Predicting Maximal Heart Rate in Racehorses: Insights for Optimal Training
Maximal heart rate (HRmax) is a critical metric in equine athletic training, particularly in racehorses. It serves as a benchmark for designing training programs that can enhance performance while monitoring the horse's health. Understanding HRmax enables trainers to tailor exercise regimens to individual horses, ensuring they train within appropriate heart rate zones that enable optimal recovery and without overexertion or overtraining.
The Importance of Maximal Heart Rate in Racehorse Training
HRmax is the highest number of beats per minute a horse's heart can reach during maximal effort. It is important to note that HRmax is a highly individual parameter, and there is a wide range of values within the thoroughbred racehorse population. The average HRmax for thoroughbred racehorses is approximately 223 beats per minute, but values can range from as low as 205 beats per minute to as high as 245 beats per minute.
Knowing what the HRmax is for a horse pivotal for defining training intensities. Training in heart rate zones, which are percentages of HRmax, allows for precise control over the exercise intensity. It ensures that the horse is working at the right level to improve cardiovascular and muscular systems without risking injury from overtraining. Heart rate zones are typically divided into different levels, each corresponding to a specific percentage of HRmax. These zones range from light aerobic training, which enhances fat metabolism and stamina, to anaerobic and neuromuscular zones, which improve speed, power, and race-day performance.
Let's take two hypothetical horses. Horse 1 has a maxHR of 225 bpm, and Horse 2 has a maxHR of 210 bpm. Each training zone represents a percentage of their maxHR, with the zones being:
Light Aerobic: 60% of maxHR
Moderate Aerobic: 70% of maxHR
Threshold: 80% of maxHR
Anaerobic: 90% of maxHR
Max Effort: 100% of maxHR
For Horse 1, the heart rate ranges are higher across all zones due to the higher maxHR. This would suggest that the training intensities, defined by the heart rate, would be set higher for Horse 1 compared to Horse 2 for the same relative exercise intensity zones.
This visualization demonstrates how two horses with different physiological profiles might require different training regimens to achieve the same relative training effects.
Horse 1 - HRMax 225
Horse 2 - HRMax 210
As you can see from the above, Horse 2 with the lower HRMax reaches anerobic threshold at just 168bpm, while Horse 1 requires exercise to 180bpm to elicit that response. Back in 1970, Krzywanek et al first discussed the relationship between speed and maximal heart rates, but it was in 2003 that Mukai et al first really outlined the relationship between sub-maximal running speed and heart rates in races, suggesting a linear relationship was at hand.
Other subsequent studies also suggested a linear relationship between speed and heart rates but more recently a large study by Schurs et al using a total of 509 Thoroughbred racehorses in-training in either Australia or France, completing a total of 1,124 and 6,016 training sessions, found that peak heart rate increased with training speed/intensity, but not linearly as found in other studies. They found that as pace increased from soft (12.6s to the furlong) to hard (11.0s/furlong) gallop, the HRmax did not change significantly and the relationship between speed at HRMax was sigmoidal, that is, it increases slowly at first, then more rapidly, and then slows down again as it approaches the maximum heart rate and speed value.
Prediction of Maximal Heart rate on Sub-maximal speed.
I decided to take a look at similar data as Schurs et al, but with a lot less horses, taking heart rates at various speeds with the idea to see if it was able to predict what the maximal heart rate would be. The underlying idea being if you could predict what the MaxHR would be of a horse when it was capable of a submaximal speed, you could then tailor a program to fit the horse earlier in its preparation to race. To start I looked at the correlations between all the variables available.
The highest correlation between HRMax and other sub-maximal speeds was found (marginally) with average HR at speed >45 km/h. A speed of 45 km/h is roughly equivalent to 12.5 meters per second. In terms of race distances, a furlong would be covered in approximately 16 seconds at this speed. For Australians this speed approaches "evens", for Americans a "two minute lick" and for Europeans "a swinger". Training at and above this speed is significant for racehorses, as it starts to simulate race conditions, allowing horses to adapt to the stresses of racing.
Let's take a look at the data:
Investigating a Polynomial Relationship
Our data analysis aimed to predict HRmax based on various speeds during training, with a particular focus on the speed of 45 km/h. We hypothesized that the average heart rate at this speed might serve as a strong predictor of HRmax.
Finding a polynomial relationship between 'Average heart rate at speed > 45 km/h (bpm)' and 'Max Heart Rate reached during training (bpm)' involved fitting a polynomial regression model to the data. Polynomial regression is an extension of linear regression where we fit a polynomial equation on the data with a degree greater than one, which allows for a curvilinear relationship between the target and the features.
The process of finding the best polynomial degree typically involves fitting the model with different degrees and evaluating their performance. A common approach is to use cross-validation to estimate the model's performance and select the degree that results in the best cross-validation score. I fitted polynomial regression models of various degrees to these two variables and evaluated their performance and looked for the model that yields the best balance between fit and complexity, as indicated by the cross-validation score. Common metrics to evaluate the model's performance include R-squared (which measures how well the observed outcomes are replicated by the model) and the root mean squared error (RMSE).
The polynomial regression models of degrees 1 through 4 were fitted and evaluated. Here are their performances:
Degree 1 (Linear Model): RMSE = 4.15, R² = 0.74
Degree 2: RMSE = 3.55, R² = 0.81
Degree 3: RMSE = 3.02, R² = 0.86
Degree 4: RMSE = 2.99, R² = 0.86
As the degree of the polynomial increases, both the Root Mean Squared Error (RMSE) and the R-squared (R²) value improve. The RMSE decreases, indicating a better fit to the data, while the R² value, which indicates the proportion of variance in the dependent variable explained by the independent variables, increases.
From degree 3 onwards, the improvements in RMSE and R² are marginal. This suggests that a polynomial of degree 3 might be a good choice, as it provides a good balance between model complexity and performance. A higher degree polynomial could potentially overfit the data, especially with the limited number of data points that I have.
The following polynomial model that captures the complex relationship between the average heart rate at speeds greater than 45 km/h and HRmax. The 3rd-degree polynomial we discovered is:
Here, y represents the 'Max Heart Rate reached during training (bpm)', and x is the 'Average heart rate at speed > 45 km/h (bpm)'. By inputting the average heart rate at speeds above 45 km/h, one can estimate the HRmax which allows us to subsequently design training programs tailored to the horse's current fitness levels and racing goals.
There is a caveat though.
In order to enter the Heart rate when the horse is galloping at about 16-15 secs furlong, the horse must be fit enough to do this and recovery parameters (immediate, 5 and 15 min recovery) all have to be at below 50% of Max heart rate. This way the heart rate at ~45 km/h is close to what it would be when the horse is fit enough to perform a maximal heart rate test.