consul-Comparison of 2 types of milk flow meters for detecting bimodality in dairy cows

The primary objective of this observational study was to investigate whether incremental milk flow rates (in the 0–15 s, 15–30 s, 30–60 s, and 60–120 s intervals) from electronic on-farm milk flow meters can be used to detect bimodal milk flow curves in dairy cows compared with the use of a portable milk flow meter. Our second objective was to study the concordance between an electronic on-farm milk flow meter and a portable milk flow meter for assessing the 2-min milk yield and total milk yield. In this cross-sectional study, data from 92 milking observations from individual cows were analyzed. We collected data on incremental milk flow rates, the 2-min milk yield, and the total milk yield simultaneously with an on-farm milk flow meter and a portable milk flow meter. Bimodality detected by the on-farm milk flow meter was defined as lower milk flow rates during any of the 15–30 s, 30–60 s, and 60–120 s intervals compared with the previous intervals (0–15 s, 15–30 s, and 30–60 s). Bimodality according to the portable milk flow meter (BIM LC ) was observed through automatic detection. κ statistics indicated good agreement between bimodality detected by the on-farm milk flow meter and BIM LC [κ (95% confidence interval): 0.69 (0.49–0.90)]. Using BIM LC as the gold standard, diagnostic test statistics for bimodality detected by the on-farm milk flow meter indicated moderate performance for sensitivity [0.73 (0.54–0.86)] as well as high performance for positive predictive value [0.83 (0.63–0.93)], specificity [0.94 (0.85–0.98)], and negative predictive value [0.90 (0.81–0.95)]. Receiver operating characteristic curve analyses revealed that the 30–60 s milk flow rate was the variable that best predicted BIM LC, yielding an area under the curve of 0.89. Pearson correlation coefficients (r) revealed a very strong correlation between the 2 devices for both the 2-min milk yield [0.97 (0.96–0.98)] and total milk yield [r (95% confidence interval), 0.97 (0.96–0.98)]. Additionally, intraclass correlation coefficients (ICC) and concordance correlation coefficients (CCC) indicated excellent agreement between the 2 devices for the 2-min milk yield [ICC, 0.97 (0.96–0.98); CCC, 0.94 (0.92–0.96)] and total milk yield [ICC, 0.97 (0.96–0.98); CCC, 0.97 (0.95–0.98)]. Therefore, we concluded that electronic on-farm milk flow meters that measure incremental milk flow rates can be used to detect bimodal-ity in dairy cows and that on-farm milk flow meters facilitate precise measurements of the 2-min milk yield and total milk yield.


INTRODUCTION
Milk flow curve dynamics offer valuable information that can improve milking and parlor efficiency, udder health, and animal well-being in dairy operations (Sandrucci et al., 2007). Among the many variables concerning milk flow curve dynamics, bimodality has been used extensively to assess the quality of premilking teat stimulation. A bimodal milk flow curve is defined by an increasing milk flow rate followed by a decreasing milk flow rate during the first 2 min of milking (Tančin et al., 2006). This decrease can present as a partial or complete cessation of milk flow and, more practically, may be identified as an "empty or dry claw" shortly after milking unit attachment (Wallace et al., 2003). Bimodality is due to removal of the cisternal milk fraction before the alveolar milk reaches the gland cistern (Bruckmaier and Blum, 1998) and is a result of insufficient stimulation before milking (Wallace et al., 2003;Schukken et al., 2005); bimodality has been associated with decreased milking efficiency (Bruckmaier and Blum, 1996), reduced milk yield (Bruckmaier, 2005;Erskine et al., 2019), and impaired udder health (Bruckmaier, 2005;Zecconi et al., 2018). Traditionally, bimodality has been detected with a portable milk flow meter (i.e., the Lactocorder, WMB AG) that measures continuous milk flow. Indeed, the Lactocorder is highly popular among veterinarians and milk quality consul-tants and has been considered the gold standard for the field assessment of bimodality in dairy cows.
Over recent decades, on-farm milk flow meter technology has substantially advanced, and the milk flow characteristics of individual cows can be recorded with greater accuracy. Specifically, several electronic onfarm milk flow meters from various manufacturers are now able to calculate and record incremental milk flow rates during 0-15 s, 15-30 s, 30-60 s, and 60-120 s in milking observations of individual cows. This offers a unique opportunity to collate these automatically recorded incremental milk flow rates and identify cows with bimodal milk flow curves. However, despite recent advancements in on-farm milk flow meter technology, incremental milk flow rates have not been rigorously investigated.
In addition to bimodality, the 2-min milk yield has been reported as a viable measure to monitor parlor performance (Reid and Stewart, 2007;Treichler and Reid, 2013;Wieland et al., 2017). The 2-min milk yield is defined as the amount of milk collected within the first 2 min of milking. This measurement has been used to evaluate the effect of different premilking stimulation regimens, providing invaluable information to improve the milk harvesting process. It has been recorded with the Lactocorder (Schukken et al., 2005) and on-farm milk flow meter technologies (Watters et al., 2012;Wieland et al., 2020), but to date, the concordance between the Lactocorder and on-farm milk flow meters has not been rigorously evaluated.
Our primary objective was to investigate whether milking characteristics obtained from on-farm milk meter technology (i.e., incremental milk flow rates, the 2-min milk yield, and average milk flow rate) can be used to detect bimodality in dairy cows. We hypothesized that milking characteristics from on-farm milk flow meters could also identify bimodality as determined with the Lactocorder. The second objective of our study was to determine the concordance between the Lactocorder and an electronic on-farm milk flow meter for assessing the 2-min milk yield. We hypothesized that reliable 2-min milk yield measurements could be obtained with the on-farm milk flow meter. Additionally, we assessed the agreement between the 2 devices for assessing the total milk yield harvested during the milking observation of a single cow.

Animals and Housing
Data for this study were obtained in conjunction with 2 milking center evaluations provided by Quality Milk Production Services of Cornell University (Ithaca, NY) on May 29 and November 18, 2019, at a commercial dairy farm located near Ithaca, New York. The Cornell University Institutional Animal Care and Use Committee reviewed and approved all procedures (protocol no. 2013-0064). Some of the data (i.e., 67/129 Lactocorder observations) were used to evaluate a portable vacuum recording device and have been reported elsewhere (Wieland et al., 2021). During the study period, approximately 4,300 lactating Holstein cows were housed in freestall pens, bedded with manure solids, and fed a TMR formulated according to the requirements outlined by the NRC (2001). The farm used DHIA services, including the individual-cow SCC option. Herd and cow [i.e., parity, stage of lactation (DIM), and SCC] data were maintained in a dairy management software program (Dairy Comp 305, Valley Agricultural Software).

Milking System
Cows were milked 3 times daily at 0100, 0900, and 1700 h in a 100-stall parallel rotary parlor (RP3100HD, DeLaval International AB). The vacuum pump (22.4 kW; 30 HP) was regulated by a variable frequency drive and set to supply a receiver operator vacuum of 44 kPa (13.0 in Hg). The milking unit was composed of the cluster MC70 (DeLaval International AB) and a milking liner with a round barrel shape (LS-01 NC, DeLaval International AB). The pulsators (EP100, DeLaval International AB) were set to a pulsation rate of 60 cycles per min, a ratio of 65:35, and a side-to-side alternating pulsation. The automatic cluster removers were set to a cluster remover milk flow threshold of 1.6 kg/min, a 1 s delay, and a vacuum decay time of 1.5 s. The milk sweep [i.e., a system to allow air admission through teatcups and move the milk remaining in the cluster into the milkline (Reinemann et al., 2021)] was initiated 3.0 s after unit retraction and lasted for 8 s. Milking system settings and milking characteristics were monitored with a dairy farm management software program (DelPro, DeLaval International AB).

Milking Routine
The rotational speed of the milking parlor was 5.3 s per stall (530 s per complete rotation). Four teat spray robots (DeLaval International AB), 2 at the parlor entrance and 2 at the parlor exit, were installed for pre-and postmilking teat dip application. The parlor was operated by two 12-h work shifts, each consisting of 4 milking technicians who were assigned to perform the following tasks at the 4 different stations: (1) wipe the teat barrel of all teats from lactating quarters with an individual clean cloth towel, (2) wipe the teat end with an individual clean cloth towel, (3) attach and align the milking unit, and (4) monitor milking liner slips, unit fall-offs, and unit kick-offs and realign or reattach the milking unit accordingly. Assuming a cow entered the rotary parlor in stall 1, the positioning of the predip teat spray robots and milking stations were robot 1, stall 3; robot 2, stall 5; milking station 1, stall 10; milking station 2, stall 11; and milking station 3, stall 22. The milking technician at milking station 4 was positioned at the halfway point of the rotary and operated within a wider range to ensure timely adjustment of the milking units. This setup resulted in a dip contact time of 27-37 s, duration of tactile stimulation (calculated as the sum of wiping duration of milking stations 1 and 2) of approximately 6 s, and a preparation lag time (i.e., time from first tactile stimulus to milking unit attachment) of approximately 64 s.

Data Acquisition
We used 2 Lactocorder devices and positioned them 5 milking stalls apart to facilitate data collection. Thus, cows were enrolled randomly based on their order of entrance into the milking parlor. We recorded the cow identification number and the time of milking unit attachment. Upon milking unit detachment, we initiated a manual milk sweep by pushing the start button to move residual milk remaining in the cluster, milk hose, and meter systems into the milkline. The following milk flow characteristics were obtained simultaneously for each milking observation with electronic on-farm flowthrough milk flow meters using near-infrared technology (MM27BC, DeLaval International AB) and recorded with the dairy farm management software (DelPro, DeLaval International AB): 0-15 s milk flow rate (i.e., average milk flow rate recorded during the first 15 s of milking, kg/min; 15S MM ), 15-30 s milk flow rate (i.e., average milk flow rate recorded during the first 15-30 s of milking, kg/min; 30S MM ), 30-60 s milk flow rate (i.e., average milk flow rate recorded during the first 30-60 s of milking, kg/min; 60S MM ), 60-120 s milk flow rate (i.e., average milk flow rate recorded during the first 60-120 s of milking, kg/min; 120S MM ), the 2-min milk yield (i.e., amount of milk harvested within the first 2 min of milking, kg; 2MIN MM ), the total milk yield (i.e., yield of milk harvested from start of milking to detachment of the milking unit, kg; MY MM ), milking unit-on time (i.e., duration from start of milking to detachment of the milking unit, s), and average milk flow rate (calculated as total milk yield per milking unit-on time, kg/min; AMF MM ). Both milk flow meters were approved by the International Committee for Animal Recording and calibrated according to the manufacturers' guidelines.
Lactocorder milk flow curves were reviewed and analyzed with the adjunct software program (LactoPro, WMB AG) by a trained investigator who was blinded to the results of the on-farm milk flow meter. The presence of a bimodal milk flow curve (BIM LC ) was automatically determined by the software program and detected during the first 96 s after milk flow exceeded 0.5 kg/min if one of the following conditions were met: (1) milk flow reflux (i.e., decrease in the milk flow rate following the initial increase) >0.2 kg/min, or (2) milk flow reflux >0.1 kg/min and an interruption of the incline phase ≥14 s. In both cases, the milk reflux had to amount to ≥16% of the maximum milk flow but a minimum of 0.5 kg/min if the milk flow of the first peak reached or exceeded 80% of the maximum milk flow. Additionally, we obtained the individual 2-min milk yield (kg; 2MIN LC ) and total milk yield (kg; MY LC ) from the adjunct software program.

Analytical Approach
The data were compiled in Microsoft Excel (2019, Microsoft Corporation). Before statistical analysis, we screened the data for missing and erroneous values by investigating distributions of the 2-min milk yields (2MIN LC and 2MIN MM ), total milk yields (MY LC and MY MM ), and milking unit-on time (s). We removed observations with missing values, outliers, or probable data errors by excluding observations with values <5 kg and >55 kg for the MY LC and MY MM , respectively; values <2 kg and >12 kg for the 2MIN LC and 2MIN MM , respectively; and values <100 s and >800 s for the milking unit-on time. Furthermore, we evaluated the integrity of Lactocorder milk flow curves and excluded observations with incomplete (i.e., milk flow graph cutoff) or erroneous (i.e., milk flow curves depicting "static milk") milk flow curves. To give each observation equal weight in the analyses, we included only the first observation from each cow. We obtained data from 129 milking observations. A total of 37 observations were excluded due to erroneous or missing data. This resulted in 92 cow milking observations that were included in the final analyses.
We calculated the sample size for Cohen's κ statistic using the "irr" package (Gamer et al., 2019) in R Statistical Software (R Core Team, 2021). The calculation was based on the frequency distribution of BIM LC and bimodal milk flow as detected with the on-farm milk flow meter (BIM MM ); specifically, the probability that the Lactocorder device would detect bimodality of 28%, the probability that the on-farm milk flow meter would identify a BIM LC of 25%, a true Cohen's κ statistic of 0.7, a value of κ under the null hypothesis of 0.4, and a 2-sided test. We applied a power of 0.8 and an α-level of 0.05. This yielded a minimum sample size of 81, indicating that the 92 available observations were sufficient to assess the agreement between the 2 devices and detect bimodality. To assess whether the sample size of 92 observations was sufficient to determine whether milking characteristics obtained from the on-farm milk meter could serve as a proxy of BIM LC , we performed a power calculation for the receiver operating curve (ROC) with the "pROC" package in R (Robin et al., 2011). We employed the frequency distribution of BIM LC (i.e., "ncases" = 26 and "ncontrols" = 66), an α-level of 0.05, and an assumed area under the curve (AUC) of 0.75. This resulted in a power of 0.95, indicating that the current study population was sufficient.
For subsequent analyses, a new categorical variable, BIM MM , was created and defined as previously described (Wieland et al., 2020): BIM MM was considered present if the incremental milk flow rates 30S MM , 60S MM , or 120S MM were lower than the previous milk flow rates (15S MM , 30S MM , or 60S MM ). We performed the statistical analyses with R Statistical Software and JMP (version 14, SAS Institute Inc.). We assessed the equality of variances of milking characteristics with the Levene's test. The Levene's test indicated homoscedasticity of all milking characteristics. Therefore, we assessed differences among observations with and without BIM LC with the Student's t-test.
To test the hypothesis that milking characteristics from the on-farm milk flow meter could identify bimodality as determined with the Lactocorder, we used 3 different approaches. First, we calculated κ statistics to assess the agreement beyond that of chance between the 2 binary variables, BIM LC and BIM MM , using the package "DescTools" in R (Signorell et al., 2022). We interpreted the κ value according to Landis and Koch (1977) as follows: a κ value <0.21 was interpreted as poor agreement, 0.21-0.40 as fair, 0.41-0.60 as moderate, 0.61-0.80 as good, and 0.81-1.00 as very good. Second, we calculated sensitivity, specificity, and positive and negative predictive values to evaluate the diagnostic performance of BIM MM in detecting bimodality, using BIM LC as the gold standard as described by Dohoo et al. (2009) , and the AUC and 95% CI were obtained. We evaluated the AUC according to Hosmer et al. (2013) as follows: an AUC of 0.5 suggests no discrimination; 0.5 < AUC < 0.7, poor discrimination; 0.7 ≤ AUC < 0.8, acceptable discrimination; 0.81 ≤ AUC < 0.9, excellent discrimination; and AUC ≥ 0.9, outstanding discrimination.
To determine the associations of MY MM with MY LC and 2MIN MM with 2MIN LC , we fitted 2 separate univariate linear regression models. MY LC and 2MIN LC were included as dependent variables, and MY MM and 2MIN MM were included as independent variables. Finally, we created correlation and Bland-Altman plots in GraphPad Prism (GraphPad Software Inc.).

RESULTS AND DISCUSSION
Among the 92 cows that each contributed 1 milking observation to the final analyses, 34 (37%) cows were in their first, 24 (26%) were in their second, and 34 (37%) were in their third or higher lactation (i.e., were multiparous). The cows were between 2 and 361 DIM (mean ± SD: 159 ± 93 DIM) and had a median SCC of 34,000 cells per milliliter. The mean (±SD) values of the milking characteristics were as follows: 2MIN LC , 7.6 ± 1.8 kg; MY LC , 13.6 ± 3.1 kg; 15S MM , 0.7 ± 0.5 kg/min; 30S MM , 3.2 ± 1.2; 60S MM , 3.5 ± 1.5 kg/min; 120S MM , 4.4 ± 1.1 kg/min; 2MIN MM , 7.1 ± 2.0 kg; MY MM , 13.9 ± 3.5 kg; milking unit-on time MM , Wieland and Sipka: BIMODALITY AND MILK METER TECHNOLOGY 246 ± 56 s; and AMF MM , 3.2 ± 0.7 kg/min. These values are in the range of those obtained by the same milk flow meter technology and reported by our group from cows that were subjected to 2 different premilking stimulation regimens (Wieland et al., 2020). Indeed, all incremental milk flow rates, as well as 2MIN MM and AMF MM , were numerically higher than those from cows that received manual fore-stripping and a cumulative stimulation time (i.e., time spent on fore-stripping plus wiping of teats) of 16 s in that study (Wieland et al., 2020). Differences in parlor design (e.g., rotary versus parallel parlor, milk hose alignment, distance between cluster and milk flow meter) and study populations (e.g., milk production) may account for any discrepancies. However, in the absence of a rigorous statistical comparison, caution should be used when comparing results among studies.
The mean ± SD values of the milking characteristics, stratified by BIM LC , are presented in Table 1. Univariate analyses revealed differences between milking observations with and without BIM LC in terms of the 2-min milk yields according to both devices, the incremental milk flow rates 30S MM and 60S MM , and AMF MM (P ≤ 0.01). In contrast, we observed no differences in the incremental milk flow rates 15S MM and 120S MM or milking unit-on time MM (P ≥ 0.26). The likelihood that differences in the total milk yields between milking observations with and without BIM LC were due to chance were 3% for MY LC and 2% for MY MM , respectively, and the numerical differences are consistent with those of previous studies Wieland et al., 2021). When interpreting these numbers, one must keep in mind that this study was not designed to detect differences in milking characteristics among cows with and without bimodality. Thus, the reader should consider the possibilities of type I and type II errors. For example, when using an α-level of 0.05, a power of 0.8, and an SD of 3.1 kg, a total sample size of 54 per group would be required to detect a 1.7-kg difference in the total milk yield.
Bimodality according to the portable milk flow meter and bimodal milk flow as detected with the on-farm milk flow meter were documented in 26 (28%) and 23 (25%) milking observations, respectively (Table 2). This frequency distribution is similar to that reported in our previous cross-sectional study on 5 New York State dairy farms (Wieland et al., 2021) and the average percentage of cows with delayed milk ejection detected with a portable vacuum recording device from 64 Michigan dairy herds, as reported by Moore-Foster et al. (2019). However, these 92 milking observations are unlikely to represent the prevalence of bimodality in the entire milking herd. Indeed, using the milk flow data extracted from the farm management software for the entire herd from the 2 observed milking sessions, the same exclusion criteria for erroneous and missing data and the algorithm described above yielded a bimodality of 35.6% (data not shown). This is the percentage of bimodality expected given a stimulation time of 6 s and a preparation lag time of 64 s and is consistent with observations made by Sandrucci et al. (2007), who employed the Lactocorder in a cross-sectional study of 82 Italian Holstein-Friesian dairy herds in Lombardy and reported a 35.1% prevalence of BIM LC .
The κ value and 95% CI for the agreement between BIM LC and BIM MM were 0.69 (0.49-0.90), indicating good agreement between the 2 devices for detecting bimodality. This κ value is slightly higher than that  . Taken together, our results suggest that incremental milk flow rates from electronic on-farm milk flow meters can be used to detect bimodal milk flow curves in dairy cows through employing the algorithm described herein. Six out of the 7 observations that were detected as bimodal milk flow curves by the Lactocorder but not by the on-farm milk meter were characterized by a rather subtle milk reflux ranging from 0.3 to 1 kg/min, whereas only 1 out of the 7 milking observation had a milk reflux of 1.5 kg/ min. Conversely, the 4 milking observations that were erroneously detected as bimodal milk flow curves by the on-farm milk meter were exclusively caused by the 120S MM being lower than the previous incremental milk flow rates (n = 2, 120S MM < 60S MM ; n = 2, 120S MM < 60S MM and 120S MM < 30S MM ). Although these are subjective measures on a small number of observations, they indicate possible shortcomings of both measuring devices and suggest opportunities to further improve the case definitions.
The AUC values (95% CI), optimal cut-points, corresponding sensitivity, and specificity of 15S MM , 30S MM , 60S MM , 120S MM , 2MIN MM , and AMF MM for predicting BIM LC , as well as coefficients of determination (R 2 ) and P-values from the logistic regression models, are presented in Table 3. The ROC curves are depicted in Figure 1. The AUC according to Hosmer et al.'s (2013) interpretation revealed excellent discrimination for the incremental milk flow rate 60S MM and acceptable discrimination for 30S MM and 2MIN MM , whereas all other milking characteristics yielded poor discrimination. The R 2 value for the logistic regression model including 60S MM indicated that 41% of the variability in BIM LC could be explained by 60S MM . Its optimal cut-point of 3.1 kg/min resulted in a sensitivity of 0.85 and a specificity of 0.79. Conversely, the other milking characteristics investigated explained only between 0.05% and 11% of the variability. Judging from the AUCs and the coefficients of determination, the best milking characteristic for predicting BIM LC is 60S MM . Thus, the incremental milk flow rate 60S MM is a valid measure to predict bimodality in dairy cows. We speculate that the observed phenomenon can be attributed to the nadir of the bimodal milk flow curve [representing the commencement of the alveolar milk ejection into the cistern (Bruckmaier and Blum, 1996)] occurring most often during the 30 to 60 s interval after the cisternal milk has been extracted. Figures 2A and B show the Lactocorder graphs of 2 exemplary milking observations, one milk flow curve with (A) and one without (B) bimodality, respectively, illustrating the differences in the incremental milk flow rates 15S MM , 30S MM , 60S MM , and 120S MM . Note that the largest numerical difference is present for the 60S MM . Our theory is supported by the results reported in Table 1 showing that 60S MM provides the best separation between the 2 groups as indicated by the largest numerical differences between milking observations with and without bimodality. They are further supported by previous work from  showing that 296/302 (98%) of cows with a "let-down time" (assessed with a portable vacuum recording device) of ≥ 30 s demonstrated bimodality, whereas bimodality was not observed in any of the 361 animals that had a let-down time <30 s.
Our results extend the literature and suggest that incremental milk flow rates from electronic on-farm milk meters are suitable for monitoring bimodal milk flow curves. Due to their inherent nature, on-farm milk flow meters allow data collection from milking observations of individual cows and thus provide identification of cows with delayed milk ejection, monitor the incidence of bimodality, and facilitate real-time decision making in dairy operations. For example, using the case definition for bimodality or the cut-point value for 60S MM for the prediction of bimodality described herein could facilitate identification of cows with chronically delayed milk ejection, as previously described (Wieland et al., 2022). In conjunction with automated premilking stimulation systems that use inherent features such as the pulsa-  tor system, cows identified with chronically delayed milk ejection could then be subjected to supplemental premilking stimulation. The application of supplemental stimulation may elicit a stronger oxytocin release through additional tactile stimulation of pressuresensitive mechanoreceptors at the teat. Furthermore, additional time between the first tactile stimulus and the initiation of the milk harvest may accommodate differences in the lag time (i.e., time between the start of tactile teat stimulation and the onset of milk ejection) among cows. This could help accommodate the physiological requirements of cows with chronically delayed milk ejection and maximize their milk ejection capacity through mitigation of the negative impact of delayed milk ejection on milking efficiency, milk yield, and udder health that have been reported previously (Bruckmaier and Blum, 1996;Bruckmaier, 2005;Erskine et al., 2019). Such a protocol would potentially improve milking and parlor efficiency, enhance milk production and udder health, and therefore increase animal welfare and the overall sustainability of dairy operations. Nonetheless, future research is warranted to test this theory and evaluate whether the milk ejection capacity of cows with bimodal milk flow curves can be augmented through supplemental automated premilking stimulation. The Pearson correlation coefficients (r, 95% CI) indicated very strong correlations between the 2 devices for both the 2-min milk yield (0.97, 0.96-0.98) and total milk yield (0.97, 0.96-0.98; Figures 3 A and  B). Similarly, the ICC (95% CI) and CCC (95% CI) revealed excellent agreement between the 2 devices for the 2-min milk yield [ICC, 0.97 (0.96-0.98); CCC, 0.94 (0.92-0.96)] and total milk yield [ICC, 0.97 (0.96-0.98); CCC, 0.97 (0.95-0.98)]. The results of the linear regression models indicated associations of 2MIN MM with 2MIN LC (P < 0.0001, R 2 = 0.95) and MY MM with MY LC (P < 0.0001, R 2 = 0.95). Additionally, Bland-Altman plots indicated that the mean bias (i.e., mean difference in accuracy of the MM27BC milk flow meter compared with the Lactocorder device that was the gold standard) was −0.45 kg for the 2-min milk yield and 0.30 kg for the total milk yield. This suggests that the 2-min milk yield was underestimated by the MM27BC milk flow meter, whereas the total milk yield was overestimated. For both yields, the mean bias increased as yields measured with the Lactocorder device increased, as indicated through increased scattering with increasing mean values of both devices ( Figures 3C and D). Users of electronic on-farm milk flow meters take notice of this bias. Our data address the paucity of research on the comparability of different milk flow meter technologies and show that on-farm milk flow meter technology can facilitate precise measurements of the 2-min milk yield and total milk yield.
Previous work showed that 16% and 21% of the variability in 2-min milk yield and milk yield, respectively, were found between days and milking session within cow (Wieland et al., 2017). In this study, we failed to collect repeated measurements over multiple milking sessions within a cow due to logistical challenges. That is, the limited number of Lactocorder devices available would have required mounting of the devices to the respective milking stall upon identification of the cow during parlor rotation, which was not possible for reasons of operational safety. Consequently, we were not able to assess the proportion of variation attributable at the cow level. Knowledge about the variance components at different levels such as milking session and day within cow and perhaps even between herds could increase the external validity and could be the subject of future studies.
Our study was carried out on only 1 dairy farm, limiting its external validity. Thus, some variables that may have influenced the measurement precision should be noted. In our experience, the presence or absence of a milk sweep can substantially alter recorded values. That is, without a milk sweep of sufficient duration, some milk may remain in the cluster, milk hose, and measuring chambers of the milk flow meters. This can Wieland and Sipka: BIMODALITY AND MILK METER TECHNOLOGY Table 3. Area under the receiver operating characteristic curve (AUC) and the 95% confidence interval (95% CI), optimal cut-point value (CPV), associated sensitivity (Se) and specificity (Sp), coefficient of determination (R 2 ), and P-value of milking characteristics as assessed with an electronic on-farm milk flow meter (indicated by subscript MM) 1 Values were used to predict bimodality as detected with the Lactocorder (WMB AG) in the univariate logistic regression model.  lead to incomplete recording of the milk yield in the current milking observation, erroneously high incremental milk flow rates and total milk yield in the subsequent milking, and the recording of "static" milk by the Lactocorder device. In our experience, the last impact can result in a false positive diagnosis of bimodality in the subsequent milking. To minimize the amount and consequences of residual milk in the system after milking, we performed an additional milk sweep at the end of each milking observation. We can only speculate on how agreement and concordance results may have varied in the absence of this step but firmly believe that they would have been negatively impacted. We therefore suggest that the cluster, milk hose, and milk flow meters should be emptied by means of a milk sweep after each milking to obtain the highest-quality data from electronic on-farm milk flow meters.
As indicated by Treichler and Reid (2013), differences in the assessment of milking characteristics exist among on-farm milk flow meters from different manufacturers (e.g., flow-through meter versus fill-and-dump meter). In addition to the influence of the milk sweep, other herd-level variables may impact incremental milk flow rates, including the milk-flow threshold of the automatic cluster remover and the speed with which the milking unit is attached. Therefore, the proposed algorithm for detecting bimodality, as well as the optimal cut-point of 3.1 kg/min for 60S MM described herein, may require adjustments at the herd level or, more specifically, at the parlor level.
More recently, researchers have used the inverse relationship between milk flow and vacuum (Borkhus and Rønningen, 2003;Bade et al., 2009) to indirectly detect bimodality with a portable vacuum recording device Moore-Foster et al., 2019;Wieland et al., 2021). In addition to the Lactocorder, other "tried-and-true" measuring devices should therefore be compared with on-farm milk meter technology.

CONCLUSIONS
Electronic on-farm milk flow meters that measure incremental milk flow rates can be used to detect bimodal milk flow curves in dairy cows. Using the case definition for bimodality [i.e., bimodality was present if the incremental milk flow rates 30S MM , 60S MM , or 120S MM were lower than the previous milk flow rates (15S MM , 30S MM , or 60S MM )] or a cut-point value for 60S MM as described herein provides an opportunity to dairy producers and milk quality consultants to identify cows whose physiological requirements for premilking stimulation are not met on a daily basis. This knowledge could be used to target individual cows and then subject them to, for example, supplemental stimulation through automated premilking stimulation systems to maximize their milk ejection capacity, though future research is needed to test this theorem. Future studies investigating the associations between bimodality and economically important variables such as milk yield and milking duration can inform the choice of the most discriminatory case definition for bimodality. Correlation and concordance coefficients indicate that on-farm milk flow meters facilitate precise measurements of the 2-min milk yield and overall milk yield, suggesting that data from portable and nonportable milk flow meters are comparable. This facilitates the comparison of data from studies where different milk flow meters have been used.