Submitted:
24 July 2025
Posted:
28 July 2025
You are already at the latest version
Abstract
Keywords:
1. Introduction
2. Materials and Methods
2.1. Data Collection, Selection and Preprocessing
2.2. Detection of Quarter-Level Milk Yield Perturbations Caused by CM
2.3. Percentage Recovery
2.4. Recovery Patterns Between Inflamed and Uninflamed Quarters
2.5. Associations Between Quarter-Level Milk Yield Recovery and Milk Loss, Somatic Cell Count, Clinical Signs, and Pathogens
3. Results
3.1. Description of the Clinical Mastitis Cases
3.2. Percentage Recovery
3.3. Recovery Between Inflamed and Uninflamed Quarters
3.4. Recovery Between Adjacent Time Intervals in Inflamed and Uninflamed Quarters
3.5. Associations Between Quarter-Level Milk Yield Recovery And Milk Loss, Somatic Cell Count, Clinical Signs, and Pathogens
3.5.1. Correlation Analysis
3.5.2. Regression Analysis
4. Discussion
4.1. Description of Clinical Mastitis Cases
4.2. Quantification of the Recovery Via Quarter-Level Milk Yield Perturbations
4.3. Percentage Recovery
4.4. Associations Between Quarter-Level Milk Yield Recovery and Milk Loss, Somatic Cell Count, Clinical Signs, and Pathogens
4.5. Application Potential and Future Work
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
| AMS | Automatic milking systems |
| APR | Average percentage recovery |
| CM | Clinical mastitis |
| dqMY | Daily quarter-level milk yield |
| dqML | Daily quarter-level milk loss |
| IQR | Interquartile ranges |
| MML | Maximum milk loss |
| MSCCD | Maximum somatic cell count deviation |
| qMRML | Quarter-level maximum relative milk loss |
| qMY | Quarter-level milk yield |
| qMYP | Quarter-level milk yield perturbation |
| SCC | Somatic cell count |
| SPR | Slope of percentage recovery |
| ULC | Unperturbed lactation curve |
| VIF | Variance inflation factors |
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| Quarter-level maximum relative milk loss | Maximum somatic cell count deviation (Mean ± Std) | Number of cases (percentage) | ||||
| Inflamed (Mean ± Std) | Uninflamed (Mean ± Std) | |||||
| Clinical severity | ||||||
| Mild | 0.50 ± 0.25 | 0.24 ± 0.20 | 3.30 ± 0.97 | 48 (41%) | ||
| Moderate | 0.67 ± 0.27 | 0.36 ± 0.22 | 3.92 ± 0.64 | 36 (31%) | ||
| Severe | 0.81 ± 0.21 | 0.59 ± 0.28 | 3.88 ± 1.13 | 33 (28%) | ||
| Causative pathogens | ||||||
| Culture negative | 0.54 ± 0.24 | 0.29 ± 0.22 | 3.9 ± 1.20 | 29 (25%) | ||
| Minor pathogens | 0.46 ± 0.22 | 0.20 ± 0.12 | 3.25 ± 0.86 | 17 (15%) | ||
| Major pathogens | 0.73 ± 0.27 | 0.46 ± 0.28 | 3.86 ± 0.84 | 71 (61%) | ||
| Total | 0.64 ± 0.28 | 0.38 ± 0.27 | 3.65 ± 0.97 | 117 (100%) | ||
| Quarter-level milk yield perturbations Numbers (percentage) |
||
| Inflamed | Uninflamed | |
| Recovered within day 1 - 3 | 10 (9%) | 64 (21%) |
| Recovered within day 4 - 7 | 13 (11%) | 50 (17%) |
| Recovered within week 2 | 13 (11%) | 36 (12%) |
| Recovered within week 3 | 10 (9%) | 27 (9%) |
| Recovered within week 4 | 9 (8%) | 26 (9%) |
| Not recovered | 62 (53%) | 96 (32%) |
| Total | 117 (100%) | 299 (100%) |
| Number of cases | Time interval | Average percentage recovery | Slope of percentage recovery | |||||||
| Inflamed | Uninflamed | Median ± IQR1 | P value | Median ± IQR1 | P value | |||||
| Inflamed | Uninflamed | Inflamed | Uninflamed | |||||||
| Quickly recovered | 36 | 150 | Days 1-3 | 0.46±0.19 | 0.47±0.22 | 0.65 | 0.1691 ± 0.0921 | 0.1700 ± 0.0766 | 0.32 | |
| Days 4-7 | 0.73±0.20 | 0.77±0.20 | 0.84 | 0.0314 ± 0.0752 | 0.0232 ± 0.0581 | 0.32 | ||||
| Week 2 | 0.91±0.07 | 0.84±0.13 | 0.06 | 0.0277 ± 0.0250 | 0.0313 ± 0.0584 | 0.16 | ||||
| Slowly recovered | 19 | 53 | Days 1-3 | 0.32±0.16 | 0.34±0.19 | 0.84 | 0.1233 ± 0.0607 | 0.1279 ± 0.0516 | 0.574 | |
| Days 4-7 | 0.60±0.16 | 0.66±0.26 | 0.36 | 0.0366 ± 0.0554 | 0.0298 ± 0.0369 | 0.51 | ||||
| Week 2 | 0.76±0.16 | 0.80±0.18 | 0.51 | 0.0142 ± 0.0227 | 0.0187 ± 0.0351 | 0.41 | ||||
| Week 3 | 0.85±0.15 | 0.88±0.14 | 1 | 0.0177 ± 0.0249 | 0.0068 ± 0.0220 | 0.02 | ||||
| Week 4 | 0.89±0.16 | 0.95±0.07 | 0.14 | 0.0092 ± 0.0140 | 0.0079 ± 0.0133 | 0.43 | ||||
| Non-recovered | 62 | 96 | Days 1-3 | 0.09±0.20 | 0.25±0.16 | <0.001 | 0.0377 ± 0.0899 | 0.0928 ± 0.0697 | <0.001 | |
| Days 4-7 | 0.25±0.50 | 0.52±0.29 | <0.001 | 0.0160 ± 0.0248 | 0.0271 ± 0.0540 | 0.11 | ||||
| Week 2 | 0.40±0.54 | 0.65±0.26 | <0.001 | 0.0087 ± 0.0150 | 0.0094 ± 0.0384 | 0.96 | ||||
| Week 3 | 0.46±0.51 | 0.70±0.27 | <0.001 | 0.0051 ± 0.0079 | 0.0080 ± 0.0254 | 0.14 | ||||
| Week 4 | 0.52±0.55 | 0.73±0.31 | <0.001 | 0.0033 ± 0.0089 | 0.0020 ± 0.0159 | 0.54 | ||||
| Total | 117 | 299 | Days 1-3 | 0.24±0.35 | 0.36±0.25 | <0.001 | 0.0902 ± 0.1276 | 0.1381 ± 0.0959 | <0.001 | |
| Days 4-7 | 0.50±0.50 | 0.66±0.31 | <0.001 | 0.0210 ± 0.0352 | 0.0279 ± 0.0512 | 0.46 | ||||
| Week 2 | 0.62±0.51 | 0.74±0.25 | <0.001 | 0.0094 ± 0.0188 | 0.0174 ± 0.0351 | 0.22 | ||||
| Week 3 | 0.63±0.56 | 0.78±0.26 | <0.001 | 0.0069 ± 0.0118 | 0.0079 ± 0.0217 | 0.67 | ||||
| Week 4 | 0.55±0.57 | 0.78±0.33 | <0.001 | 0.0038 ± 0.0086 | 0.0031 ± 0.0148 | 0.64 | ||||
| IQR1: Interquartile range, representing the difference between the 75% and 25% quantile. | ||||||||||
| Model parameters | VIF1 | Days 1-3 | Days 4-7 | Week 2 | Week 3 | Week 4 | |||||||||||
| Inflamed | Uninflamed | Inflamed | Uninflamed | Inflamed | Uninflamed | Inflamed | Uninflamed | Inflamed | Uninflamed | ||||||||
| qMRMLi2 | 1.97 | -0.07*** | 0.01 | -0.10*** | 0.02 | -0.13** | 0.02 | -0.11* | 0.03 | -0.09 | 0.04 | ||||||
| qMRMLu3 | 2.1 | -0.06** | -0.09*** | -0.08** | -0.09*** | -0.11** | -0.04** | -0.09* | 0 | -0.07 | 0.02 | ||||||
| MSCCD4 | 1.15 | 0.03* | 0 | 0.05* | 0 | 0.08** | 0.02 | 0.07* | 0.02 | 0.04 | -0.03 | ||||||
| Clinical severity | 1.45 | ||||||||||||||||
| Mild | |||||||||||||||||
| Moderate | -0.09* | 0.02 | -0.13* | 0.07 | -0.01 | 0.06 | -0.08 | 0.06* | -0.08 | 0.15*** | |||||||
| Severe | -0.03 | 0.02 | -0.01 | 0.07 | 0.12 | 0.12*** | 0.15 | 0.15*** | 0.08 | 0.22*** | |||||||
| Pathogens | 1.17 | ||||||||||||||||
| Culture-negative | |||||||||||||||||
| Minor pathogens | 0.07 | -0.05 | -0.03 | -0.12* | -0.07 | -0.13** | -0.13 | -0.17*** | -0.09 | -0.07 | |||||||
| Major pathogens | -0.04 | -0.07** | -0.13* | -0.07* | -0.13* | 0.06 | -0.21** | -0.04 | -0.24** | -0.07 | |||||||
| Intercept | 21.51 | 0.32*** | 0.41*** | 0.60*** | 0.65*** | 0.64*** | 0.62*** | 0.72*** | 0.71*** | 0.75*** | 0.69*** | ||||||
| R2 | 50.52% | 30.14% | 52.93% | 13.44% | 48.01% | 23.69% | 43.07% | 46.62% | 44.28% | 45.38% | |||||||
| “*”, “**”, “***” represent P-value of the estimated coefficient is < 0.05, < 0.01 and < 0.001 respectively, implying a meaningful association between the fixed effect and APR in different time intervals. VIF1: variance inflation factor (VIF) qMRMLi2: quarter-level maximum relative milk loss for inflamed quarters qMRMLu3: quarter-level maximum relative milk loss for uninflamed quarters MSCCD4: maximum somatic cell counts deviation | |||||||||||||||||
| Model parameters | VIF1 | Days 1-3 | Days 4-7 | Week 2 | Week 3 | Week 4 | |||||||||
| Inflamed | Uninflamed | Inflamed | Uninflamed | Inflamed | Uninflamed | Inflamed | Uninflamed | Inflamed | Uninflamed | ||||||
| qMRMLi2 | 1.97 | -0.0182* | 0.0067 | -0.0143** | -0.007 | 0.0042 | -0.0028 | -0.0017 | -0.0098*** | -0.0007 | -0.0001 | ||||
| qMRMLu3 | 2.1 | -0.0223** | -0.0332*** | 0.0022 | 0.0012 | -0.002 | 0.0060* | 0.0008 | 0.0069* | -0.0001 | 0.0008 | ||||
| MSCCD4 | 1.15 | 0.0122* | -0.0016 | -0.0072* | 0.0044 | 0.002 | -0.0016 | -0.0027 | -0.002 | -0.0037* | -0.0012 | ||||
| Clinical severity | 1.45 | ||||||||||||||
| Mild | |||||||||||||||
| Moderate | -0.0434*** | 0.0101 | 0.0212* | 0.0081 | 0.002 | 0.0022 | 0.0073 | 0.0182*** | 0.0012 | -0.0011 | |||||
| Severe | -0.0143 | 0.0107 | 0.0290** | 0.0122 | 0.0039 | 0.0125* | 0.0036 | 0.0147* | 0.0038 | 0.0028 | |||||
| Pathogens | 1.17 | ||||||||||||||
| Culture-negative | |||||||||||||||
| Minor pathogens | 0.0096 | -0.0193 | -0.0075 | 0.0226* | 0.0022 | 0.0141 | -0.0083 | -0.0116 | 0.0134 | 0.0136* | |||||
| Major pathogens | -0.0273* | -0.0118 | 0.0066 | 0.0132 | -0.0076 | 0.0094 | -0.0089* | -0.0063 | 0.0017 | 0.003 | |||||
| Intercept | 21.51 | 0.1295*** | 0.1396*** | 0.008 | 0.0093 | 0.0142*** | 0.0001 | 0.0103* | 0.0006 | 0.0014 | -0.0003 | ||||
| R2 | 51.46% | 22.47% | 16.48% | 7.71% | 9.19% | 10.69% | 15.25% | 19.27% | 15.82% | 6.75% | |||||
| “*”, “**”, “***” represent P-value of the estimated coefficient is < 0.05, < 0.01 and < 0.001 respectively, implying a meaningful association between the fixed effect and APR in different time intervals. VIF1: variance inflation factor qMRMLi2: quarter-level maximum relative milk loss for inflamed quarters qMRMLu3: quarter-level maximum relative milk loss for uninflamed quarters MSCCD4: maximum somatic cell counts deviation | |||||||||||||||
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