Londeree and Moeschberger (1982) conducted a meta-analysis and established with the use of multivariate analysis that age accounts for 70–75% of the HRmax variance, the other factors being sex, level of fitness, type of ergometer used, continent of residence and race. (2010) the rate of decline is significantly different in various age groups, lower in the younger population, and higher in the older population, actually being curvilinear. This is partly due to the fact that the rate of decline of HRmax is non-linear, as demonstrated by Zhu et al. The HRmax is difficult to predict exactly ( Robergs and Landwehr, 2002). One of the more recent formulae is that published by Nes et al. There are also less frequently used equations, including Inbar’s formula ( Inbar et al., 1994), or the Londeree and Moeschberger formula ( Londeree and Moeschberger, 1982). The Tanaka equation is currently quite often applied, alone or with the Fox equation ( Nikolaidis et al., 2018). (2001) described a new formula (208–0.7 ∗age) in 2002, calculated from a meta-analysis of 351 studies involving 18,712 subjects, which was then validated on a group of over 500 subjects. The downside to its simplicity is the high standard error of estimate (SEE) of ∼7–12 beats per minute (bpm) ( Robergs and Landwehr, 2002). The most simple and widely used is the 220-age formula, the origin of which is unclear, but first appeared in scientific writing in a review by Fox and Haskell (1970). Since determining an individual’s actual HRmax (with the use of a maximal exercise test) is difficult and not always possible or advisable, it is usually estimated with the use of several formulae ( Robergs and Landwehr, 2002). All of these differences make accurate comparison of the results of different studies on maximum exertion parameters difficult ( Beltz et al., 2016). These tests may use a stepwise increase in speed/Watts, or a ramped increase and they may also vary in length. Several test protocols exist which are commonly used, depending on the clinic’s experience, or the type of patient (e.g., sportspeople or patients with cardiovascular disease). HRmax is measured in a graded exercise test, often along with other parameters like maximum oxygen uptake (VO 2max) or respiratory exchange ratio (RER), usually with a treadmill or cycle ergometry, until maximum exertion is achieved ( Pescatello et al., 2006 Beltz et al., 2016). HRmax is useful to prescribe exertion levels in sports training, or to carry out electrocardiogram (ECG) or ECHO exercise stress tests ( Robergs and Landwehr, 2002). HR increases in a linear way with increasing physical exertion, until a maximum (HRmax) is reached by the individual at maximal workload ( Kostis et al., 1982). Heart rate (HR) is a commonly measured parameter, often used in clinical practice, sports and scientific research it is easy to reliably measure with very little equipment ( Robergs and Landwehr, 2002). In conclusion, adding the studied variables in multiple regression models improves the accuracy of prediction only slightly over age alone and is unlikely to be useful in clinical practice. Tanaka’s formula offers the second best overall prediction, while the 220-age formula yields remarkably high mean errors of up to 9 bpm. The 202.5–0.53 ∗age formula developed in the present study was the best in the studied population, yielding lowest mean errors in most groups, suggesting it could be used in more active individuals. Previously published formulae were less precise in the more outlying groups of the studied population, overestimating HRmax in older age groups and underestimating in younger. Multiple linear regression, stepwise and LASSO yielded an R 2 of 0.224, while Ridge yielded R 2 0.20. The weak relationship may be explained by the similar age with small standard deviation (SD). HRmax was univariately explained by a 202.5–0.53 ∗age formula ( R 2 = 19.18). Mean HRmax predictions calculated with 5 previously published formulae were evaluated in subgroups created according to all variables. Linear, multiple linear, stepwise, Ridge and LASSO regression modeling were applied to establish the relationship between HRmax, age, fitness level, VO 2max, body mass, age, testing modality and body mass index (BMI). Cardiopulmonary exercise tests (CPET) were carried out on treadmills or cycle ergometers to evaluate HRmax and VO 2max. The present study was carried out on 3374 healthy Caucasian, Polish men and women, clients of a sports clinic, mostly sportspeople, with a mean age of 36.57 years, body mass 74.54 kg, maximum oxygen uptake (VO 2max, ml ∗kg –1 ∗min –1) 50.07. Maximal heart rate (HRmax) is associated mostly with age, but age alone explains the variance in HRmax to a limited degree and may not be adequate to predict HRmax in certain groups.
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