Athena Vale
In biomechanics, Hill's muscle model refers to the three-element model consisting of a contractile element (CE) in series with a lightly damped elastic spring element (SE) and in parallel with a lightly damped elastic parallel element (PE). The model was introduced in 1938 by the famous physiologist Archibald Vivian Hill, who had already won the Nobel Prize for Physiology by that time. The model is used to predict muscle performance under varying conditions and is frequently used in musculoskeletal simulations of movement. The three elements of the model are the contractile element, which shortens when activated, the series element, and the parallel element, which represents the passive force of connective tissues surrounding the contractile element. This model has also been applied to simulations of muscle mechanics and musculoskeletal simulations. Interestingly, Hill's equation, which describes the relationship between muscle force and shortening velocity, has been revived due to its connection to the kinetics of the myosin cross-bridge cycle.
| Characteristics | Values |
|---|---|
| Name | Muscle Hill |
| Date of Birth | February 15, 2006 |
| Birthplace | Chesapeake City, Maryland |
| Owner(s) | Jerry Silva, TLP Racing Stable, and Southwind Farm |
| Trainer | Greg Peck |
| Driver | Brian Sears |
| Lifetime Race Record | 21-20-1-0 |
| Notable Achievements | Undefeated in 12 starts as a three-year-old in 2009, including major victories in the Hambletonian, Canadian Trotting Classic, Breeders Crown, World Trotting Derby, Kentucky Futurity, and American-National |
| Awards | 2008 Dan Patch Two-Year-Old Trotting Colt of the Year |
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What You'll Learn
World champion trotter Muscle Hill
Muscle Hill is a world champion trotting stallion and one of the best of his generation. Bred by Winbak Farm, Muscle Hill was foaled on 15 February 2006 in Chesapeake City, Maryland. During his racing career, he was owned by Jerry Silva, TLP Racing Stable and Southwind Farm, trained by Greg Peck, and driven by Brian Sears.
Muscle Hill showed great promise as a two-year-old, winning the Peter Haughton Memorial and the 2008 Breeders Crown Two-Year-Old Colt Trot. He also set a world record of 1:53.3 for two-year-old trotting colts on a mile track. He finished his first season with earnings of $817,301, winning eight out of nine races, and was named the United States 2-Year-Old Colt Trotter of the Year.
In 2009, Muscle Hill won all of his races as a three-year-old, including major victories in the Hambletonian, Canadian Trotting Classic, Breeders Crown, World Trotting Derby, Kentucky Futurity, and American-National. His Hambletonian win was particularly notable, as he won in 1:50.1, tying the fastest time for a trotter of any age at The Meadowlands. This win also earned him a stakes record, with a large winning margin of six lengths. At the end of the 2009 season, Muscle Hill retired with career prize money of $3,273,342, having won 20 out of 21 races.
Muscle Hill's achievements in 2009 earned him several prestigious titles, including the United States Harness Horse of the Year, Dan Patch Trotter of the Year, and O'Brien Three-Year-Old Trotting Colt of the Year. He was also the first trotter to win Horse of the Year after an unbeaten season. In addition, his single-season earnings of $2,456,041 set a record for both trotters and pacers.
Muscle Hill has continued to cement his legacy by siring numerous successful offspring, including winners of over $15 million in prize money. He has produced top performers such as Trixton, Ramona Hill, and Mission Brief, who have followed in their sire's footsteps by winning coveted races like the Hambletonian and Breeders Crown.
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Hill's equation for muscle tension
Hill's equation, developed by Archibald Vivian Hill, is a fundamental concept in muscle mechanics that describes the relationship between muscle tension and velocity of contraction. The equation, introduced in 1938, is based on careful experiments involving tetanized muscle contractions where various muscle loads and associated velocities were measured.
The equation itself is written as (T+a)*v, where T represents muscle tension, v represents velocity, and a is a constant. This equation demonstrates that the relationship between muscle tension and velocity is hyperbolic in nature. In other words, as the load applied to a muscle increases, the contraction velocity decreases, and vice versa. This relationship is described by the equation F·v = Power, where F represents force and is directly related to tension.
The three-element Hill muscle model is a key component of Hill's equation and muscle mechanics. This model consists of a contractile element (CE) and two non-linear spring elements, one in series (SE) and another in parallel (PE). The active force of the contractile element is generated by the interaction of actin and myosin cross-bridges at the sarcomere level. The connective tissues surrounding the contractile element influence the muscle's force-length curve.
Hill's equation has been widely applied in the study of muscle performance and locomotion. It provides insights into the mechanical performance of muscles, with applications in both historical and contemporary contexts. The equation has been used to analyze isometric tension potentiation and redevelopment, revealing the impact of phosphorylation on muscle power and force-velocity properties. Additionally, Hill's equation serves as a tool for understanding animal locomotion and optimizing the design of muscle-powered devices, such as bicycles.
While Hill's equation has been highly regarded for its descriptive nature and applicability, it was initially considered purely empirical and lacking in physiological insight. However, advancements in the field, such as Huxley's 1957 model and Piazzesi et al.'s 2007 study, have provided molecular mechanistic insights that enhance our understanding of the equation's underlying principles.
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Hill-type muscle models
The default Hill-type model contains a contractile element that represents the forces acting between the myosin and actin myofilaments, combined with series and parallel elasticity. The contractile element is assigned the properties of homogeneous fibres, and its activation is simplified based on temporal features of myoelectric (EMG) activation recorded from the muscle. The three-element Hill muscle model is constituted by a contractile element (CE) and two non-linear spring elements, one in series (SE) and another in parallel (PE). The active force of the contractile element comes from the force generated by the actin and myosin cross-bridges at the sarcomere level. It is fully extensible when inactive but capable of shortening when activated.
The force-length (F-L) and force-velocity (F-V) properties of the muscle are based on data combined from studies of different muscles in different animal species. The force generated by a fibre is characterised as a function of its activation and its instantaneous length and velocity. The force-velocity relation for the contractile element is usually modelled by what is commonly called Hill's equation, which demonstrates that the relationship between F and v is hyperbolic. Therefore, the higher the load applied to the muscle, the lower the contraction velocity, and vice versa.
Over the last three decades, Hill-type muscle models have gained broad use for assessing muscle functions across different movements and analysing changes that occur with ageing, neuromuscular diseases, or rehabilitation from injury. However, there are few ways to validate a Hill-type model in vivo, and direct measurement of muscle force in humans remains a challenge.
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The three-element Hill muscle model
The three elements of this model are:
- The contractile element (CE): This represents the interactions between myofilaments and is responsible for generating the active force of the muscle. The active force in this element comes from the force generated by the actin and myosin cross-bridges at the sarcomere level. It is fully extensible when inactive but can shorten when activated.
- The series elastic element (SE): This represents the tendon and the intrinsic elasticity of the myofilaments. It is in series with the contractile element.
- The parallel elastic element (PE): This represents the connective tissues (fascia, epimysium, perimysium, and endomysium) and their passive force. The parallel element is responsible for the muscle's passive behaviour when stretched, even when the contractile element is inactive.
However, it is important to note that the Hill muscle model has some limitations. It does not accurately represent the realistic muscle architecture and internal sequential events. Additionally, it requires knowledge of various parameters, such as the length and speed of muscle fibre contraction, which can vary between individuals and lead to estimation errors.
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Hill's muscle model in biomechanics
In biomechanics, Hill's muscle model is a popular state equation that can be applied to skeletal muscle to demonstrate its tension-velocity relationship. The model was derived by the famous physiologist Archibald Vivian Hill, who introduced the model and equation by 1938, before going on to publish in this area until 1970. Hill had already won the Nobel Prize for Physiology by the time he introduced this model.
Hill's muscle model refers to the 3-element model consisting of a contractile element (CE) in series with a lightly damped elastic spring element (SE) and in parallel with a lightly damped elastic parallel element (PE). The active force of the contractile element comes from the force generated by the actin and myosin cross-bridges at the sarcomere level. It is fully extensible when inactive but capable of shortening when activated. The connective tissues (fascia, epimysium, perimysium and endomysium) that surround the contractile element influence the muscle's force-length curve. The parallel element represents the passive force of these connective tissues and has a soft tissue mechanical behaviour.
The three-element Hill muscle model is a representation of the muscle's mechanical response. The model is constituted by a contractile element and two non-linear spring elements, one in series and another in parallel. The net force-length characteristics of a muscle is a combination of the force-length characteristics of both active and passive elements. During isometric contractions, the series elastic component is under tension and therefore stretched by a finite amount. As the overall length of the muscle is kept constant, the stretching of the series element can only occur if there is an equal shortening of the contractile element.
Hill-type models are used to predict muscle performance under varying conditions, ranging from in situ production of isometric force to in vivo dynamics of muscle length change and force in response to activation. They are also used in musculoskeletal simulations of movement, particularly in studies of human motor performance. The models are computationally efficient and require relatively few parameters to operate, which has contributed to their broad use.
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Frequently asked questions
Hill's muscle model refers to the three-element model consisting of a contractile element (CE) in series with a lightly-damped elastic spring element (SE) and in parallel with a lightly-damped elastic parallel element (PE).
The model was introduced in 1938 by the famous physiologist Archibald Vivian (A.V.) Hill, who had already won a Nobel Prize for Physiology by that time.
Hill's equation is used to illustrate the relationship between muscle shortening velocity and load. It is still the predominant method used to characterise muscle performance, despite being regarded as lacking precision in predicting velocities at high and low loads.
Hill-type muscle models are frequently used in musculoskeletal simulations of movement, particularly in studies of human motor performance. They are also used to evaluate the comparative and evolutionary aspects of locomotor performance in different animal species.
