- axis) are given by the average axial resolution of the instrument (8.3 µ;m) as shown in Table 3.2.
Fluorimetric error (y- axis) is given as ± 10%, as calculated by Henderson et al.27 84 Figure 5.2:
Example dual- modality data for 33% VFS dilution of fluorescein- labeled FACTS- 001 gel.
mLCI measurements are plotted in the x- coordinate and fluorimetry are plotted in the y- coordinate.
The 95% confidence interval is shown with the dashed lines.
Traditional linear regression analysis which typically uses a least squares method for calculation is not applicable in this case, because increasing error exists with increasing depth, and error exists in both coordinates.
For example, if x- coordinate measurements were made with no error, the line of best fit is the line that minimizes the sum of squares of the y- coordinate residuals.
However, error exists in both coordinates and the error in the x- axis cannot simply be ignored.
Instead, a weighted least- squares regression was performed, based on work by Krysteck and Anton.79 Their regression minimizes the residuals in both coordinates and accounts for varying degrees, or weights, of error that occur with the fluorimetry measurements.
A Mathematica algorithm (Wolfram Research, Inc.) was created which minimized χ2 in Eqn.
where (xk, yk) are n data pairs, with uncertainties (ux,k, uy,k), and (Xk, Yk) are the points of a straight line given by y = mx+b.79, 81 Before fitting data, the Mathematica algorithm was verified by using the dataset provided by York, and the results were similar to those provided by York and Krysteck and Anton.79, 81 The confidence interval is shown with dashed lines in Figure 5.2, and the interval was calculated with the Eqn.
here σm and σb are the standard deviation in the slope and intercept.
The weighted least squares regression was performed on the series of gel dilutions, and the results are provided in Table 5.2.
Standard deviation values for the slope and intercept are also provided.
These values are used in Eqn.
(5.2) to determine the confidence intervals shown in Figure 5.2.
Calculated line of best fit from weighted least- squares regression for each of the serial dilutions.
(SD = standard deviation).
86 Next, the slope values in Table 5.2 were plotted against percentage dilution by volume of gel with VFS, and the data was fit to a sigmoid using a logistic 4p regression.
This plot is shown below in Figure 5.3.
where θ1 is the minimum asymptote, θ2 is the minimum asymptote, θ3 is the slope factor, and θ4 is the inflection point.
The maximum asymptote was given by the slope at 0% dilution, or 0.765.
The minimum asymptote was set to zero, and the inflection point and slope factor were optimized iteratively with JMP.
The slope factor was determined to be 0.105 (S.E.
= 0.012) and the optimal inflection point was found to be 37.115 (S.E.
= 87 1.24).
The errobars in the y- axis represent the standard deviation of the slopes resulting from the weighted least squares regression in Table 5.2.
The equation in Figure 5.3, can be inverted and solving for x, yields
which can be used to calculated a dilution percentage from the slope of the thickness values measured by the dual- modality instrument.
An error analysis of Eqn.
(5.4) was performed to test the sensitivity of the calculation to small perturbations in calculated slopes.
(5.4) was first used to inversely calculate dilution for the slope values, m, in Table 5.2.
The calculation was repeated for m ± SD to test the sensitivity of the Eqn.
(5.4) to the range of values within the confidence interval of one standard deviation.
Table 5.3 shows the results of the analysis.
An example dilution calculation was then performed with human gel thickness distribution data from Section 4.4, in order to show the complete method of dilution calculation with the dual- modality instrument.
The dataset was from a 10- min, 88 sit/stand/sit protocol, and Figure 5.4 shows the method of calculating dilution of a microbicide gel in vivo.
First, the modalities’ data in part (a) are azimuthally averaged, resulting in the plot shown in part (b).
A region of interest (ROI) is selected in which dilution will be calculated.
The mLCI and fluorimetry measurements are plotted as in part (c) and the data is fit using the weighted least- squares method (Eqn.
(6.1)), to find the slope of the regression, in this case m = 0.717.
As in part (d), this slope is then used with Eqn.
6.4, to calculate dilution, in this example 11.4%.
Diagram of the method for dilution calculation using data obtained with the dual- modality optical imaging instrument.
Part (a) shows the topological plots from human in vivo microbicide gel distributions.
Part (b) shows the azimuthally averaged gel thicknesses as a function of axial distance.
A region of interest (ROI) for which dilution will be calculated is selected.
Part (c) then shows the weighted least- squares fit of the mLCI and fluorimetry values in the ROI.
Part (d) reveals a dilution of 11.4% for the ROI as found with the calibration curve in Figure 5.3.
5.4 Discussion This study presented a methodology of determining the extent of microbicide gel dilution, using a dual- modality optical imaging device.
A placebo microbicide gel, FACTS- 001 HEC gel, which is currently in clinical trials, was diluted with a vaginal fluid simulant to a range of dilutions which are predicted to exist in the human vagina.45 The diluted gels were inserted into a test socket and measured with the dual- modality instrument.
A weighted least- squares linear regression was then performed on the measurements of the modalities, and a slope ratio was found for each dilution.
A calibration curve was then created (Figure 5.3) which can then be used to find gel dilution at local areas.
An example calculation of he methodology using in vivo data from Chapter 4 is then presented to demonstrate the complete process of calculating gel dilution.
The calculation was performed on a 10- min, sit/stand/sit protocol (discussed in Section 4.2) and the ROI was chosen in an area near the leading edge of the gel distribution, where some dilution is expected.
It was calculated that the gel experienced a dilution of 11.4% in this region, and this extent seems reasonable based on previous work by Lai et al.
on estimating the extent of in vivo gel dilution.45 It was also determined that dilution with VFS does change the index of refraction of FACTS- 001 gel, which in turn affects the accuracy of mLCI measurements.
However, this change is minimal.
The undiluted FACTS- 001 HEC gel had an index of refraction of 1.43, and the 50% dilution had an index of refraction of 1.37, for a change of 4%.
It is 91 hypothesized that this change is not significant and can be ignored in future measurements of in vivo dilution data.
At large gel thickness, the uncertainty of the fluorimetry measurement increases, and the confidence interval of the weighted least- squares regression gets larger.
This decreases the accuracy in which dilution can be calculated with this methodology at large thicknesses.
The sigmoid shape of the calibration curve in Figure 5.3 also reveals a non- linear response in the dilution calculation method.
At very low dilutions (20%) and high dilutions (50%), the curve is relatively flat, so small perturbations in slope will result in proportionally larger changes in calculated dilution, as compared to the linear center region of the calibration curve.
The non- linear response at the extremes can act magnify error in slope calculations, and may greatly change the resultant dilution calculation output.
Table 5.2 reveals that the y- intercept values from the weighted least- squares regression are not zero.
It is hypothesized that this occurs because the fluorimetry method itself does not respond perfectly linear with depth.
At low fluorophore concentrations, i.e., small gel thicknesses, the device tends to overestimate the thickness.
The reverse is true at large depths, where falloff of the fluorimetry signal is seen.
These two factors act to shift the regression line and add an offset.
However, since all y- intercept values are relatively small, it is hypothesized that the slope ratios are not greatly affected, and in vivo data will maintain a similar y- intercept.
92 However, even with these potential hazards, the instrument remains useful in measuring microbicide gel dilutions.
Lai et al.
concluded that gel dilutions on the order of 10- 30% by volume resulted in observable changes in rheological properties and coating flows.45 The dual- modality technique is capable of measuring gel dilutions at such a resolution.
The output dilution information can then be used in biophysical models of gel behavior to aid in the development of microbicide products.
Chapter5 presented a methodology for calculating the extent of microbicide gel dilution using the measurement data from the dual- modality optical imaging instrument.
The study design was initially covered.
The study used the a placebo HEC gel that is currently in a phase III clinical trial, and it was diluted with a vaginal fluid simulant to a range of dilutions which may be encountered in the human vagina.
The gels were put into the calibration socket and imaged simultaneously with fluorimetry and mLCI.
The data was then presented in Section 5.3 where it was found that the slope ratio of the measurements could be used to calculate local gel dilution.
A calibration curve was created, and example in vivo data was used to show the complete methodology in calculating dilutions.
The accuracy of the measurements were then determined to be sufficient for assessing the effects of gel dilution on rheological properties such as coating flow.
Currently a study is underway which is using the dual- modality instrument in 93 measuring coating efficacy, and this methodology can be used to provide information on the role of gel dilution in coating.
94 6 Ex vivo a/LCI cervical dysplasia study