Department of Anatomy & Histology and Institute for Biomedical Research, University of Sydney, NSW 2006, Australia
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Abstract |
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Key words: fractal/human/hyperactivation/motility/spermatozoa
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Introduction |
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However, capacitating spermatozoa do not always have regular trajectories, and hyperactivated spermatozoa exhibit many random direction changes. These complex trajectories often do not show obvious peaks and troughs, making the calculation of an average path difficult, and the concept of ALH almost meaningless. These factors contribute to the possibility of potentially erroneous results being obtained for capacitating spermatozoa. Different CASA instruments use different algorithms for the calculation of average path, and different methods to approximate the `ends' of the smoothed path. This can alter the apparent length of the average path, and can also alter the ALH, which is calculated relative to the average path. A combination of these factors can result in potentially large differences in the kinematic values attributed to a trajectory, depending upon both its complexity and the analysis method used.
Recently, it has been suggested that research should be directed towards the development of smoothing-independent kinematic measures which could be applied to any CASA instrument, thereby removing some of the sources of error common in present kinematic analysis (ESHRE Andrology Special Interest Group 1996, 1998
). The aim of the present study was to investigate the potential for the development and application of new smoothing-independent measures of the movement of capacitating human spermatozoa.
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Materials and methods |
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The `ideal tracks' comprised the (x,y) coordinates of a group of 40 `ideal' hyperactivated and 40 `ideal' non-hyperactivated trajectories (Mortimer and Swan, 1995a). The 28 sperm trajectories selected for the `long tracks' had changes in their motility pattern, did not collide with another spermatozoon and were tracked for >1.5 s movement (range of track lengths 103536 points, corresponding to 1.68.9 s of movement;Mortimer and Swan, 1995b
). The `segments of long tracks' were constructed by breaking the long tracks into 255 sequential 31 point segments and analysing the (x,y) coordinates of each segment separately. The `circling tracks' comprised a group of ten non-hyperactivated trajectories which described a circle, some of which were included in a study of fractal dimension (Mortimeret al., 1996
).
CASA-derived track sets 1 and 2 were prepared by either swim-up from semen into human tubal fluid (HTF) medium containing 30 mg/ml human serum albumin or by selection on discontinuous Percoll gradients. The sperm preparations were loaded into~32 µm deep chambers and sperm movement visualized using a x10 negative high phase-contrast D-Plan objective (A10NH 0.25 160/0.17; Olympus, Japan) with a x6.7 camera ocular and a x1.5 intermediate lens. The spermatozoa were videotaped using a Sony SLV-X811AS VCR and analysedpost hoc using an IVOS CASA instrument (Integrated Visual Optical System, version 10.6t; Hamilton Thorne Research, Beverley, MA, USA) with 60 Hz track reconstruction and an acquisition time of 0.5 s. The track coordinates generated by the IVOS were transferred into Excel spreadsheets and the trajectories re-analysed by Cartesian methods. The final magnification used in the trajectory reconstruction by the IVOS had to be confirmed so that the correct magnification correction factor could be applied. To determine this, the VCL and VSL were calculated for five trajectories using a variety of magnification correction factors. The value which gave the same VSL and VCL values using Cartesian methods as those given by the IVOS (± 1%) was 0.98. This value was used for all of the trajectories, and the agreement between the IVOS- and Cartesian-generated VSL and VCL values remained within 1%.
Study 1: Examination of velocity profiles of capacitating human spermatozoa
The instantaneous velocity (VIN) is the velocity of the centroid between consecutive track points. The distance travelled between two consecutive points was calculated using the equation:
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and then VIN was calculated for each interval between track points along the trajectory as:
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where mcf = magnification correction factor (in this case 3.54, reflecting a final magnification of x3540, calculated by measurement of the distance between the lines of a stage micrometer which had been recorded at the beginning of the videotape). The consecutive VIN values were plotted for each trajectory and the relative changes in VIN compared between hyperactivated and non-hyperactivated tracks.
Study 2: Development of smoothing-independent kinematic values
In this study, the new smoothing-independent kinematic values were calculated from the (x,y) coordinates of the `ideal tracks', `long tracks`and `circling tracks'.
Instantaneous velocity values
The VIN was determined for each interval along a trajectory (i.e. between points 1 and 2, 2 and 3,et seq.). VINmax was the maximum instantaneous velocity of a trajectory and AVmax was the average of the three highest VIN values for a trajectory. VINmean was the mean of the local maxima of VIN. VINmean and AVmax were not necessarily the same because VINmean selected the highest VIN in an area of the track (in the same way that ALHmean was calculated from the mean of the local riser maxima), whereas AVmax took the three highest VIN values for the track, irrespective of whether the values were from consecutive intervals or not.
Velocityangle measure (VAM)
Velocityangle measure was the product of the change in direction of the centroid movement (measured in radians) and the instantaneous velocity of the following segment. It was calculated from (x,y) coordinates using spreadsheets (Excel v5.0; Microsoft Corporation, Redmond, WA, USA). No attempt was made to determine this value by manual methods. The distance between consecutive track points was determined as for VIN. The angle of direction change was found using the cosine rule (Figure 1). Infrequently, the value of cos B was 1 exactly, and the arc cosine could not be determined. In these cases, 1x108 was added to the cos value before calculating B. The angle B (radians) was then multiplied by the distance between points B and C (Figure 1
), for each segment along the trajectory. The sum of these values was found, then corrected for magnification. The time base correction was made as for the track velocity values and the units for VAM were therefore rad.µm/s.
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Statistics
For comparisons between hyperactivated and non-hyperactivated tracks, either unpairedt-tests or unpaired Wilcoxon tests were used, depending upon the distribution of the data (i.e. whether the distribution was normal). Receiver operating characteristic (ROC) analyses were used to derive threshold levels for hyperactivated motility for each kinematic measure (MedCalc; MedCalc Software, Mariakerke, Belgium). The relationships of the new kinematic values to the established kinematic values were determined by multiple regression analysis, and calculation of correlation coefficients.
Study 3: Evaluation of the relationship between the established and smoothing-independent kinematic values
Discriminant function analyses of previously analysed tracks
Discriminant function (DF) analyses were performed on all of the Cartesian-derived kinematic values for the `ideal tracks' as well as the `segments of long tracks'. Only 220 of the latter track segments were included because the segment had to be classified as either hyperactivated or non-hyperactivated for the DF analysis, so any segments which included a phase switch were omitted. All of the kinematic values were included in the data set, and there were no missing variables in any of the analyses. The kinematic measures dancemean (DNCmean;Robertsonet al., 1988) and mean angular displacement (MAD;Boyerset al., 1989
) were included in these analyses.
The DF analyses were performed using SPSS/PC+ v4.0 (Statistical Program for the Social Sciences; SPSS Inc., Chicago, IL, USA). Different combinations of kinematic values were included in the analyses to determine their relative value in predicting trajectories as hyperactivated or non-hyperactivated. Both the kinematic values which were included by the analysis and the DF equation were noted for each combination tested.
Analysis of new trajectories using the DF analysis results
CASA-derived track set 1.
The DF equation for the smoothing-independent kinematic values was applied to this data set of 100 trajectories by including the equation in a spreadsheet. Also, the threshold values for hyperactivation determined by ROC curve analysis of the `ideal tracks' and `segments of long tracks' were applied to this data set, but only for those kinematic values included in the DF equation. The results were evaluated by comparison of the classification of each trajectory by the new definitions for hyperactivation with the classification obtained using the established kinematic definitions for hyperactivation. This comparison was made using `IF' and `AND' statements within the spreadsheet, as well as the `auto filter' feature.
CASA-derived track set 2.
The smoothing-independent kinematic definitions for hyperactivation suggested by the analysis of track set 1 were then tested on track set 2 which comprised 387 trajectories.
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Results |
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Ideal tracks.
The 40 hyperactivated and 40 non-hyperactivated trajectories used in study 1 were re-analysed to determine VINmax, VINmean and AVmax. The hyperactivated tracks had significantly higher VINmean, VINmax and AVmax values than the non-hyperactivated tracks (ranges: VINmean 228.9440.9 versus 93.2241.0; VINmax 346.5741.0 versus 158.4389.6; AVmax 319.1613.4 versus 144.4330.4; allP < 0.0001 by unpairedt-tests; Figure 3). Because VCL is effectively the average of all the VIN values for a trajectory, correlation coefficients were determined for VCL and VINmean, VINmax and AVmax. As expected, all were strongly correlated with VCL (VINmean, r = 0.98 ; VINmax,r = 0.91; and AVmax,r = 0.94).
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The `ideal' trajectories and the 0.5 s `segments of long tracks' were combined and ROC curve analysis performed to determine threshold values for hyperactivation. For VINmax, the `best' threshold value was >364.3 µm/s, but the threshold which gave 100% sensitivity and maximum specificity was >273.8 µm/s (Table I). The `best' threshold value was that with the least number of false positive and false negative results, while the 100 % sensitivity value was that with no false negative values and the least number of false positives. For VINmean, the `best' threshold value was >249.5 µm/s, while the 100% sensitivity threshold value was >221.8 µm/s (Table I
). For AVmax, >330.4 µm/s was the `best' threshold value, while >272.2 µm/s was the 100% sensitivity and maximum specificity value (Table I
).
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Circling tracks.
The ten circling tracks were re-analysed to determine whether their VINmax, VINmean or AVmax values exceeded the hyperactivation threshold levels. By the `best' hyperactivation thresholds determined by ROC curve analysis, all of the VINmean values were in the non-hyperactivated range while two tracks had AVmax and VINmax above the hyperactivation threshold levels. If the alternative thresholds giving 100% sensitivity and maximum specificity were applied, there were three tracks for which VINmean, six for which AVmax and seven for which VINmax were above the hyperactivation threshold. The three tracks common to all of these had the highest VCL values. From these results it was concluded that none of these kinematic values could be used alone to classify trajectories as hyperactivated.
Multiple regression analysis.
Multiple regression analyses were performed to determine whether these velocity values were correlated with the established kinematic values. The best multiple regression result for AVmax and for VINmax was with VCL and ALHmax (r2 = 0.86 and 0.76, respectively). For VINmean, the highest correlation was with VCL and ALHmean (r2 = 0.94).
In summary, it was possible to use VINmax, VINmean and AVmax to discriminate between hyperactivated and non-hyperactivated 60 Hz trajectories. Since they are not track-averaged, the advantage of these values over VCL was that only a relatively small component of the trajectory needed to be hyperactivated for these values to cross their threshold levels for hyperactivation.
Velocityangle measure (VAM)
Ideal tracks.
The VAM values were normally distributed for both the hyperactivated and non-hyperactivated tracks. The mean VAM was 246.1 rad.µm/s (range = 138.0349.2 rad.µm/s) for the non-hyperactivated tracks and 485.3 rad.µm/s (range = 299.2610.9 rad.µm/s) for the hyperactivated tracks (Figure 4). Despite the overlap in ranges, the VAM values for the hyperactivated tracks were significantly higher than for the non-hyperactivated tracks (t = 16.99,P < 0.0001), indicating that the internal angle between consecutive vectors and VIN were generally higher for the hyperactivated trajectories, as postulated.
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Whole long tracks.
The VAM values for the entire long trajectories were determined. The track VAM values were >300 rad.µm/s for all but three of the tracks analysed and these tracks contained 0/4, 5/12 and 5/7 hyperactivated short segments, whereas those with VAM above 300 rad.µm/s contained a range of hyperactivated segments from 1/11 to 100%. To investigate this further, theproportion of a trajectory which was hyperactivated (by established criteria) was rated (0 = 059% of the trajectory hyperactivated, 1 = 60 to 79% of the trajectory hyperactivated and 2 = 80100% of the trajectory hyperactivated). One-way analysis of variance revealed a significant effect of the proportion of the trajectory which was hyperactivated upon the VAM value (F = 3.853,P = 0.037).
Because VAM could be above hyperactivation threshold levels even though the whole track was not hyperactivated, the minimum proportion of a trajectory needed for VAM to be above the hyperactivation threshold level was determined. Track segments were analysed stepwise, with the VAM calculated for a hyperactivated 0.5 s segment, then for a 1.0 s segment containing the first segment and the next (non-hyperactivated) 0.5s segment, etc. (i.e. VAM was calculated for segment 1, then segments 1 and 2, then segments 1 to 3, segments 1 to 4, etc.) until the VAM fell below the hyperactivation threshold level. The proportion of the track which was composed of hyperactivated segments and the VAM values were recorded until the VAM fell to <300 rad.µm/s. ROC curve analysis of these results gave a cut-off of 33%, so that if at least one-third of a track segment had hyperactivated motility, the VAM value could be expected to be >300 rad.µm/s (76% specificity, 82% sensitivity).
Circling tracks.
To determine whether the difference in VAM observed between hyperactivated and non-hyperactivated trajectories was due to a difference in LIN, the ten circling tracks were re-analysed for VAM. The median VAM value was 240.8 rad.µm/s (range 153.0287.9 rad.µm/s). All of these values were below the hyperactivation threshold of 297.4 rad.µm/s derived by ROC curve analysis (Table I). These results suggested that VAM could be used to distinguish hyperactivated tracks from circling, non-hyperactivated tracks, although the existence of overlapping ranges of VAM for hyperactivated and non-hyperactivated tracks would preclude its use as the sole discriminator of hyperactivated motility at 60 Hz.
Multiple regression analysis.
A series of multiple regressions was performed to determine whether VAM had a significant relationship to any of the established kinematic values, using the same data set as for the ROC curve analysis. VAM was correlated significantly with all of the established kinematic values, with the highest correlations with ALHmax (r2 = 0.81) and with ALHmean (r2 = 0.90). The highest multiple regression coefficients were for VCL, ALHmean and LIN (r2 = 0.94) and for VCL, LIN, STR and ALHmean (r2 = 0.96). These results illustrated that all but 46% of the variance in VAM in the data set could be accounted for by the combination of the established kinematic criteria, although the highest proportion of variance (r2 = 0.90) was accounted for by ALHmean alone.
Three-point area values [TPAmax, TPAmean, TPAmxmn, TPAmax(f), TPAmean(f), TPAmxmn(f)]
Ideal tracks.
All of the TPA values were normally distributed and the hyperactivated tracks had significantly higher TPAmax, TPAmean and TPAmxmn values by unpairedt-tests (respective ranges: TPAmax 8.0335.83 versus 1.968.86; TPAmean 2.309.26 versus 0.572.92; TPAmxmn 7.4928.78 versus 1.797.66; allP < 0.0001). The area contained by three consecutive track points would be expected to decrease with increasing image sampling frequency, as there would be less distance between consecutive track points. In an attempt to counter this, three more TPA values were developed, TPAmax(f), TPAmean(f) and TPAmxmn(f). These were calculated by multiplying the values by the image sampling frequency so, for example, the TPAmax(f) for a 60 Hz track would be:
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When these values were calculated for the `ideal' tracks the relationship between the values for the hyperactivated and non-hyperactivated tracks was as above, since the same proportional changes were made to each track.
Segments of long tracks.
The TPA values of the 0.5 s `segments of long tracks' were determined to investigate their usefulness in discriminating between non-ideal hyperactivated and non-hyperactivated trajectories. Not all of the values were normally distributed, so the data were analysed by unpaired Wilcoxon tests. The hyperactivated track segments had significantly higher TPAmax, TPAmean and TPAmxmn than the non-hyperactivated segments (allZ < 9.4,P < 0.0001) (Figure 5). The hyperactivated segments were then subclassified as progressive and non-progressive hyperactivated and re-analysed. The TPAmax values were significantly higher in the non-progressive hyperactivated segments (t = 2.13,P < 0.05), but there was no significant difference between the TPAmean and TPAmxmn values.
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Circling tracks.
To determine whether the TPA values were influenced by LIN, TPAmean, TPAmax and TPAmxmn were derived for the ten `circling tracks'. There were three tracks with all TPA values above the 100% sensitivity ROC curve threshold values for hyperactivation (ranges: TPAmax 3.2013.54 µm2; TPAmean 1.094.59 µm2; TPAmxmn 2.9112.23 µm2), meaning that the tracks would have been classified as hyperactivated if TPA had been the only criterion for classification. These tracks had the highest VCL values, so it would be expected that the area bounded by three consecutive track points would increase with increasing VIN (and hence VCL).
Multiple regression analysis.
To determine whether a relationship existed between the TPA kinematic measures and the established kinematic measures, a series of multiple regression analyses were performed using the same data set as for the ROC curve analyses. For TPAmax the best regression components were LIN, ALHmax and VCL (r2 = 0.48), for TPAmean the most significant predictor was VCL (r2 = 0.67) while for TPAmxmn the best regression components were VCL, ALHmax and STR (r2 = 0.50). Although all of these results were significant, there was still one half to a third of the variance in the data sets left unaccounted for by these parameters. As noted in the analysis of the circling tracks, VCL had a significant influence on the TPA values. The correlation coefficients for TPA and VCL werer = 0.65 for TPAmax and TPAmax(f);r = 0.82 for TPAmean and TPAmean(f); andr = 0.67 for TPAmxmn and TPAmxmn(f). In summary, the TPAmax, TPAmean and TPAmxmn values could be used in the discrimination of hyperactivated trajectories, but none could be used as the sole criterion.
Therefore, while none of these new measures could be used alone to distinguish hyperactivated tracks, all had high sensitivity and specificity warranting further analysis to determine whether a group of these values could be defined which would allow the identification of hyperactivated tracks independently of smoothing-dependent kinematic criteria.
Study 3: Evaluation of the relationship between the established and smoothing-independen kinematic values
Discriminant function analyses of previously analysed tracks
Although the new kinematic values appeared to be useful, it was necessary to determine whether they could be used to identify hyperactivated motility using unselected track data. Before this could be done, however, a combination of kinematic values which would allow the best discrimination between hyperactivated and non-hyperactivated trajectories had to be determined.
Established kinematic values.
Initially, only the previously published kinematic values (excluding fractal dimension) were included in the DF analysis to give an indication of the level of correct classification which could be expected, since the DF equation developed as part of the analysis is then used to re-classify the data sets. These established kinematic values were: VCL, VSL, VAP, LIN, STR, WOB, ALHmean, ALHmax, BCF, MAD and DNCmean. The kinematic values included by the analysis were LIN, VCL, MAD, DNCmean and ALHmax (Wilks' = 0.179). The DF equation was:
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with group centroids 2.745 for non-hyperactivated tracks, 1.659 for hyperactivated tracks, and midpoint value = 0.543, i.e. for non-hyperactivated trajectories, DF > 0.543 and for hyperactivated trajectories, DF < 0.543. The proportion of cases correctly classified was 96.5% for non-hyperactivated tracks and 100% for hyperactivated tracks, with an overall agreement of 98.7% for the previously published kinematic values (Table II). This gave an indication of the level of correct classification which would be required before a new kinematic definition for hyperactivation could be used with confidence.
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with group centroids 2.208 for non-hyperactivated tracks, 1.33 for hyperactivated tracks, and midpoint value = 0.437, i.e. for non-hyperactivated trajectories, DF < 0.437 and for hyperactivated trajectories, DF > 0.437. The proportion of cases classified correctly as non-hyperactivated was 98.2%, the proportion classified correctly as hyperactivated was 95.7%, with an overall correct classification of 96.7% (Table II).
All kinematic values.
To determine the relative importance of the kinematic criteria, all were included in a DF analysis. Most of the variables selected were those already selected in the separate DF analyses, although VINmean and TPAmxmn and TPAmean were also included. Both ALHmean and ALHmax were represented initially, but ALHmax was removed as the analysis progressed, resulting in replacement of its variance component by other kinematic variables. At the conclusion of the analysis, the smoothing-dependent parameters included in the equation were ALHmean and DNCmean, which includes VCL and VSL (i.e. a form of LIN) and ALHmean in its calculation (Wilks' = 0.164). The DF equation was:
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with group centroids 2.892 for non-hyperactivated tracks, 1.747 for hyperactivated tracks, and the midpoint value = 0.572, i.e. for non-hyperactivated trajectories, DF > 0.572 and for hyperactivated trajectories, DF < 0.572. The proportion of cases classified correctly using this equation was 94.7% of the non-hyperactivated and 100% of the hyperactivated tracks, with an overall correct classification of 98.0% (Table II). This value was slightly higher than that achieved using either the established or new kinematic values only. However, the problems identified previously with the smoothing-dependent values, as well as with VCL when phase-switching occurred, precluded the use of this equation and, similarly, these values for a Boolean argument for the definition of hyperactivated motility.
Smoothing-independent kinematic values.
The final DF analysis only included the smoothing-independent kinematic values, except for VCL, which was excluded because it was found that it tended to drop below the hyperactivation threshold level if phase switching occurred in the segment under analysis. The values VAM, LIN, VINmax, fractal dimension and TPAmean were selected by the DF analysis with a very low Wilks' (0.195), indicating that <20% of the variability in the data set was unaccounted for when these values were used for the discrimination of hyperactivated and non-hyperactivated tracks. The DF equation was:
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with group centroids 2.603 for non-hyperactivated tracks, 1.573 for hyperactivated tracks, and the midpoint value = 0.515, i.e. for non-hyperactivated trajectories, DF > 0.515 and for hyperactivated trajectories, DF < 0.515. Using this equation, 98.2% of the non-hyperactivated tracks and 98.9% of the hyperactivated tracks were classified correctly, with an overall correct classification of 98.7%. This was the same as the proportion correctly classified when the established kinematic values were used (Table II). This final DF analysis was used both to define the values which would be best included in a new Boolean argument for the definition of human sperm hyperactivation, and to give an equation (the DF equation) which could be used to test the reliability of the new Boolean arguments on separate series of tracks which had not been analysed previously in this study.
Analysis of new trajectories using the DF analysis results
Two sets of tracks were used to test these new kinematic definitions for hyperactivation. IVOS-generated tracks were used firstly because a large number of trajectories was available, and secondly because any new kinematic values would need to be applicable to a CASA instrument. Hence, the use of IVOS-generated (x,y) co-ordinates was considered to be a better indication of the likely outcome when a CASA instrument was used. The initial classification of the tracks as hyperactivated or non-hyperactivated was made using the classifications developed for use with IVOS trajectories (Study 1.5,Mortimer, 1997), i.e.
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CASA-derived track set 1
This set of tracks comprised 23 non-hyperactivated tracks and 77 hyperactivated tracks, according to the established kinematic criteria. A relatively high proportion of hyperactivated tracks was included in this set because it was being used to test the hyperactivation thresholds, so a large variety of hyperactivated tracks was considered to be useful. They were used to test the equation produced by the DF analysis in which only smoothing-independent kinematic values were included to determine whether the equation could be applied successfully to an unrelated data set. At thesame time, the DF analysis results were used in a different way, with the kinematic values VAM, LIN, fractal dimension, VINmax and TPAmean (i.e. those selected by DF analysis) included in a Boolean argument with the hyperactivation threshold values generated by ROC curve analysis used as the discriminators (Table I). However, since the `best' hyperactivation threshold values given for each parameter by ROC curve analysis balanced the highest sensitivity and specificity values, it was acknowledged that these threshold values could be too stringent, resulting in misclassification of tracks. Accordingly, a third analysis of the new tracks was carried out, in which the hyperactivation threshold level for each kinematic value was that with 100% sensitivity and the highest specificity in the ROC curve analyses (Table III
). When the kinematic values were combined in the classification of the tracks, the overall correct classification was higher when the maximum sensitivity thresholds were used, as expected (Table III
). However, the classification was not as good as the DF classification (89% versus 86% correctly classified).
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When these altered threshold values were applied to the 100 tracks, there was a 95% total agreement, with no false negatives and five false positives (Table III, `Alternative threshold'). When the false positives were investigated, it was found that two of the tracks were classified as non-hyperactivated by the IVOS solely because their ALHmax values fell below the 7.0 µm threshold (values were 6.4 and 6.3 µm), while another two had VCL and ALHmax values below the threshold levels (values were 148.1 µm/s and 6.7 µm; and 149.4 µm/s and 5.8 µm), and the final track had VCL below the threshold (value was 146.4 µm/s). The ALHmax values were recalculated using the (x,y) coordinates and seven-point smoothing, and were >7.0 µm for 4/5 tracks, including both tracks which had been originally classified as non-hyperactivated because of low ALHmax. This demonstrated again the effect that different smoothing methods can have on trajectory classification. Finally, with the adjusted thresholds for hyperactivation, and the conversion of two of the false negative values to true positives, the overall agreement between the established and new kinematic values for this set of 100 tracks was 97%, with 85% agreement for the non-hyperactivated and 100% agreement for the hyperactivated tracks. Because these threshold values were tailored using this data set, they had to be tested against another data set.
CASA-derived track set 2.
This track set comprised 54 hyperactivated and 333 non-hyperactivated 60 Hz tracks, as classified by the IVOS. Unlike the set of 100 tracks above, this set was not enriched with hyperactivated trajectories and reflected the more common observation of a lower proportion of hyperactivated tracks in a population. To circumvent the possibility of a problem with ALHmax (as was observed with track set 1), all of the ALHmax values were recalculated using 7-point smoothing. When the adjusted threshold values for hyperactivation were applied to these tracks, an overall agreement of 99% was found between the established and new kinematic criteria for hyperactivation, with four false negatives and one false positive, relative to the IVOS classification. The false negative tracks had VAM below the threshold level (range was 121.3218.9 rad.µm/s), whereas the false positive track had VCL = 139.4 µm/s and ALHmax = 6.8 µm. The high level of agreement observed indicated that the new kinematic values were able to discriminate between hyperactivated and non-hyperactivated tracks. Consequently, the proposed smoothing-independent kinematic criteria for the definition of tracks as hyperactivated were:
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which gave 99% overall agreement with established kinematic criteria in trajectory classification.
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Discussion |
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In the initial phase of the study, the velocity profiles of hyperactivated and non-hyperactivated trajectories were found to be quite different, with hyperactivated trajectories having marked changes in instantaneous velocity (Figure 2). The observation that hyperactivated spermatozoa have a higher velocity than non-hyperactivated spermatozoa is not novel, since curvilinear velocity has figured prominently in the definition of hyperactivation (Robertsonet al., 1988
;Mortimer and Mortimer, 1990
;Burkman, 1991
). However, the observation that the instantaneous velocity was not consistently higher for hyperactivated than non-hyperactivated tracks suggested that the determination of maximal instantaneous velocity values may be of value. It has been demonstrated that hyperactivation is not a consistent state for human spermatozoa, with spermatozoa switching motility patterns apparently at random (Mortimer and Swan, 1995b
). A potential complication arises as a result of this phase switching: the track-averaged VCL may fall below the threshold level required for classification of a trajectory as hyperactivated if a phase switch occurs during the period of track analysis (Mortimer and Swan, 1995b
). The use of maximal instantaneous velocity values could remove this complication, as only hyperactivated spermatozoa would be expected to demonstrate high instantaneous velocities. However, it is also possible that during manual trajectory reconstruction a track point may be missed, meaning that an artificially high instantaneous velocity value could be calculated for that track segment. To circumvent this potential problem three instantaneous velocity values were determined in the present study, VINmax (the maximum instantaneous velocity in the track segment), AVmax (the average of the three highest instantaneous velocities in the track segment) and VINmean (the average of all of the local instantaneous velocity maxima in the track segment). Each of these values was highly correlated with VCL, but had the advantage of not being track-averaged. This meant that if any portion of the track segment analysed showed hyperactivated motility, then the instantaneous velocity value would still be high enough for the track to be classified as hyperactivated. The use of VIN as a discriminating value would therefore reduce some of the `noise' introduced by phase-switching in the classification of tracks as hyperactivated or non-hyperactivated.
Further consideration of the shape of hyperactivated trajectories reconstructed at 60 Hz (Figure 2) illustrated that immediately preceding the burst of instantaneous velocity, there was a change in the direction of head movement. This observation resulted in the development of the novel kinematic value VAM (velocityangle measure), which was the product of the angle between the movement vectors and the subsequent instantaneous velocity (Figure 1
). VAM was found to be significantly higher for hyperactivated than for non-hyperactivated 60 Hz trajectories (Figure 4
), although circling non-hyperactivated trajectories also had high VAM values. This meant that VAM could not be used as the sole kinematic value for the definition of hyperactivation. However, there were some positive attributes of VAM, namely that if as little as one-third of the total track segment was hyperactivated, the VAM value was still above the hyperactivation threshold; and also that VAM was highly correlated with all of the criteria commonly used for the definition of hyperactivation (i.e. VCL, ALH, LIN and STR). The major problem in the calculation of VAM was in the determination of the angle, when the arc cosine value for 1 exactly could not be determined. This problem was addressed on an ad-hoc basis in the study, by adding 1x108 to the value, but it would have to be addressed more systematically by a CASA instrument.
The third group of new kinematic values introduced and evaluated in this study were the three-point area (TPA) values which gave the area bounded by three consecutive track points (Figure 1). The increased instantaneous velocity associated with hyperactivation meant that the TPA values were significantly higher for hyperactivated than for non-hyperactivated tracks (Figure 5
). However, none of the TPA values could be used to discriminate between hyperactivated and circling, non-hyperactivated tracks. As would be expected, all of the TPA values were significantly correlated with VCL, and both TPAmax and TPAmxmn were also significantly correlated with ALHmax, an important value in the definition of hyperactivated motility (Mortimer and Mortimer, 1990
;Burkman, 1991
). A major disadvantage of TPA is that the values would be expected to be highly inversely correlated with the image sampling frequency used, with an increased number of track points sampled per second resulting in a reduction in the area bounded by three consecutive track points. The TPA(f) values (the product of TPA and the image sampling frequency) were developed in an attempt to standardize TPA values across image sampling frequencies. The applicability of such values at different image sampling frequencies has been addressed in a separate study (Mortimer and Swan, 1999
).
After the new kinematic values had been developed, a series of DF analyses were carried out to determine which of the values had the potential to replace the `established' kinematic values for the identification of hyperactivated tracks. The same trajectories which had been used for the development of the new kinematic values were used in this study. The initial DF analysis was to confirm which of the established kinematic values best described hyperactivated motility, and to obtain a benchmark for the new kinematic values in the ability to discriminate between hyperactivated and non-hyperactivated trajectories. The second DF analysis only included the new kinematic values and the fractal dimension. The fractal dimension was included in this analysis as a previous study had showed it to be a good indicator of track complexity and hence hyperactivated motility (Mortimeret al., 1996). The result of this DF analysis was good, but did not give quite as high a level of discrimination between hyperactivated and non-hyperactivated tracks as the established kinematic values. The third DF analysis, in which all of the kinematic values were included, gave an equation which incorporated both established and new kinematic values, indicating that neither group was superior to the other. The final DF analysis, in which only smoothing-independent kinematic values were included, allowed the equivalent classification of tracks as hyperactivated or non-hyperactivated as the established kinematic values alone. This result was important because although the ability of the established values to discriminate between hyperactivated and non-hyperactivated tracks was a given in this case (especially since these values were used in the initial classification of the trajectories), an equivalent level of classification was obtained by the use of smoothing-independent variables which would be less likely to exhibit inter-CASA machine variation.
However, the identification of a trajectory as hyperactivated by a CASA instrument does not rely upon the application of a DF equation, but rather the determination of whether all of a number of kinematic criteria are met. Also, while the threshold level selected for each kinematic value may allow the inclusion of false positives, it may not allow the exclusion of false negatives as this would result in the exclusion of a hyperactivated track. Therefore the threshold values for classification of a 60 Hz trajectory as hyperactivated were determined by a series of ROC curve analyses of the manually reconstructed 60 Hz trajectories for each of the kinematic measures identified by the DF equation. The threshold values determined were those which gave 100% correct classification of hyperactivated trajectories.
A group of 100 CASA-derived 60 Hz trajectories was then classified as hyperactivated or non-hyperactivated using the threshold kinematic values derived using the manually reconstructed trajectories. The classifications of each trajectory by the established kinematic measures and by the smoothing-independent kinematic measures were compared. Those which had been `incorrectly' classified (in comparison with the established kinematic values) were identified and the reasons for the misclassification ascertained. For example in the case of LIN the threshold values obtained using manually reconstructed `ideal' tracks were found to be too stringent and so they were relaxed to a level found previously to be useful in the classification of 60 Hz hyperactivated tracks for the same CASA instrument as used in this study (Mortimeret al., 1998). This approach meant that more of the tracks previously classified as hyperactivated by the established kinematic criteria were also identified as hyperactivated by the smoothing-independent kinematic criteria. The new Boolean argument, with less stringent kinematic definitions, was then applied to another set of 387 trajectories which had been reconstructed at 60 Hz by the same CASA instrument. The overall correct classification of tracks as hyperactivated and non-hyperactivated using the new Boolean argument (which only included smoothing-independent kinematic variables) was 99%.
This result indicates that the new kinematic measures were equivalent to the established kinematic measures in the identification of hyperactivated human spermatozoa analysed at 60 Hz. The importance of this finding is that the new kinematic values are smoothing-independent, and hence similar values would be expected to be obtained for trajectories analysed at 60 Hz using any CASA instrument, although this remains to be tested. Also, the threshold values were determined using 60 Hz trajectories, and may not be valid for trajectories reconstructed using different image sampling frequencies. The relative effect of image sampling frequency upon the new kinematic values for hyperactivated and non-hyperactivated trajectories forms the basis of a subsequent study (Mortimer and Swan, 1999). Further studies are required to evaluate the applicability of the smoothing-independent kinematic values to a range of CASA instruments.
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Submitted on April 24, 1998; accepted on December 9, 1998.