The equations of motion of the runner: is there a trade-off between mechanical efficiency and risk of injury when running?

The title of my blog reflects my initial goal: promoting discussion of issues related to running efficiency.  Perhaps the beginning of a new year is a good time to take stock of my current understanding of the topic.   An additional reason for a review at this time is the recent protracted debate between Robert and myself waged in the comment section of my page on the Dance with the Devil (see side panel).  This debate was fairly adversarial in character at times, and it prompted me to re-examine some of the issues related to the perennially thorny topic of gravitational torque.  Robert’s challenges led me to do some computations, which as a by-product revealed some findings regarding linear velocity during the gait cycle.  Because linear velocity is related to progress towards the finishing line, I think linear velocity is a more important aspect of running mechanics than the rotational motion arising from gravitational torque, which is largely about going around in circles (or preventing such motion).  So I am grateful to Robert for re-focussing my attention on running mechanics and running style.  Though first, it is important to put the issue of running style in a larger context.

Granted that races at distance ranging from 5000m to marathon are run at a paces either a little above or a little below the anaerobic threshold, the greatest determinant of efficiency is the ability to achieve a high pace at threshold so as to minimise the amount of fuel-inefficient anaerobic metabolism.    If the goal is efficiency, much of one’s training efforts should be directed at this raising the threshold pace.  Whether this goal is best achieved by emphasis on high volume or high intensity training (or both) remains a controversial topic, but that is not the question I will focus on in this post.   Instead, I will return to the less important but nonetheless intriguing question of running style.

Almost certainly, the most important issue in considering the effects of running style on efficiency is minimization of risk of injury.  Injury impairs not only performance at the time of injury but also leads to missed training and loss of aerobic fitness.  Unfortunately, the evidence suggests there might be a trade-off between mechanical efficiency and safety.  I think this can be illustrated most readily by examining solving the equations of motion of the running body (though if you are willing to accept my calculations, you do not need to do the maths yourself – I will illustrate the results pictorially).  The complete solutions of the equations describing a multiply-jointed body made of viscoelastic tissues (i.e. tissues in which change of shape depends on how rapidly the force is applied) is of course horrendously complex.  Nonetheless a great deal can be learned by focussing on the equations that describe the motion of the centre of gravity of the body (COG).  If we know the time course of the external forces acting on the body – namely gravity; ground reaction force (GRF); and wind resistance – it is possible to perform an accurate computation of the motion of the COG.

On the surface of the earth, the force of gravity is constant.  It is the product of mass multiplied by the acceleration due to gravity (g), which has the value 9.8 metres/second/second (or 32 feet/sec/sec in Imperial units).  Ground reaction force is the reaction of the ground to the push of the body against the ground.  We can measure the push of the body against the ground quite precisely using a force plate, and therefore, since action and reaction are equal and opposite, we can deduce the GRF. Estimation of wind resistance is trickier, and for the purpose of this post, I will assume that wind resistance is negligible.   I have presented the equations and a description of how I solved them, in the calculations page (see the sidebar).

Ground reaction forces

For simplicity I have assumed that the vertical component of ground reaction force (vGRF) varies sinusoidally while the runner is on stance, as shown in figure 1.   This is a moderately good approximation to real data for a forefoot runner, and is convenient from the computational point of view.   vGRF rises rapidly from zero after footfall, reaches a peak at mid-stance and then falls away to zero as the runner approaches take-off.  I do not think the main conclusions I will draw will be appreciably influenced by the exact shape of the time course of vGRF, though at the price a little more computation, I could solve the equations using real data for vGRF.

One crucial feature regarding vGRF is that the value of vGRF averaged over the entire gait cycle must equal the downward force of gravity (mg, where m is mass) since gravity acts constantly throughout the gait cycle.  Otherwise, there would be a net vertical impulse that would either cause the runner to continue to float upwards after the completion of the gait cycle if average vGRF exceeded mg, or alternatively to be pulled to the ground if average vGRF was less than mg.  One inevitable consequence is that when time on stance is short compared with the total period of the gait cycle, peak vGRF must be high (as is illustrated by the ochre dashed curve in figure 1) compared with the situation where time on stance is a large faction of the total duration of the gait cycle (as illustrated by the dashed blue line in figure 1).

Fig 1: vGRF (dashed line) and hGRF (solid line) for relatively long time on stance (blue) and short time on stance (ochre). Vertical lines denote footfall, mid- stance and take-off. (Force units are Newtons)

Once vGRF is known, the horizontal GRF (hGRF) can readily be computed assuming the total GRF acts along the line from point of support to the COG (as shown in equation 5 on the calculations page).  The hGRF associated with a sinusoidal  time course of vGRF is depicted by the solid ochre and blue lines in figure 1.   In early stance, vGRF is negative, indicating that it exerts a braking effect on the runner.   Early in the stance phase magnitude of hGRF increases as vGRF increases, but because hGRF is only appreciable when the line joining point of support to COG  is oblique, the magnitude of hGRF begins to decrease despite the continued rise in vGRF as the runner approaches mid-stance.  By mid-stance, the COG is directly above the point of support, total GRF is vertical and hGRF is zero.  After mid-stance, the line from COG to point of support is directed obliquely backwards, so hGRF is now directed forwards and has an accelerating effect on the runner that reveres the braking effect in early stance phase.   One feature of interest is that when the runner spends a long time on stance, the peak magnitude of hGRF is almost the same as when the runner spends only a short time on stance, despite the much greater peak vGRF when stance is short.  The reason is that when time on stance is short, the line from COG to point of support is never far from vertical so hGRF does not rise as high is it would if this line was more obliquely inclined.   The fact that the magnitude of peak hGRF is similar for both short and long times on stance means that the braking effect is actually much greater when time on stance is longer, because the braking force acts for a longer time.

Vertical and horizontal components of velocity

Figure 2 depicts the time course of the velocity of the body in both vertical and horizontal direction throughout the gait cycle, based on the solution of equations 1 and 2 shown on the calculation page.

Fig 2: Vertical velocity (dashed line) and change in horizontal velocity from airborne phase, V(a), due to braking and acceleration. Blue: long stance; Ochre: short stance. Running speed: 4 m/sec.

If we focus first of all on the vertical velocity in the case where time on stance is a large proportion of the total gait cycle (the dashed blue line), we see that starting from the high point at mid-flight, downwards velocity increases at a steady rate under the influence of the uniform accelerating effect of gravity.  After foot-fall, as vGRF rises, the rate of acceleration slows and once vGRF exceeds mg, the downwards acceleration ceases, though the body still continues to move downwards at a decreasing rate until mid-stance, by which time vertical velocity is zero.  After mid-stance, the body accelerates upwards under the influence of vGRF.  Once vGRF has fallen below mg, the acceleration diminishes, though the velocity remains upwards.  After the body becomes airborne, vGRF is zero and the upwards velocity continues to decrease at a constant rate as gravity retards the ascent.  By the middle of the airborne period (the end of the cycle in figure 2) the vertical velocity is zero.

In the case in which time on stance is short (the ochre dashed line in figure 2), the constant increase in downwards velocity during the airborne phase continues for a longer period than when time on stance is long (blue dashed line).  Consequently, when stance time is short, the downwards velocity is much greater at foot-fall.   As vGRF rises in the first half of the stance phase, the downwards velocity decreases reaching zero at mid-stance.  After mid-stance, the high vGRF causes a greater upwards acceleration than in the case where time on stance is longer, so that upward velocity at take off is higher.  The body rises to a greater height before its ascent is arrested by gravity in the middle of the airborne phase.  Using equation 3 to compute distances travelled, in the case where horizontal velocity at mid-stance is 4 m/sec, it can be shown that in the case when peak vGRF is 2mg, the total vertical distance travelled between mid-stance and airborne peak is 5.8 cm whereas it is 9.8 cm when peak vGRF is 4mg.

In contrast, in the case of horizontal velocity (solid lines in figure 2) the amount of slowing between footfall and mid-stance is appreciably greater when time on stance is longer, because, as we have seen, the braking force (hGRF) is of similar magnitude but acts for a longer period of time.

Implications for efficiency

What do these calculations tell us about mechanical efficiency?  It is important to note that a substantial proportion of the kinetic energy of the falling body is absorbed and stored as elastic energy during the first half of stance, and is recovered by elastic recoil after mid-stance.  The proportion that is recovered is likely to be higher when time on stance is short because tendons and muscle as viscoelastic, meaning that up to a certain point, they are more elastic when the force is applied over a shorter period of time.  In similar manner, some of the kinetic energy lost due to the braking effect of  hGRF in early stance can be stored as elastic energy and recovered after mid-stance.  Again, the proportion recovered is likely to be higher when time on stance is shorter.  However, irrespective of whether time on stance is short or long, only a proportion of the kinetic energy lost during the first half of stance can be recovered.  Thus, in general efficiency will be less when the total amount of work that must be done to reverse the braking effect and to elevate the body back to its peak height is large.  We have already seen that the braking effect is greater when time on stance is long, whereas the amount of upwards acceleration required to elevate the body to its peak height is greater when time on stance is shorter.  Which of these effects demands more energy?

Energy required

The amount of work done when a force is applied can be computed using equation 6.  The results are shown in table 1 for a running speed of 4 m/sec.

Table 1: the work done per step after mid-stance to reverse the braking effect by hGRF and to elevate the body from mid-stance to peak height in mid-flight. Less of the required energy is derived from elastic recoil at longer time on stance (i.e lower vGRFmax). Work per Km is 750 times greater.

At both short and long times on stance, the energy required to overcome braking is greater than the energy required to elevate the body from its low point at mid-stance to its high point in the airborne phase.  Thus, the sum of the amounts of energy required to overcome braking and to elevate the body is substantially greater when time on stance is longer.  Since the proportion of energy recovered by elastic recoil is likely to be less under these circumstances, it is clear that mechanical efficiency is less when time on stance is long.  It should be noted that these calculations refer to the work done to counteract the effects of external forces acting on the body.  Some additional work is also done repositioning the limbs, and at very high running speeds this can become appreciable, but is beyond the scope of this discussion.

Conclusions

The calculations confirm that mechanical efficiency is increased by shorter time on stance.  Although many coaches believe this, it is not universally accepted, so it is re-assuring to see that the equations provide a clear confirmation.  In practice a shorter time on stance can be achieved though stiffening the hip, knee and ankle joints by applying greater tension in the muscles that flex and extend these joints, especially the hamstrings and quads.  The BK method of running developed by Frans Bosch and Ronald Klomp focuses on decreasing time on stance via plyometric drills that develop the strength necessary to maintain adequate leg stiffness.   However, the equations also provide a clear warning regarding the increased ground reaction force.  As shown in figure 1, when time on stance is short, the peak vertical forces acting on the body are much larger, and the potential risk of injury is potentially greater.

It is noteworthy that in the late stages of a marathon, many runners automatically increase their time on stance.  This is probably due in part to the fact that as muscle strength diminishes it is harder to maintain the required tension in the hamstrings and quads, but also might be an unconscious defensive reaction to protect the body from injury at a stage where tired muscles are less able to withstand stress.

So far we have not addressed the issue of cadence.  For a given proportion of the gait cycle spent on stance, the magnitude of peak vGRF required to achieve a specified proportion of the gait cycle airborne is lower at high cadence because both airborne time and stance time decrease at higher cadence.  In my next post I will discuss cadence.  The interim conclusion is that there is a trade off between mechanical efficiency and risk of injury.  Efficiency can be increased by spending a shorter period of the gait cycle on stance, but the risk of injury is greater.  Therefore, a style which entails greater leg stiffness should be adopted cautiously, and requires careful conditioning of the muscles, tendons and joints to allow them to withstand the greater forces.

 

Note added 27^th  Feb 2112:

In the discussion below, Simon drew attention to the fact that by emphasising the trade off between increased efficiency and increased risk of injury that appears to arise in the circumstances described in this post, I do not acknowledge that for a recreational runner who habitually runs at a cadence in the vicinity of 160, it is possible to increase efficiency with no appreciable increase in injury risk simply by increasing cadence from 160 to 180 steps per minute.  I agree that such an increase in cadence will lead to a decrease in braking cost without the need to increase vGRF.  The potential benefits of increasing cadence from 180 to 200 are less clear-cut, and are discussed in my posts of Feb 6^th and Feb 27^th.

The athlete’s heart

The human heart is an enigma, and the athlete’s heart especially so. It is no accident that the heart is the body part that acts as the final defender keeping mortality at bay while serving as the icon for our aspirations and passions.  It is no accident because this mundane but crucial pump beats autonomously, but is also modulated by subtle, ethereal influences.  It is governed by the non-conscious autonomic nervous system – the exciting sympathetic division often dominating in the duel with the soothing parasympathetic division – and also by a multitude of hormones: adrenaline and the adrenal steroids; insulin and growth hormone; and also the sex steroids, oestrogen and testosterone, which might explain the greater vulnerability of the male runner’s heart – a topic we shall return to later.   Oxytocin, the hormone released in response to human touch that fosters not only the bond between a mother and her infant but also the bonds between lovers, can reduce the inflammatory processes that appear to contribute to the over-training syndrome, and even prevent cell death in an injured heart – at least in rats[1].

Perhaps to the non-runner, the enigma is why runners are so devoted to their sport.  It is of course relatively easy to comprehend the mind of the elite athlete striving for Olympic glory, but a surprising passion is found  across the entire spectrum for those whose ambition is to run 10 Km in an hour to those aiming to run a half-marathon in that time.  In the internet era, running has become a major social event.  On web-sites such as Fetch Everyone, hundreds of runners not only record hundreds of thousands of training miles, diverse races and numerous hard-won PB’s,  but also engage in a wide range of chatter, most of it mutually supportive but sometimes it is bitchy and at other times ribald.   The austere amateur spirit that permeated athletics when it was largely the preserve a small group of dedicated, almost monastic, individuals in the 1950’s has given way to something of a carnival.  Though of course the ribald graffiti occasionally uncovered on medieval monastic cell walls suggest that monasticism has always been only a thin veil over seething passion.

John Hadd

But to runners the enigma of the heart is more profound.   Sadly, this was illustrated by the recent death of John ‘Hadd’ Walsh.  He was the founder and a guiding spirit of the Malta marathon in the 26 years since its inception, but by virtue of his generous spirit, thoughtful analysis of heart physiology, and pugnacious writing, his influence extended far beyond the island of Malta and shaped the training programs of runners worldwide.    He was devoted to his wife, the marathon runner, Carol Galea.   He was 8 years her senior, and declared that he would train with a dedication sufficient to ensure that he lived to be 108, so they would not be separated prematurely.  Tragically, his promise was not fulfilled as he died, apparently of a totally unanticipated heart attack, during an early morning run at age 56 [2].  Though a personal tragedy, his death, along with the occasional reports of other untimely deaths of athletes and coaches, might merely be taken as confirmation of the widespread acceptance that running does indeed place an immediate stress upon the heart, but overall, the health benefits of running far outweigh the risks [3].

However the picture is a little more complex.   While at least some premature cardiac deaths among athletes are due to previously unidentified congenital defects, or to unsuspected coronary artery disease in those who take up running in middle age, the challenging question is: does endurance training actually produce persisting damage to the heart?

Two of the greats

The evidence is extensive and controversial, but before dipping into the vast body of scientific evidence, it is illuminating to look at the cases of two other athletes.  The first, Wally Hayward, a legendary figure in the history of the Comrades Marathon, did almost make it to his hundredth birthday.    Hayward first won that gruelling hilly 90 Km ultra-marathon between Durban to Pietermaritzburg  in 1930 at age 21; he was the winner again on four occasions in the 1950’s; and became the oldest person to complete the race when he staggered across the finishing line at age 80 in 1989.    He died in 2006 a few months before his 98^th birthday.   At age 70, at a stage when he had engaged in regular training for 52 years, he underwent extensive physiological testing [4]. A treadmill exercise test revealed no ischaemic ECG abnormalities and an excellent functional capacity (VO2max = 58.6 ml/kg/min).  His overall fitness was exceptional for a 70 year-old.  The only two abnormalities reported were frequent premature atrial contractions (PACs) and moderately increased thickness of the left ventricular wall.

The second case is that of Emil Zatopek, world record holder at 5000m and 10,000m in the 1950’s and winner of gold medals in the 5000 m, 10,000m and marathon in the Helsinki Olympics in 1952.   Unlike Wally Hayward, he retired from competitive running at age 35, after 17 years of training that had included a hitherto unheard of combination of intensity and volume.   He continued to be active in the Communist Party in his native Czechoslovakia, but due to his support for the democratic wing of the party during the Prague Spring in 1968, he was banished to work in a uranium mine.  At age 71, three years after his after his rehabilitation as a national hero by Vaclav Havel in 1990, he underwent extensive medical and physiological testing at the Institute of Sports Medicine in Prague [5].   Perhaps as a legacy of the privations of the uranium mine his muscles were flabby and he was a pale shadow of his former self, though it is noteworthy that his joints were remarkable free of the degenerative changes common in his age group.   Of particular interest in the current context, his heart showed some ischaemic changes and he had both atrial fibrillation and ectopic ventricular contractions.

Ventricular hypertrophy and PACs

General conclusions should not be drawn from anecdotes of exceptional athletes.  Nonetheless, the two abnormalities reported in Wally Hayward, hypertrophy of the muscular wall of the left ventricule and frequent premature atrial contractions are both well documented features of the elderly athlete’s heart.  For example, in a study comparing 11 elderly male athletes (mean age 73) with a life-long history of strenuous exercise with matched controls (mean age 74), Jensen-Urstad and colleagues [6] found that 9 of the 11 athletes had more than 100 premature atrial contractions in24 hours compared with 4 of the controls, while 8 of the athletes had multiform ventricular ectopics (indicating multiple maverick electrical sources in the ventricles) compared with 2 of the controls.

Of course ventricular hypertrophy in athletes is only to be expected.  It contributes to the powerful contraction of the well-trained heart.  Unlike the hypertrophy associated with pathological conditions in non-athletes, in which there is decreased blood supply to the heart muscle via myocardial capillaries,  the hypertrophy in athletes is usually accompanied by normal or increased capillary density [7].

Cardiac damage and remodelling

Nonetheless it is probable that the remodelling of cardiac muscle produced by endurance training involves some breakdown of muscle cells, similar to that which can readily be observed in skeletal muscle following intense training.  For example, following demanding endurance events, increased levels of the cardiac enzyme troponin are found in the blood stream, implying damage to heart muscle cells.  Immediately after the 2004 Otztal Radmarathon, troponin levels in the cyclists’ blood were increased 10 fold relative to baseline, and returned to baseline one week later [8].

In skeletal muscle, the muscle cells damaged by training are rebuilt stronger than before.  The persistence of collagen fibres that formed a scaffold during repair is of little importance provided the fibres become well aligned along the direction of pull of the muscle.  On the other hand, heart muscle is different.  Cardiac muscle performs not only physical work of contraction, but the muscle cells themselves from part of the conducting system that initiates and transmits the electrical signal that triggers contraction.   If the heart is to pump efficiently, this electrical signal must be transmitted across the myocardium from the sinoatrial node in the right atrium via the atrioventriclar node to the ventricles, in a well coordinated manner.  It is plausible that misplaced collagen fibres might upset the orderly transmission of the signal and perhaps even cause maverick muscle cells to take over the pace-maker role, generating ectopic beats.  As reported by Jensen-Urstad [6], premature atrial beats and also multiple maverick ventricular sources are substantially more frequent in elderly athletes than in age-matched non-athletes.

Atrial fibrillation

Premature atrial contractions are of little functional importance, but the crucial issue is whether they can lead to the chaotic ill-coordinated contraction that is atrial fibrillation.  In a large population-based study of men and women aged 55-75 in Denmark, Binici and colleagues found that a frequency of premature ectopic atrial contractions greater than 30 /hour, or runs of more than 20 consecutive atrial ectopic beats, was associated with an almost three fold increased risk of hospital admission for atrial fibrillation in the follow-up period of approximately 6 years [9].  There is also worrying evidence of a similar risk in endurance athletes.    The anecdotal account of Emil Zatopek’s atrial fibrillation is consistent with the findings of several large, well designed scientific studies.  For example in an 11 year follow-up study of 252 marathon runners, with mean age 39 at recruitment, the risk of symptomatic atrial fibrillation, based on an observed annual onset rate of 0.48 per 100,  was 8.8 times greater than in a comparison sample of 305 sedentary men, after adjusting or other risk factors such as high blood pressure [10].

Although far less serious than ventricular fibrillation (which is usually lethal) atrial fibrillation has some life-threatening consequences.  It predisposes to the formation of blood clots in the atrium which can subsequently be released into the blood stream, causing a myocardial infarction if they lodge in the coronary arêtes or a stroke if they lodge in the brain.   However, despite the quite compelling evidence for an increased incidence of atrial fibrillation in middle-aged and elderly runners, the balance of evidence does not indicate that the commonly observed heart rhythm abnormalities lead to an increase rate of serious adverse cardiovascular events in middle-aged athletes.   For example, in a 5 year follow-up of 117 middle-aged and elderly cross-country skiers, Lie and Erikssen [11] found that while persisting abnormalities of heart rhythm and also ventricular hypertrophy were common, only 2 developed angina and none suffered a myocardial infarction.  They concluded that the ECG abnormalities were mainly related to physiological adaptation to training and that training seems to protect against coronary heart disease.

Coronary obstruction

So far, we have focussed mainly on possible disturbances of heart rhythm.  In contrast, we have noted that capillary blood supply to the myocardium is often enhanced in athletes, and coronary disease might in fact be reduced.   However, perhaps the most disconcerting study of all is a recently reported investigation of calcified plaques furring-up the coronary blood vessels of elderly men who have participated in multiple marathons.  Schwartz and colleagues found that the prevalence of calcified plaques in the coronary arteries of men who had run in the Twin Cities Marathon annually for at least 25 years was almost twice as high as in age matched sedentary comparison subjects [12].  Enigmatically, the same research group carried out a similar study in female marathoners, with the opposite result: namely, the female runners had far fewer calcified plaques than the matched comparison subjects, though it is noteworthy that the female runners had run at least one marathon annually for only a period of 10 years.   The results of both of these studies should be treated with extreme caution until they have been replicated.  Despite the evidence that the male heart is generally more vulnerable to injury than the female heart, the diametrically opposite findings in the two sexes raise doubt about the generalizability of the findings.  Furthermore, it should be noted that the finding in males might reflect the consequences of running a larger number of marathons.

At least for the time being, the majority of the evidence suggests that despite the fairly high likelihood that long term endurance training will lead to an increased number of premature atrial contractions, the overall effect of endurance training is to increase life expectancy.    In future posts I will examine the evidence in greater detail, and also describe my discoveries about my own heart rhythm since acquiring a heart rate monitor that records the time intervals between consecutive beats.   More formal investigations have demonstrated that my heart is functioning well.  Nonetheless, in light of the growing evidence that elderly endurance athletes face a significant risk of atrial fibrillation, my current opinion is that monitoring heart rate beat by beat is indeed a sensible way of screening for possible increases in frequency of premature atrial contraction.  It would of course be foolish to make any definitive diagnosis based on one’s own observations using equipment that is demonstrably fallible.  It would be similarly foolish to curtail an activity that I enjoy passionately, when even the risk of atrial fibrillation is less daunting than the risk of a sedentary life style.

References

[1] Jankowski M, Bissonauth V, Gao L, Gangal M, Wang D, Danalache B, Wang Y, Stoyanova E, Cloutier G, Blaise G, Gutkowska J. 2010 Anti-inflammatory effect of oxytocin in rat myocardial infarction. Basic Res Cardiol. 105(2):205-18.

[2] Times of Malta, Saturday, September 17, 2011. Malta marathon founder dies  [http://www.timesofmalta.com/articles/view/20110917/athletics/malta-marathon-founder-dies.385085]

[3] Thompson PD, et al. (2007) Exercise and acute cardiovascular events placing the risks into perspective: a scientific statement from the American Heart Association Council on Nutrition, Physical Activity, and Metabolism and the Council on Clinical Cardiology. Circulation. 115(17):2358-68.

[4] Maud PJ, Pollock ML, Foster C, Anholm JD, Guten G, Al-Nouri M, Hellman C, Schmidt DH. (1981) Fifty years of training and competition in the marathon: Wally Hayward, age 70–a physiological profile. S Afr Med J. 31;59(5):153-7.

[5] Novotný V, Brandejský P, BaráckováM, Boudová L, Vilikus Z, Streda A, Novotný A.(1994) Medical and anthropological study of a world and Olympic champion, long-distance runner, 35 years after the end his racing career. Sbornik Lekarsky (Journal of Czech Physicians and the Czech Medical Society) 95(2):139-55.

[6] K Jensen-Urstad,F Bouvier,B Saltin,M Jensen-Urstad (1998) High prevalence of arrhythmias in elderly male athletes with a lifelong history of regular strenuous exercise.Heart 79:161–164

[7] Hudlicka O, Brown M, Egginton S. (1992) Angiogenesis in skeletal and cardiac muscle.  Physiol Rev. 72(2):369-417.

[8] Neumayr G, Pfister R, Mitterbauer G, Eibl G, Hoertnagl H. (2005) Effect of competitive marathon cycling on plasma N-terminal pro-brain natriuretic peptide and cardiac troponin T in healthy recreational cyclists. Am J Cardiol.;96(5):732-5.

[9]  Binici Z, Intzilakis T, Nielsen OW, Køber L, Sajadieh A. (2010) Excessive supraventricular ectopic activity and increased risk of atrial fibrillation and stroke. Circulation. 121(17):1904-11.

[10] Molina L, Mont L, Marrugat J, Berruezo A, Brugada J, Bruguera J, Rebato C, Elosua R. (2008)  Long-term endurance sport practice increases the incidence of lone atrial fibrillation in men: a follow-up study. Europace. 10(5):618-23.

[11] Lie H, Erikssen J. (1984)  Five-year follow-up of ECG aberrations, latent coronary heart disease and cardiopulmonary fitness in various age groups of Norwegian cross-country skiers. Acta Med Scand. 216(4):377-83.

[12] Schwartz JG, Merkel-Kraus S, Duval S, Harri K, Peichel G, Lesser JR, Knickelbine T, Flygenring B, Longe TR, Pastorius C, Roberts WR, Oesterle SC, Schwartz RS (2010) Does long term endurance running enhance or inhibit coronary artery plaque formation? A prospective multidetector CFA study of men completing marathons for least 25 consecutive years.  J. Am. Coll. Cardiol. 55;A173.E1624