The association between teat shape and bimodal milk ejection in Holstein dairy cows

Our objectives were to investigate the association of teat shape with (1) bimodality (2) incremental milk flow rates (average flow rates during the first 15 s, 15–30 s, 30–60 s, and 60–120 s of milking), and (3) peak milk flow rate in Holstein dairy cows milked 3 times per day. In this prospective cohort study, we analyzed 220,928 milking observations that were collected from 2,520 cows from a single dairy herd over a period of 31 d. Teat shape was visually assessed and classified into 1 of 4 categories as follows: (1) triangular barrel and pointed teat end (TP), (2) square barrel and round teat end (SR), (3) square barrel, round teat end, and flat in the area of the teat orifice (SRF), and (4) square barrel and flat teat end (SF). Individual cow-level milk flow rates were obtained using electronic on-farm milk meters. We considered bimodality to be present if any of the incremental milk flow rates (flow rates during 15–30 s, 30–60 s, or 60–120 s) were lower than any of the previous rates (flow rates during the first 15 s, 15–30 s, or 30–60 s). The frequency distribution of cows with different teat shapes was as follows: TP, 96 (3.8%); SR, 1,751 (69.5%); SRF, 617 (24.5%); and SF, 56 (2.2%). A generalized linear mixed model revealed differences in the odds of bimodality among cows with different teat shapes. Compared with cows in category SR, the odds (95% confidence interval) of bimodality of cows in other categories were as follows: TP, 0.68 (0.48–0.97); SF, 1.96 (1.21–3.19); and SRF, 1.46 (1.23–1.72). General linear mixed models indicated an association between teat shape and all incremental milk flow rates, with higher milk flow rates being present for cows with teat shapes in the SRF and SF categories. The general linear mixed model for the dependent variable peak milk flow rate indicated an association between teat shape and peak milk flow rate. Least squares means and 95% confidence intervals were 5.1 (4.9–5.3) kg/min for TP, 5.8 (5.5–6.1) kg/min for SF, 5.6 (5.5–5.7) for SRF, and 5.3 (5.3–5.4) for SR, respectively. We conclude that in this study cohort, bimodality is more likely to occur in cows with flat teat ends compared with those with a round teat ends. We attribute this relationship to the difference in milking speed across cows with different teat shapes. Teat shape may serve as a useful phenotype to identify cows that are more likely to exhibit bimodality. Because our study population was unique, future studies considering different circumstances such as breed, milking system, and milking routine are needed before results can be extrapolated.


INTRODUCTION
Delayed milk ejection -most often presented as bimodality -occurs when the cisternal milk fraction is removed before the alveolar milk reaches the gland cistern (Bruckmaier and Blum, 1998).This phenomenon is thought to occur due to a discrepancy between the intensity and the timing of premilking udder stimulation and the physiological requirements of the cow (Kaskous and Bruckmaier, 2011).Bimodality has been associated with decreased milking efficiency (Bruckmaier and Blum, 1996), reduced milk yield (Erskine et al., 2019), and impaired teat and udder health (Bruckmaier and Blum, 1996;Bruckmaier and Hilger, 2001;Zecconi et al., 2018).Multiple research groups have investigated the risk factors for bimodality and identified breed (Dodenhoff et al., 1999), stage of lactation (Sandrucci et al., 2007), the degree of udder filling (Bruckmaier and Hilger, 2001), chronic mastitis (Zecconi et al., 2018), and health and management events (Wieland et al., 2022) as factors associated with the occurrence of bimodality.The results from a recent study by our group showed that cows with flat teat ends had higher milk flow during the first 2 min of milking (Wieland et al., 2017), thus suggesting that differences in the incremental milk flow rates and the occurrence of bimodality may exist among cows with different teat characteristics.Despite this evidence, the relationship between bimodality and teat characteristics (e.g., teat shape) has not been investigated in depth.
Traditionally, bimodality has been evaluated with portable electronic milk meters that measure continuous milk flow.Over recent decades, the Lactocorder (WMB AG, Balgach, Switzerland) has gained significant popularity among portable milk meters.Milk quality consultants and researchers have been using the Lactocorder to evaluate milking machine settings (Wallace et al., 2003), premilking udder stimulation (Schukken et al., 2005), and genetic evaluations of milk flow traits (Tamburini et al., 2010;Gray et al., 2011;Samoré et al., 2011).More recently, a research group from Michigan used a digital vacuum recorder device (VaDia, Biocontrol, Rakkestad, Norway) to indirectly detect delayed milk ejection and bimodality using the principle of a linear relationship between vacuum and milk flow (Borkhus and Rønningen, 2003;Bade et al., 2009).However, on-farm milk meter technology has advanced significantly in recent decades, and there has been an increase in the accuracy of recording individual cow milk flow characteristics.Multiple electronic onfarm milk meters from different manufacturers are capable of recording milk flow rates from 0 to 15 s, 15-30 s, 30-60 s, and 60-120 s.These incremental milk flow rates can be used to identify the bimodality of cows' individual milking observations and provide realtime assessment of the milking performance of an entire herd (Wieland and Sipka, 2023).The objectives of this study were to investigate the association of teat shape with (1) bimodality and (2) incremental milk flow rates recorded with electronic on-farm milk flow meters.We hypothesized that differences in the (1) occurrence of bimodality and (2) incremental milk flow rates existed among cows with different teat shapes.An extension of our study was to investigate the association between teat shape and peak milk flow rate.

Animals and Housing
This prospective cohort study was conducted at a commercial dairy farm near Ithaca, New York.All animal procedures were reviewed and approved by the Cornell University Institutional Animal Care and Use Committee (protocol no. 2013-0064).During the study period, approximately 4,100 lactating Holstein cows were housed in free-stall pens, bedded with manure solids, and fed a total mixed ration that was formulated in accordance with the requirements set forth by the National Research Council (NRC, 2001).The farm used a dairy management software program (Dairy Comp 305, Valley Agricultural Software, Tulare, CA) for herd data maintenance, as well as monthly DHI(A) services including the individual-cow SCC.The rolling herd key performance indicators were average milk production (14,058 kg), mean test day SCC (261,000 cells/mL) and monthly clinical mastitis incidence (13.6%).

Milking System
Cows were milked 3 times daily at 8-h intervals in a 100-stall parallel rotary parlor (RP3100HD, DeLaval International AB, Tumba, Sweden).The vacuum pump (22.4 kW; 30 HP) was set to supply a receiver operator vacuum of 46.1 kPa (13.6 inHg).The pulsators (EP100, DeLaval International AB) were set to a pulsation rate of 60 cycles/min, a ratio of 65:35, and a side-to-side alternating pulsation condition.The pulsation phases under load, assessed with a digital vacuum recorder (VPR200, DeLaval International AB), were 177 ms for the a-phase, 470 ms for the b-phase, 115 ms for the c-phase, and 238 ms for the d-phase.The milking unit consisted of the cluster MC70 (DeLaval International AB) and a milking liner with a round barrel design (LS-01 NC, DeLaval International AB).The average claw vacuum during the peak milk flow period was calculated from 10 milking observations using a digital vacuum recorder (VPR200, DeLaval International AB) according to the guidelines outlined by the National Mastitis Council (NMC, 2012) and was 38.9 kPa (11.5 inHg).The automatic cluster removers were set to a cluster remover milk flow threshold of 1.3 kg/min, a 2-s delay, and a vacuum decay time of 1.5 s.The milk sweep was inactivated.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 4.9 s/ stall (530 s/complete rotation), resulting in a theoretical throughput of 679 cows/h.The parlor was operated in 2 12-h work shifts, each containing 4 milking technicians assigned to perform the following tasks at 4 different stations: (1) cleaning all teats in lactating quarters with an automated teat brush at stall 3, (2) manually forestripping 2 teats and applying teat disinfectant to all teats at stall 5, (3) wiping all teats with an individual clean cloth towel at stall 16, and (4) attaching and aligning the milking unit (at stall 22 for early-and mid-lactation cows; at stall 27 for late-lactation cows).This setup resulted in a dip contact time of 54 s, total tactile stimulation duration (calculated as the sum of cleaning of all teats with the teat brush at station 1 and manual forestripping of 2 teats at station 2) of approximately 6 s, and a preparation lag time (i.e., time from the first tactile stimulation to milking unit attachment) of approximately 93 s (early-and mid-lactation cows) or 118 s (late-lactation animals).The forced retraction of the milking unit was initiated at stall 90, resulting in a maximum milking unit-on time of 333 s (early-and mid-lactation animals) or 309 s (late-lactation cows).Two teat spray robots (TSRs, DeLaval International AB) were installed at the parlor exit for postmilking teat dip application at positions 92-93 and 94-95 (cows exited the milking parlor at stalls 96-100).

Data Acquisition
Cow Characteristics.Cow characteristics (i.e., lactation number, stage of lactation, and SCC) were obtained from the dairy management software program (Dairy Comp 305, Valley Agricultural Software, Tulare, CA).We used the results from the DHI(A) testing of December 2021 (month in which the study started) for most cows to obtain SCC data; for cows that had no test day information for the month of December, we used data from either the month of November 2021 or January 2022 based on availability.
Milk Flow Characteristics.The following milk flow characteristics were assessed at each milking: milk yield (i.e., yield of milk harvested from start of milking to detachment of the milking unit in each milking session; kg), milking unit-on time (i.e., time recorded from start of milking to detachment of the milking unit; s), average milk flow rate (calculated as milk yield/milking unit-on time; kg/min), first 15 s milk flow rate (i.e., average milk flow rate recorded in the first 15 s of milking; kg/min; 15S), 15-30 s milk flow rate (i.e., average milk flow rate recorded during the 15 to 30 s of milking; kg/min; 30S), 30-60 s milk flow rate (i.e., average milk flow rate recorded during the 30 to 60 s of milking; kg/ min; 60S), 60-120 s milk flow rate (i.e., average milk flow rate recorded during the 60 to 120 s of milking; kg/min; 120S), 2-min milk yield (i.e., amount of milk harvested within the first 2 min of milking; kg), and peak milk flow rate (i.e., maximum 60-s milk flow rate; kg/min).These parameters were assessed with electronic on-farm milk meters using near-infrared technology (MM27BC, DeLaval International AB), which are approved by the International Committee for Animal Recording, and they were recorded with the dairy farm management software DelPro (DeLaval International AB).For this purpose, a report was created in DelPro to automatically record the milk flow characteristics of each milking session and export them to a comma separated (.csv) file once per day.
Teat Shape and Presence of Nonlactating Quarter.Teat shape and the presence of nonlactating quarters were visually assessed on December 22, 2021 from all lactating cows, by 1 investigator (MW) during 1 milking session between stations 3 and 4. For the classification of the teat shape, we employed the principle outlined by Seykora and McDaniel (1985), who used the shapes of the teat barrel and the teat end to classify teats into different categories.That is, we classified individual teats into 1 of 4 categories as follows: (1) triangular barrel and pointed teat end (TP), (2) square barrel and round teat end (SR), (3) square barrel, round teat end, and flat in the area of the teat orifice (SRF), and (4) square barrel and flat teat end [SF, (Figure 1)].Because the teats of nonlactating quarters are subject to different types of deformation due to injury or inflammation, the teat shape of nonlactating quarters was not assessed.

Study Design.
The study period during which milk flow characteristics were obtained was defined as 31 d from December 22, 2021, to January 21, 2022.We chose a convenient sample size, which was based on the availability of all lactating cows during the study period.The target population consisted of all lactating cows during the study period.The study population consisted of cows with a uniform teat shape and 4 lactating quarters.
Cows with 2 or more different teat shapes and those with 1 or more nonlactating quarters were excluded from the analyses.
Analytical Approach.Data were maintained in Excel (Microsoft Corp.) and JMP Pro (version 15, SAS Institute Inc., Cary, NC).Before statistical analyses, we investigated the data for missing and erroneous values.We removed observations with missing values, outliers, or probable data errors by excluding observations with values of <2.5 kg for milk yield, values > 800 s for milking unit-on time, values < 0.2 and > 10 for peak milk flow rate, and values < 0.1 kg/min and > 6 kg/ min for average milk flow rate.Statistical analyses were performed with R (Team, 2023).
Teat Shape and Bimodality.For subsequent analyses, a new binary variable to capture bimodality was created and defined as previously described by Wieland and Sipka (2023).A bimodal milk flow curve was considered present if any of the incremental milk flow rates 30S, 60S, or 120S were lower than any of the previous rates (15S, 30S, 60S); otherwise, bimodality was considered to be absent.The milk flow meter system records milk flow rates to 2 decimal places.Therefore, the minimum required difference between 2 incremental milk flow rates was 0.01 kg/min.
To determine the association between teat shape and bimodality, we built a generalized linear mixed model with a logit link and a binomial distribution with the 'lme4' package (Bates et al., 2015) in R. Cow was in- We considered that a coefficient of > |0.66| indicated collinearity.Manual backward elimination was performed until each of the variables had a P-value <0.05.Finally, we tested the interactions between lactation number and teat shape, as well as stage of lactation and teat shape.We evaluated the final model's predictive ability by calculating a receiver operating characteristic curve with the 'pROC' package (Robin et al., 2011).
Teat Shape and Milk Flow Rates.To study the association between teat shape and the incremental milk flow rates 15S, 30S, 60S, 120S, and peak milk flow rate, we fitted 5 separate general linear mixed models with the 'nlme' package (Pinheiro et al., 2016) in R. The following steps were consistent for all 5 models.To account for the clustering of milking observations within cows and days, we included cows and days nested within cows as random effects.To model the covariance of repeated observations within cows, the autoregressive order 1 covariance structure was used.Teat shape was entered into each model as a fixed effect.The following additional independent variables were considered and included in each model: lactation number (1st, 2nd, and ≥3rd lactation), stage of lactation (≤100, 101-200, > 200 DIM), milk yield (kg/ milking session), logSCC, and the preparation lag time (short, 93 s vs. long, 118 s).To control for the familywise error rate when comparing a family of estimates, we applied Tukey-Kramer's post hoc test.Finally, we inspected residual plots versus corresponding predicted values and examined quantile-quantile residual plots to assess whether the assumptions of homoscedasticity and normality of residuals were met.

Teat Shape and Bimodality
Bimodality was documented in 62,307/220,928 (28.2%) milking observations.Table 1 depicts the frequency distribution of bimodality stratified by teat shape.The final model included teat shape (P < 0.0001), lactation number (P < 0.0001), stage of lactation (P < 0.0001), milk yield (P < 0.0001), logSCC (P < 0.0001), and preparation lag time (P < 0.0001).The interactions between lactation number and teat shape and between stage of lactation and teat shape revealed P ≥ 0.48 and, thus, were not retained in the final model.Figure 2 depicts odds ratios and 95% confidence intervals (95% CI).Cows in 1st lactation had lower odds of bimodality compared with those in lactation 3 and greater.Compared with cows in the 3rd or greater lactation, the odds ratios (95% CI) were 0.39 (0.33−0.48) and 0.99 (0.84−1.19) for cows in the 1st and 2nd lactation, respectively.Similarly, early or mid-lactation cows had lower odds of bimodality than late-lactation animals.The odds ratios (95% CI) were 0.41 (0.34−0.48) and 0.48 (0.40−0.57) in early and mid-lactation cows, respectively, compared with late lactation cows.The area under the receiver operating characteristic curve was 0.89.

Teat Shape and Milk Flow Rates
The final models revealed that teat shape was associated with all 4 incremental milk flow rates (P ≤ 0.0005).Table 2 and Figure 3 depict LSM and 95% CI for 15S, 30S, 60S, and 120S, stratified by teat shape.The final model for the dependent variable peak milk flow rate revealed an association between teat shape and peak milk flow rate (P < 0.0001).Controlling for the effects of lactation number (P < 0.0001), stage of lactation (P < 0.0001), milk yield (P < 0.0001), logSCC (P = 0.18), and preparation lag time (P < 0.0001), LSM and 95% CI for peak milk flow rate were 5.1 (4.9-5.3)kg/min for TP, 5.8 (5.5-6.1)kg/min for SF, 5.6 (5.5-5.7) for SRF, and 5.3 (5.3-5.4) for SR, respectively.Figure 4 depicts LSM and 95% CI for peak milk flow rates stratified by teat shape.Based on the inspection of residual plots versus corresponding predicted values and examined quantile-quantile residual plots, the assumptions of homoscedasticity and normality of residuals were met.

4
120S: 60 to 120 s milk flow rate; estimates controlled for the effects of lactation number (P = 0.0007), stage of lactation (P < 0.0001), SCC (log 10 -transformed; P = 0.47), milk yield (P < 0.0001), preparation lag time (P = 0.03), and teat shape (P < 0.0001).(Bruckmaier and Blum, 1996;Bruckmaier and Hilger, 2001;Zecconi et al., 2018).Our results are therefore of particular importance, as they may help in deciphering some of the previously unexplained variability of milk flow dynamics (i.e., bimodality) that have a reported impact on milk production, well-being, and milking efficiency in dairy cows.Bimodality has been described because of insufficient premilking stimulation, improper timing of milking unit attachment or a combination of both (Bruckmaier and Blum, 1998).Further, data from our own group showed that health (i.e., lameness) and management (i.e., vaccination) events were risk factors for bimodality (Wieland et al., 2022).Our current findings extend the existing body of literature and suggest that teat shape may serve as a useful phenotype to identify cows that are more likely to exhibit bimodality, but additional research enrolling more herds that utilize differing milking systems, milking routines and breeds are necessary to confirm that this finding can be extended to other herds.We hypothesize that the observed difference in the odds of bimodality is attributable to the difference in milking speed among cows with different teat shapes.A bimodal milk flow curve is due to removal of the cisternal milk fraction before the alveolar milk reaches the gland cistern.In fast milking cows, the gland cistern is likely emptied faster, making it more likely that milk flow decreases before the alveolar milk is ejected into the cistern.This is supported by our data showing that cows in groups SF and SRF had higher peak milk flow rate than those in groups TP and SR.Our theory is also supported by results reported by other researchers investigating bimodality in dairy cows (Dodenhoff et al., 1999;Sandrucci et al., 2007;Samoré et al., 2011).In a German study (Dodenhoff et al., 1999), the researchers analyzed 1,424,647 milking observations obtained with a portable milk flow meter (Lactocorder, WMB AG, Balgach, Switzerland) from 256,667 cows in 13,127 dairy herds of Bavaria, Germany for genetic evaluation of milkability.They found that cows with a bimodal milk flow curve had a considerably larger maximum milk flow rate (i.e., largest milk flow rate during milking over a 22-s period) than animals that did not show bimodality.The authors concluded that inadequate premilking stimulation resulting in bimodality is more likely to occur in cows with a larger maximum milk flow rate as the milk from the gland cistern is removed quickly (Dodenhoff et al., 1999).A study from Italy (Sandrucci et al., 2007) analyzed 2,486 milk flow curves recorded with the Lactocorder from 82 Italian Holstein-Friesian dairy herds of the Lombardy region.The researchers showed that the percentage of bimodal milk flow curves increased to 25.0, 30.6, and 42.0% as the peak milk flow rate increased from <3 to 3-4 and > 4 kg/min, respectively.Samoré et al. (2011) conducted a study to investigate milk flow traits in Italian Holstein-Friesian cows and obtained 2,886 records from 133 herds in northern Italy using the Lactocorder.
Their findings supported the results of previous works (Dodenhoff et al., 1999;Sandrucci et al., 2007), and the authors suggested that "quicker milk flow over a shorter period would increase the frequency of bimodal curves in milking" (Samoré et al., 2011).
We found an association between lactation number and bimodality such that cows in lactation number 1 had lower odds of bimodality than those in lactation 3 or greater.Previous studies (McDonald, 1968;Appleman, 1970) reported that the teat diameter of cows increases with successive lactation and that teats with larger diameters have larger orifices (Rathore and Sheldrake, 1977).This could accelerate the emptying of the cisternal reserve of milk, leading to bimodality.In a previous study, we reported that second-lactation animals had the highest odds of bimodality (Wieland et al., 2022).Differences in bimodality between cows <150 DIM ( = 27.3%) and >150 DIM ( = 40.6%)were also observed by Sandrucci et al. (2007).The authors hypothesized that differences were due to (1) delayed milk ejection of the alveolar milk consequent to a reduction of the udder filling throughout lactation as outlined by Bruckmaier and Hilger (2001) and (2) a progressive decrease in cisternal milk with advancing lactation as has been reported previously (Caja et al., 2004).Our findings are in contrast to those reported by others, who found no differences in bimodality between firstlactation cows and animals in lactation 2 and greater (Sandrucci et al., 2007) and between cows in parities 1, 2, and 3 (Dodenhoff et al., 1999).The authors of a recent study on a 3,600-cow Michigan dairy investigating the relationship between bimodal milk flow and milk yield reported no evidence of differences in the probability of delayed milk ejection within categories of stage of lactation (Erskine et al., 2019).The reason for the disparity across studies is most likely due to differences in study population, milking systems, premilking teat stimulation regimens, diagnostic techniques, case definitions of bimodality, and thresholds used to assign lactation number and stage of lactation categories, respectively.
The presence of an association between milk yield and bimodality supports descriptions by other researchers who investigated the relationship between udder filling and milk ejection (Bruckmaier and Hilger, 2001;Kaskous and Bruckmaier, 2011).The investigators estimated the degree of udder filling as a function of the actual milk yield and maximum storage capacity and found that the delay until the start of milk ejection increased with decreasing udder filling (Bruckmaier and Hilger, 2001;Kaskous and Bruckmaier, 2011).A 1-unit increase in logSCC increased the odds of bimodality milk letdown by 39%.This finding is in accordance with results reported by Zecconi et al. (2018), who studied the effect of nonsteroidal anti-inflammatory drug (i.e., ketoprofen) administration on the milk ejection curve in cows with chronic subclinical mastitis.Their results showed that anti-inflammatory treatment with ketoprofen reduced the frequency of bimodality [32.3% in chronic cows receiving ketoprofen (n = 19) versus 45.2% in chronic cows without treatment (n = 15)].The authors attributed the positive effect of ketoprofen on the milk flow pattern to a reduction in inflammation, which in turn is thought to impact oxytocin activity in cows with chronic subclinical mastitis (Zecconi et al., 2018).Last, we found that cows subjected to a preparation lag time of 118 s had lower odds of bimodality compared with those that received a lag time of 93 s.This finding is in accordance with results from previous work from our group (Singh et al., 2023).
Last, our data showed that, overall, the incremental milk flow rates were higher in cows in categories SF and SRF compared with those in groups TP and SR.Our findings are in accordance with results from a previous study from our group showing that cows with flat teatends had higher 2-min milk yields compared with those with pointed and round teat-end shapes (Wieland et al., 2017).One possible explanation for the observed differences in the incremental milk flow rates and, thus, the milkability during the first 2 min of milking among cows with different teat shapes could be differences in teat canal length (Grindal et al., 1991) and teat canal diameter (Rathore and Sheldrake, 1977) among cows with different teat shapes.Another possible factor could be differences in the adrenoceptor pattern among cows with different teat shapes, as previously reported (Roets et al., 1986;Roets et al., 1989).However, because we did not assess teat canal length, teat canal diameter, or adrenoceptor pattern among cows with different teat shapes, these possible explanations remain speculative.

Study Limitations and Future Research
Although our results are promising and we begin to better be able to discern the variability of milk flow dynamics during the first 2 min of milking, there are limitations that need to be considered.First, this study was conducted at a single New York dairy farm with Holstein cows that were milked 3 times per day.Our results are therefore likely to reflect what would happen in this unique target population (i.e., all lactating cows in the study herd).However, before these results can be extrapolated, this study needs to be replicated considering different study population (e.g., breed and distribution of lactation numbers and stages of lactation), milking systems, and milking routines (i.e., premilking stimulation regimen) in different regions.Second, the case definition for bimodality was based on previous reports from multiple investigators globally (Bruckmaier and Blum, 1996;Tančin et al., 2006;Samoré et al., 2011) who defined bimodality as the presence of an increasing milk flow rate that is followed by a decreasing flow rate during the first 2 min of milking observation.However, the minimum value of the milk reflux (i.e., the magnitude of milk flow decline after the initial increase), as outlined by previous authors (Watters et al., 2012), has not been considered.Therefore, although we have previously evaluated the employed case definition on the same study farm and found good agreement between the on-farm milk flow meter and the Lactocorder device (Wieland and Sipka, 2023), more work is needed to determine the biological relevance of bimodality as assessed with incremental milk flow rates from on-farm milk meters.Third, we believe that differences between teat shapes are nuanced, a principle that has been employed previously using a continuous scale to evaluate teat traits (Seykora and McDaniel, 1985).Although attempts have been made to best represent the distribution of the target population, we acknowledge that the chosen thresholds were subject to subjectivity.Another limitation of this study was that teat shape was assessed by a single investigator only and only once at the beginning of the study period.The determination of teat shape would have been more robust if more investigators had performed the scoring at different time points throughout the study.Previous research has shown an association of other phenotypes, such as teat length and diameter, with milk flow rates (Johansson and Malven, 1960;Rathore and Sheldrake, 1977).Therefore, adding these phenotypes to the analysis might have helped explain some of the residual variability in this study.Future research should focus on standardizing the assessment of teat traits and incorporating additional traits such as teat dimensions.Such work should consider milk production and udder health parameters.

CONCLUSION
The results of this study confirmed our hypothesis that differences in the occurrence of bimodality exist among cows with different cow characteristics such as teat shape.We attributed this relationship to the differences in milking speed across cows with different teat shapes.We conclude that in this study cohort, bimodality is more likely to occur in cows with flat teat ends compared with those with a round teat end.Teat shape may serve as a useful phenotype to identify cows that are more likely to exhibit bimodal milk flow curves, though future research is needed before our results can be extrapolated.
Wieland et al.: BIMODALITY AND TEAT SHAPEcluded as a random effect to account for the correlated structure of the data.Teat shape was entered into the model as a fixed effect.The lactation number (1st, 2nd, and ≥3rd lactation), stage of lactation (≤100, 101-200, > 200 DIM), milk yield (kg/milking session), log 10transformed SCC (logSCC), and preparation lag time (short, 93 s vs. long, 118 s) were included as additional variables.To assess collinearity among eligible variables, we calculated Spearman correlation coefficients.

Figure 1 .
Figure 1.Classification system of teat shapes.TP, triangular barrel and pointed teat end; SR, square barrel and round teat end; SRF, square barrel, round teat end, flat in the area of the teat orifice; and SF, square barrel and flat teat end.
any of the incremental milk flow rates 30S, 60S, or 120S were lower than any of the previous ones (15S, 30S, 60S).

Figure 2 .
Figure 2. Results from the multivariable generalized linear mixed model showing the association of lactation number, stage of lactation (DIM), milk yield, SCC (LogSCC; SCC log 10 -transformed), preparation lag time, and teat shape with the occurrence of bimodality.TP, triangular barrel and pointed teat end; SF, square barrel and flat teat end; SRF, square barrel, round teat end, flat in the area of the teat orifice; and SR, square barrel and round teat end.

Figure 3 .
Figure 3. Least squares means from general linear mixed models showing the association between teat shape and first 15 s milk flow rate (A), 15-30 s milk flow rate (B), 30-60 s milk flow rate (C), and 60-120 s milk flow rate (D).TP, triangular barrel and pointed teat end; SF, square barrel and flat teat end; SRF, square barrel, round teat end, flat in the area of the teat orifice; and SR, square barrel and round teat end.Levels marked with different letters (a-c) differ at a level of P < 0.05 in Tukey-Kramer's post hoc test.
Figure 4. Least squares means from general linear mixed models showing the association between teat shape and peak milk flow rate.TP, triangular barrel and pointed teat end; SF, square barrel and flat teat end; SRF, square barrel, round teat end, flat in the area of the teat orifice; and SR, square barrel and round teat end.Error bars represent 95% confidence intervals.Levels marked with different letters (a-b) differ at a level of P < 0.05 in Tukey-Kramer's post hoc test.
Wieland et al.: BIMODALITY AND TEAT SHAPE Wieland et al.: BIMODALITY AND TEAT SHAPE

Table 1 .
Wieland et al.: BIMODALITY AND TEAT SHAPE Descriptive statistics of milk yield and milk flow characteristics from 220,928 milking observations of 2,520 Holstein dairy cows stratified by teat shape.TP, triangular barrel and pointed teat end; SR, square barrel and round teat end; SRF, square barrel, round teat end, and flat in the area of the teat orifice; and SF, square barrel and flat teat end.The results are expressed as the mean values and standard deviation unless otherwise stated 2 30S: 15 to 30 s milk flow rate.360S: 30 to 60 s milk flow rate.