TEXT FOR ENGINEERS, ORTHOPEDIC SURGEONS, EPIDEMIOLOGISTS AND PHYSIOLOGISTS:
The release decision of a ski-binding is based on the structural capacity of individual tibia physiology — plus a margin — as indirectly prescribed by the international alpine ski-binding standards, ISO 9462 and ISO 8061. Howell SkiBindings also provide a unique 3rd-mode of non-pre-releasing lateral heel release that favorably-exceeds these minimum international standards — plausibly providing ACL-friendly and MCL-friendly skiing, too (see Part 2, below).
Ski-bindings are force-imparting and force-sensing mechanisms that — when combined together with the length of the boot sole — react to (a) torsional-torque about the long-axis of the tibia through the use of a non-pre-releasing toe-piece; (b) forward bending-moments about the long-axis of the tibia through the use of a non-pre-releasing heel-unit (see footnote-1 for the engineering-definition of 'moment'); (c) strain across the ACL and the MCL through the use of an open-art, non-pre-releasing lateral heel release mechanism that is uniquely built into the heel-unit of Howell SkiBindings (see Part 2, below).
For important information about the retention-function of ski-bindings, see the other sub-tab — 'Retention' (retention is the 1st functional requirement of a ski-binding).
Part 1 — Tibia-Friendly Release
Technical definition, tibia-friendly release
Ski-bindings limit their holding-force — in conjunction with the position of the fulcrum-points that are stationed between the boot and the ski — by converting potential injury-producing loads (footnote 2) that are applied to the tibia into a release-response.
When engineering a building-structure it's essential to know the strength of concrete, steel, wood and the strength of the other construction materials that form the structure. The same principle applies to ski-bindings: first, we must know the strength of the tibia to mitigate injury to the tibia.
Strength of average male tibia
The 'average' adult male tibia fractures at ~11.3 daNm during slow-torsion and ~25 daNm during slow forward-bending. These average values apply to male skiers who weigh ~170-pounds and who are aged between 20 and 53 years. The full range of tibia fracture-limits in torsion, bending, and combined torsion-bending — as a function of weight, age and gender — are documented in the biomechanical data of Ernst Asang of Munich, Germany [footnotes 3]. For practical use with ski-bindings, Asang's tibia-fracture data is reorganized, biomechanically [footnote 4]. This essay discusses some of Asang's reorganized tibia-fracture data.
Weakest section of the tibia
The tibia is weakest in bending where skiing stresses are also the largest — near the top of the boot. In torsion, the top two-thirds of the tibia are the most vulnerable sections.
No protection of the tibia by muscle activity
Muscle activity cannot add strength to the tibia because skiing injury-loads can occur faster than 'fast-twitch' muscles can be turned-on. There is no experimental, epidemiological or observational scientific proof that muscle activity can subtract appreciable strength from the tibia. The failure criteria of the tibia must therefore be based on the most conservative condition — the unprotected tibia.
The role of the ski-boot
The desire for complete "tibia safety in skiing" is impossible since, for example, during some injury-producing events, the boot can be partially constrained by snow — causing an injury-producing load to not flow through the binding. Boot-fit and boot-buckling contribute significantly to the transfer of loads between the ski and the tibia: a binding cannot read or react to loads that are not transmitted to a binding as a consequence of a ‘weak-link’ between the foot / leg / ski-boot. If a boot is buckled too loosely — an injury-producing-load cannot be fully-transferred to the binding. Boots must be buckled snugly.
Factors effecting tibia strength
• Tibia diameter / skier weight — The diameter of a cylinder effects its strength in torsion. In the case of bending loads, strength is effected by the ratio of the diameter to the length. In practice, large variation in the clinical-measurement of tibia-diameters is an uncontrollable problem, even when the measurement is performed by orthopedic surgeons [footnote 5]. Therefore, the measurement of tibia diameter is impractical for selecting ski-binding settings. However, (1) tibia diameter correlates to skier weight — if the skier is not over-weight. A correction for an over-weight condition is determined by the ratio of the skier's height-to-weight. Over-weight corrections — based on height — are found within all of the ski-binding release adjustment charts that are supplied by all of the binding manufacturers. Corrected skier-weight is a practical predictor of tibia strength. Further, however, (2) the application of x-ray-derived tibia anthropometrics for research — such as tibia diameter metrics that relate to the strength characteristics of the tibia — is essential to define ski-binding function at the binding-manufacturer level.
• Age related tibia strength — Children and adolescents under 19-years have soft-weak bones. Females over 40 have the possibility of reduced bone strength. Males over 53 have the possibility of brittle-weak bones. See graph, below. Reasonable exercise and diet (see text, below) can mitigate a large reduction in tibia strength.
• Velocity of loading — Bones are stronger during 'fast' (dynamic) loading compared with slow (quasi-static) loading. The velocity-effect on bone-strength is called 'visco-elasticity'. There can be as much as an ~18% difference in tibia-strength between slow and fast loading. Ski-bindings must function to accommodate the worst-case scenario — slow loading — even though the issues of friction that are found in nearly all mechanical systems become compounded during slow-moving mechanical operations. See graph, below.
• Combined-loading — Bones are weaker during combined torsion-bending loading when compared with pure-torsional loading. See graph, below.
• Cyclical stress / exercise — As described by Wolfe's Law, bones can become stronger when exposed to repeated cyclical loading. Racers who ski extensively on hardpacked snow and ice can develop stronger tibia's. Astronauts — in the absence of gravitational loading — experience weakened bones.
• Diet — A calcium-rich diet together with vitamin D can mitigate a reduction in bone strength. Excessive phytates (non-soaked beans), meat, salt, oxalates (such as spinach), wheat bran, caffeine (coffee & tea), alcohol and soft drinks are adverse to bone strength [ref: U.S. National Osteoporosis Foundation].
• Disease — Certain diseases can reduce bone strength. A doctor should provide medical advice about whether skiing is appropriate during the course of certain diseases.
• Gender — When comparing male tibia strength to female tibia strength, there is no difference in the strength of the same size tibia's — noting of course that the average size of male and female tibia's are different. However, natural calcium depletion in older females can reduce bone strength if calcium is not supplanted (vitamin D is also needed to cause calcium supplements to become effective);
• Previous fracture — Properly healed, a bone has the possibility of becoming stronger than normal (but don't count on it being stronger than normal), and bones that are supplanted with titanium pins can become stronger after bone-fibers grow into the titanium (but here also, don’t count on it being stronger). Bone fractures that are not fully healed can be significantly weaker than normal-strength bones. Skiing should not take place until after a fractured tibia is fully-healed (typically, 10-weeks after proper medical care ... but this time-duration can vary depending many factors that must be assessed by a doctor).
• Other factors — There are other biomechanical and physiological factors that effect tibia strength, but the above factors are the main factors.
Nothing written here should be construed as medical advice: please consult a doctor for medical advice.
Practical reality of ski-binding release-settings.
The relationship between an individual's unique physiology and bone strength is significant. Ski binding release settings are 'adjustable' expressly to attempt to accommodate the prime factors that effect tibia strength — but it's impossible to dial-in a binding's release settings to become perfectly aligned with all of the above-noted factors because they are difficult to quantify in a 'net result'. This is one of many reasons why 'release settings' should be aligned with a binding's ability to supply 'retention' at low release settings (please see 'Retention' sub-section).
Engineering-philosophy differences about ski-binding function & release settings
There are long-running debates between the Germanic and the French approaches toward the interaction between ski-binding function and release settings.
The Germanic approach is to design the binding to supply maximum retention. Then, if the retention-function of the binding is performing as defined in the 'Retention / Anti-Pre-Release' section of this website — the binding's setting is adjusted to a biomechanical release threshold.
The French approach is to design the binding to supply maximum multi-directional release. Then, if the release-function of the binding is performing as defined throughout this essay — the binding's setting is adjusted to a skiable retention threshold.
Howell SkiBindings company believes that a binding's design must functionally-decouple the release-function from the retention-function — as in 2 separate systems. The binding's setting can then be adjusted to a certain 'pre-setting' based on the guidelines of international standard ISO 8061. The pre-setting can then be fine-tuned through the proper use of the 'Self-Release Method' (see below). With Howell SkiBindings it appears that most skiers can leave the pre-settings — as recommended by ISO 8061 — unchanged.
Only Howell SkiBindings are fully-functionally-decoupled between the retention-function and the release-function:
The principles of Axiomatic Design Engineering, formalized as the first new engineering discipline in over 100-years by MIT Engineering Professor, Nam Suh, are utilized robustly in developing new Howell SkiBindings. In this way, release is smooth — only when needed, biomechanically — and retention / anti-pre-release is powerful — always available when performing controlled, aggressive, skiing. Only Howell SkiBindings deploy fully-decoupled Axiomatic Design Engineering technology. Only Howell SkiBindings deliver powerful anti-pre-release independently of the settings. Howell SkiBindings are uniquely the 1st bindings that can be skied at 'chart settings' without pre-release. This is a 1st within the category of alpine ski bindings.
Self-Release Method 
Strong, fast, aggressive skiers and racers who need settings higher than the ‘recommended settings’ on the Howell Release Adjustment Chart can use the Self-Release Method to obtain special 'discretionary settings' — only when the method is used correctly. The correct Self-Release Method also helps to (a) assure that the settings that are necessary for strong, fast, aggressive skiers are not grossly overtightened / not too high as is otherwise typical in the absence of using the Self-Release Method; and (b) — for all levels of skiers — the Self-Release Method helps to assure that there is no ‘gross impediment to release’.
First — together with your skis and boots — have Howell SkiBindings mounted and adjusted for proper function by a Certified Howell SkiBinding Technician (you can become one, on-line).
Next, select the proper ‘pre-setting’ from the Howell Release Setting Chart . Adjust the binding’s indicator-settings to the chart-recommended ‘pre-settings’.
Forward Heel Self-Release Setting:
- Stand on one foot only with the boot firmly buckled as it is buckled during skiing.
- The ski must not be held fixed.
- Release the heel by assertively moving the top of the lower leg forward-and-downward — toward the near-forebody of the ski. Not too fast. Do NOT lunge forward with the opposite leg because this action can rupture the achillies tendon. Hold the back of a turned-around dining-room chair to mitigate falling.
- Readjust the heel setting until release occurs at the ‘comfort threshold’.
- Do not repeat this test more than 4 times with one leg in one session.
Lateral Toe Self-Release Setting:
- Place one ski on its inside edge by moving the knee slightly-inward; place weight on the ball of the foot; then slowly but assertively — cause the toe of the boot to move inward ... toward the ground … to cause full-lateral-toe-release. Fast movement must be avoided because this action does not cause the desired effect that is necessary for proper selection of the binding’s setting.
- Readjust the toe setting until full-release occurs at the ‘comfort threshold’.
- Do not repeat this test more than 4 times with one leg in one session.
Lateral Heel Self-Release Setting:
• Match the lateral toe setting that is derived by the Self-Release Method onto the lateral heel indicator-setting.
WARNINGS ! Injury can occur during improper use of the process to seek settings that are derived by the Self-Release Method: follow the above process, closely, to avoid injury. During skiing, lowered settings may cause inadvertent pre-release; increased settings may block necessary-release; Self-Release settings are ineffective if the binding is not supplying proper function as defined in the Howell SkiBindings Technical Manual.
A Howell Certified Technician should (optionally) measure the release of the complete ski-boot-binding system using measuring instruments — lateral-toe; forward-heel; lateral-heel — as described in the Howell SkiBindings Technical Manual; take appropriate service-action if necessary; record the measurements; provide a copy of the recorded measurements to the skier; provide Howell SkiBindings in-box instructions to the skier.
We require that all Howell SkiBindings are mounted and serviced by a Howell SkiBindings Certified Technician (you can become one, on-line) — and we recommend that you know you’re settings and know what constitutes proper ski binding function. Please see the complete in-box instructions that are supplied with Howell SkiBindings for all of the necessary service-information.
Howell SkiBindings have been designed to release the ski from the boot laterally at the toe; vertically-downward as well as laterally-outward at the heel — (3 modes) — and to retain the ski to the boot during controlled skiing maneuvers. Despite these features, injury may result from simply falling down or from impact with an object. An appropriately functioning ski binding may not release under all injury-producing circumstances. Skiing, like all athletic endeavors, involves a certain degree of risk that must be recognized and accepted. Additional information about the care and maintenance of Howell SkiBindings can be reviewed in the Howell SkiBindings in-box instructions and through the on-line Howell SkiBindings Help Center.
 This optional Self-Release Method is not part of ISO 8061 or any standards.
 The recommended settings on the Howell Release Adjustment Chart conform to ISO 8061 and conform to related provisions within ISO 9462. Boots must conform to ISO 5355. Howell SkiBindings are not compatible with AT ski boots that have metal inserts for pin-bindings. Howell’s SkiBindings are Grip Sole compatible with the use of the optional Grip Sole AFD’s that are supplied, standard, with each purchase.
Testing the release-function of alpine ski-bindings.
Proper 'testing' of the release-function of the complete ski-boot-binding system must involve the use of properly calibrated release measuring instruments by a certified ski-binding technician. Testing with measuring instruments should take place at least once every 30-days of skiing — or before the beginning of each ski season — which ever comes first.
Levels of ski-binding testing
Release testing ski bindings can be performed at many levels — skier, retailer, distributor, manufacturer, or independent testing lab. Testing ski-bindings for release — at any level — can focus on demonstration, calibration, or scientific validation. We respectfully encourage you to ignore blogs and 'published' ski-binding test reports that do not involve the use of release measuring instruments.
Consumer-level ski-binding 'inspection'
Beyond the Self Release Method to fine-tune settings and identify gross impediments to release — skiers should come to know what constitutes proper ski binding function. Howell SkiBindings in-box instructions provides a wealth of information in this way (link under construction).
Retailer-level ski-binding testing
At the retailer-level, there are several tests that must be performed — as required by Howell SkiBindings certification / indemnification programs (link under construction). Uniquely, skiers can also become Qualified Mechanics by Howell SkiBindings company. Standards are in-place by the American Society for Testing and Materials (ASTM) that guide ski retailers on generic ski-binding testing procedures.
The objective of consumer and/or retailer ski-binding testing is to assure that the actual release-limits that are being measured are testing within the expected release tolerances that are supplied by each respective ski-binding company. If the actual release-limits are measured to be outside of the expected release tolerances — then service must be performed to the binding, the boot, or both, as specified by Howell SkiBindings. If after proper service is performed the measured release still remains outside of the expected tolerances, the binding should be returned to Howell SkiBindings company; the boot should be returned to the boot company; both should be returned to their respective origins for service or warranty replacement; or if the binding is outside of the warranty-period, the binding should be retired — not sent to a 2nd-hand event.
Manufacturer-level release-testing for tibia-friendly skiing
Release should occur in a way that limits the selected peak-torsional-torque or the peak-bending-moment on the tibia — to be as nearly as constant as possible — independently of the location of where an injury-producing force enters the ski. This requirement is a fact of nature: a tibia cannot 'know' where a potential injury-producing force enters a ski. However, in practice, it is nearly impossible to achieve a constant peak loading threshold on the tibia independently of where a force enters a ski. Never-the-less, it's important for binding-function to seek this objective as best as possible.
To test the practical reality of the above requirement — ski-binding companies apply test-forces to a broad range of positions along the length of a test-ski while a ski-boot is held rigidly in the air by a metallic foot and metallic tibia. The opposite end of the metallic tibia is rigidly connected to a test frame. This special type of test apparatus allows the simulation of 'rigid-body mechanics' at peak loading conditions — in a way that allows the ski to 'float' as it would in skiing. When a simulated injury-force is applied to a test ski to control its motion in one direction (in one degree), i.e. laterally — this test method allows the ski to remain unconstrained in the other 5 degrees of motion so that the ski can seek its easiest path of release ... which path is controlled by the unique kinematics of each binding design. The unconstrained path of the ski's release effects the magnitude and the direction of the load on the tibia. The metallic tibia is instrumented with strain gauges to measure: (a) torque about the long-axis of the metallic tibia, and (b) the bending-moment, mid-shaft, on the metallic tibia. Some binding companies have metallic tibia's that are instrumented in two positions so that peak bending-moments can be determined at any position on the metallic tibia, through the use of vector-transposition.
Expressing the results
A graphic representation of the test-results obtained from the use of the above test method can be depicted by plotting the peak resultant-torque that is applied to the tibia — at ski-binding release — as a specific graphic-point in space that is located laterally of the center-line of the ski, next to each point where the force is applied to the ski. Each graphic-point in space that corresponds to each point of applied-force, can then be graphically-connected to form a 2D 'release-envelope'. Graphically, the ideal shape of a 2D release-envelope is a line, parallel to the ski, 45cm forward of the projected-axis of the tibia on the ski and a line that is 45cm behind the projected-axis of the tibia on the ski. This ideal 2D graphic-representation would depict a binding that limits the torsional torque that is applied to the tibia — to a constant magnitude — no matter where the force is applied along the length of the ski, forward of 45cm or aftward of 45cm of the projected axis of the tibia on the ski. See graphs, below — both of which graphs are close to the ‘above-defined ideal’ in terms of peak torsional-tibia-torque at release (see the lines with square boxes). The valgus (abduction) moment graphs will be referenced, below, in the text that discusses ACL-friendly ski-binding function.
Conflicting paradigms of tibia strength and ski-binding function
The ideal shape of a release-envelope — to accommodate the tibia — is contradictory to basic physics. In a standard physics-model, the torque that's applied to a tibia varies directly as a function of the position of a constant-magnitude-force that is applied to the ski, relative to the position of the tibia. 'But, as noted above — from a biomechanical perspective — the tibia does not know (or care) where a force enters the ski: the tibia fractures at a constant magnitude of torsional-torque, or at a constant magnitude of bending-moment. In order for the resultant-peak torsional-torque or the peak bending-moment on the tibia to remain as constant as possible to satisfy the natural structural characteristics of the tibia — no matter where a force is applied to a ski — the magnitude of the force that is applied to the ski must change. 'But is is not possible to control the position or the magnitude of an injury producing force: the nature of skiing controls this phenomena.
Practical considerations for tibia-friendly ski-binding function
Therefore, the binding must modulate the relationship between these variables of force, leverage, fulcrum-positioning, torsional-torque, bending-moments — relative to the position of the applied-loading.
Influence of fulcrums on tibia-friendly ski-binding function
A binding is a force-limiting mechanism that — together with the leverage supplied by the ski boot — can modulate, to a certain degree, the effect of ski-length on the resultant torque that is applied to the tibia. The modulation of loading-consistency that is applied to the tibia' that is supplied by the binding is also a function of where the ski pivots during release — where the fulcrum-points are located relative to the boot; and where the ski pivots during release relative to the projected axis of the tibia. In practice, the actual shape of a typical release-envelope — which depicts the peak resultant torsional-torques and bending-moments that are applied to the tibia as a function of where the force enters the ski — approaches zero in the center of the ski and remains nearly constant 45cm forward and 45cm aftward of the projected axis of the tibia. Again, this phenomena is a result of the binding's built-in design-function relating to the leverage-effect of the binding's pivot-points and fulcrum-positions.
The actual leverage-effect of the ski boot is important and its effect is more precisely defined by the distance between the toe-piece of the binding and the center-of-rotation between the boot and the ski — relative also to the projected-axis of the tibia — during torsional-release. In the case of forward-bending release — the leverage-effect is defined by the distance between the heel-unit and the leading edge of the anti-friction-device (AFD) that's located under the ball of the foot or near the tip of the ski boot. The leading edge of the AFD forms the fulcrum for forward release. In these 2 modes of release — lateral at the toe and vertical at the heel — it's important to remember the simple relationship of torque = force X distance. The equation is not, torque = 2(force) X distance ... or 3(force) X distance, etc. Distance (leverage) has an equal effect on torque as does force. Release torque is not controlled solely by changing the force setting of the binding. The built-in design of a ski-binding's pivot-points in torsion and in bending — the distance between the force-imparting mechanisms, the bindings, and the pivot-points and fulcrums — has an equal effect on the resultant torque applied to the tibia as does the force supplied by the binding toe-piece or heel-unit [see footnote 7]. All Howell SkiBindings deploy this functional-element of uniquely building-in specially-positioned pivot-points and fulcrums to intentionally flatten the release-envelope, as best as possible, forward of 45cm and aftward of -45cm from the projected axis of the tibia — thus holding the peak torque that is applied to the tibia as close to 'constant' as possible no matter where an injury-producing force enters the ski. This special nearly-constant release effect that is uniquely supplied by Howell SkiBindings can actually be 'felt' by skiers during necessary release: the 'feeling' is a "remarkably smooth release". Other ski-bindings do not deploy this effect in the way of Howell SkiBindings.
Unique functional-signature of each binding design
Each binding design has unique release-envelope signature — a unique shape — in relation to each binding's release-function. The release setting simply moves the whole uniquely-shaped release-envelope 'upward' or 'downward' relative to the peak loading that is being applied into the ski and/or being resolved into the tibia.
Interestingly, the release settings that are measured by ski-shop's torque-testing equipment (or force-testing equipment) provides only one-point on a ski-binding's unique release-envelope. Graphically, this point is projected, laterally, from the tip of the ski (footnote 8). The problem that is caused by the highly-limited aspect of measuring only one-point within a full-release envelope is that — bindings with poor release-function (that have distorted but unseen, un-fully-measured, release-envelopes) — transmit loads to the tibia that are not within a desired range of function — relative to the singular, one-point-release-setting. Ski shop testing for release produces no information that is useful toward determining a ski-binding's overall release-function: ski-shop testing for release is useful only if the pre-established overall release-function is robustly meeting ISO 9462 Method-B — where the release-envelope is nearly-parallel to the ski. Bindings with minimal distortion within their release-envelopes induce relatively-consistent peak-loading on the tibia, independently of where an injury-producing force enters the ski.
Combined loading function of ski-bindings for tibia integrity
During a combined forward-twisting injury-producing event, the tibia becomes weaker (combined loads weaken a structure). Graphically representing the results of ski-binding release-function during combined loading is accomplished through the use of 3D release-envelopes. A combined-load test involves the application of a preload in one direction — for example, a forward bending-moment — while at the same time, a lateral (torsional) load is applied to the ski until the ski-binding releases at the toe or at the heel. The forward bending preload is represented, graphically, by plotting a point a certain distance above the top surface of the ski: this distance represents the magnitude of the applied pre-load. Another point is then applied to the graphic representation in the 3rd-dimension — laterally of the first-point — at a distance that is proportional to the peak torsional torque that is applied to the tibia at ski-binding release. This approach generates a 3-dimensional release-envelope. An ideal 3D release-envelope is shaped like 2 rectangular boxes — one box is positioned 45cm forward of the projected-axis of the tibia, the other box is positioned 45cm aft of the projected-axis of the tibia. In practice, however, there are distortions in a 3D release-envelope that are caused by the necessary-positions of the fulcrums that define the points about which the boot rotates during release, relative to the position of the tibia. Bindings with the smallest distortions in their 3D release-envelopes hold the peak loading on the tibia (in both torsion and bending — at release) to be as close to constant as possible.
Howell Ski Bindings have the least distorted 3D envelope of any binding. This highly desirable function is accomplished through the use of dual-alternate pivot-points in torsion and by locating the leading edge of the anti-friction-device far aft of the tip of the boot (the unique AFD-location of Howell SkiBindings provides additional benefits for edge-control, too).
Overall epidemiology of tibia fractures in skiing
Classical tibia-fractures involving adult skiers barely exist today. Classic torsional and forward-bending fractures in adults have a prevalence of only 3% of all skiing injuries and an incidence (not 'incidents') of ~20,000 mean-days-between-injuries (MDBI). This means that adult bindings and the settings are doing their job — a very good job. However, please also note that other bindings that do not supply strong retention and that are set according to the above guidelines can pre-release — thereby potentially shifting the injury-pattern to an upper-body injury such as to the head, spine, shoulder, wrist, spleen, etc. Upper body injuries can be more severe than a tibia fracture. Pre-release can be averted through the use of robust binding function — that precludes the need for elevated settings (see sub-topic herein — Retention).
Sub-notes regarding tibia-friendly ski-binding release function
1— Tibia fractures among children-skiers are on the rise (prevalence = 5% of all children's skiing injuries; incidence = 36,000 MDBI — compared with 3% and 45,000 MDBI 10-years ago). Children need super-low friction interfaces between their boots and bindings. Children's boots must have shells that are made of materials that are hard, above 50 D-Shore, in order for the ski-boot-binding system to provide proper release-function and proper retention-function. Children's boots must be well fitting — not overly-large to grow into. Boots must be firmly buckled at all times while skiing. 'And children's bindings should include an AFD with a well-defined leading edge (a well-defined fulcrum) that is located 3cm aft of the tip of the boot sole.
2— Significantly, other types of previously obscure tibia-fracture are now on the rise: severe, high-energy tibia-plateau fractures, severe tibial-tuberosity fractures, and high-energy spiral-tibia-fractures. Each of these types of tibia-fractures comprise the fastest-growing categories of injuries in skiing — paralleling the advent of fat-skis and pin-bindings. The high-energy nature of the new types of skiing fractures involve multiple-fragments, difficult surgical reconstruction, and 10 to 15-months of aggressive rehabilitation. Many skiers who sustain these new types of tibia fractures can never ski again. Fat skis on firm snow; and pin-bindings in any snow (except Trab TR2 pin bindings) — are a serious problem for the sustainability of our beautiful sport. Howell SkiBindings principle, Rick Howell, has tested and generated extensive release-envelopes involving about 20 brands of pin-bindings. All pin-binding release-function (except the Trab TR2) is horrendous at best, many times requiring 2 Very High Level releases in order for the ski to release from the boot ... meaning that the tibia becomes fractured twice during one injury-producing event. Pin bindings have nearly zero lateral elasticity — thus causing 'high-energy' tibia fractures involving many bone-fragments. Fat skis are causing tibia-tuberosity fractures (and MCL-injuries) because the wide-width of fat skis — when skiing on firm snow — induces large lateral bending-moments (abduction-moments) at the top (proximal end) of the tibia. Fractures in this location often extend into the tibial plateau causing damage to the menisci that are seated on the top of the tibia plateau. The negligent, overly-loose ISO standards for pin-bindings (wrongly called 'tech-bindings' — they are hardly 'tech') must be changed to reflect human-biomechanics, not just manufacturing tolerances that have nothing to do with basic human biomechanical requirements [see footnote 10]. Fat skis are great in powder or in loose-snow — but skiers should be advised that skiing on fat skis (wider than 87mm at the waist) on firm snow could end one's skiing career. Do not use fat skis on firm snow. Pin-bindings on fat skis invites double trouble. If you are skiing with pin-bindings (other than the Trab TR2) — no matter the settings — do not fall.
3— Dispersion of the settings for different size skiers. The extensive biomechanical engineering work that was performed from late 1960's throughout the early 1970's by several leaders in the field of tibia-friendly skiing — produced data that allows the above ski-binding engineering principles to be applied across a wide range of individual skier-physiologies, mostly focusing on: height (adjusted by weight); velocity ("skier type"); age; gender (as specified by French Afnor standards); and by Howell SkiBindings); and boot sole length. The anthropometric-based range of settings is then also backed-up by their relationship to tibia strength.
Conclusion: tibia-related release-function of alpine ski-bindings
Integrating robust release-function into top-of-the-line alpine ski-bindings is well within the domain of Howell SkiBindings designed by Rick Howell of Stowe, Vermont. Rick Howell's experience in ski-bindings is unprecedented in the binding industry (see 'About Us'). In fact, Howell SkiBindings provide every function that is noted above — with less parts than other bindings. This means that Howell SkiBindings can be reliable and durable, too.
The release function of a ski-binding is highly regulated by international ski binding standards. All ski-bindings must be certified for their compliance with the minimum international ski-binding release-function standard — ISO 9462 — through testing and certification by the only independent ski-binding testing lab in the world — by TÜV, in Munich, Germany [see footnote 9]. Even if there is no 'local rule' enforcing ski-binding certification — for example, there are no certification-enforcement rules in USA or Canada — we urge you to seek only ski-bindings that are independently certified by TÜV for their function according to ISO 9462, ISO 9465 and ISO 11087 — and that meet ‘Standard Industry Practice’ for anti-pre-release and durability.
It is anticipated that Howell SkiBindings will be independently Certified before being shipped into the stream of commerce.
Part 2 — ACL-Friendly Release
The remarkable, low-stand-height, non-pre-releasing, ACL-Friendly (sm) alpine ski binding function that is unique to Howell SkiBindings is explained in detail in the slide-show presentation given by Rick Howell to the International Olympic Committee (IOC) conference — Prevention of Injury in Sports — on March 17, 2017 in Monte Carlo, Monaco. This presentation was updated at the International Society for Skiing Safety (ISSS) conference in Innsbruck, Austria in April of 2017. The updated PDF slideshow — Mitigation of ACL Rupture in Skiing through 3-Mode Bindings — is available by email, free, here.
How Howell SkiBindings uniquely provide ACL-Friendly skiing
... first, the epidemiology of skiing-ACL injuries.
ACL-injuries — ~80% of which are Grade-III, complete rupture — are by far the most prevalent injury in skiing: prevalence = ~21% of all skiing injuries; incidence = ~2500 mean-days-between-injury (MDBI). MCL-injuries are the 2nd most prevalent in skiing: ~12% of all skiing injuries; incidence = ~4200 MDBI. Higher 'incidence' values are better when there are more "days between injuries". The incidence (MDBI) of skiing-ACL injuries is improving, favorably, during the past 10-years; whereas the incidence of MCL injuries is worsening during the past 8-years. The improvement (in the USA) is most likely due to Vermont Safety Research's 'ACL Awareness Training' behavior modification programs (available on video from Vermont Safety Research); and in Sweden, the improvement is due to Maria Westin's Proprioception Training Program. Never-the-less, ACL and MCL injuries remain, by far, the most frequent injury in skiing. Further, ACL injuries are severe, requiring between US$20,000 to US$50,000 for diagnosis, treatment and rehabilitation (not including loss of work) as well as ~200 days of less-than-normal athletic-function. ~50% of all skiers with Grade-III ACL ruptures develop osteoarthritis within 10-years of reconstructive surgery. Skiing-ACL injuries are both frequent (~2500 MDBI) and severe (~200 days of sub-optimal knee function).
Female skiing-ACL epidemiology
Female skiers incur ~3-times the amount of ACL injuries compared with male skiers (8-times in basketball—different injury-mechanisms are involved). It appears to leading ACL orthopedic researchers that some of the main underlying causes of this gender-difference in skiing-ACL injuries may include: (1) greater valgus-angle (Q-angle); (2) sharper femoral-notch in which the ACL is positioned through the distal end of the femur; (3) a lower ratio of ACL-strength to body-weight; (4) steeper tibial-plateau; and (5) weakening of the ACL during the pre-ovulatory phase of the menstrual cycle — but the evidence-based research on definitive-causation for each of the 5 above factors remains scientifically unclear at this time (June, 2018), especially in view of age (the studies were not normalized for age).
Skiing ACL injury mechanisms
The most frequent skiing-ACL 'injury-mechanism' is the Slip-Catch ACL-injury-mechanism-scenario, which is somewhat similar to the Phantom-Foot ACL-injury-mechanism-scenario. The Slip-Catch ACL-injury-mechanism-scenario is shown at the instant of ACL-rupture in this photo:
In the above Slip-Catch scenario, the outside ski 'slipped' in loose snow, then the ski 'bit' during the compressive-build-up of snow that formed under the slipping-ski ... while at the same instant, the skier had already loaded the ski on-edge just-before it slipped. This situation causes the lateral component (lateral and co-planar to the top and bottom surfaces of the ski) of the force that enters the inside-edge (medial edge) of the outside-ski to push the ski at a point that is centrally-located, slightly behind the projected-axis of the tibia — creating an abduction-force — that acts over the length of the tibia plus the thickness of the boot plus the stand-height of the binding — to produce an abduction-bending-moment (valgus-moment) at the knee.
Because, in the photo of skier above, the ski slipped while the skier's resistive-body inertia continued to load the edged-ski, the knee was forced into an exaggerated valgus-angle, which valgus-angle became further-amplified by the horizontal-component of the compressive-load (at both the ski, and in the opposite direction, at the knee) — to generate the combination of (a) a very large 'abduction-moment' (previously called 'valgus-moment' or 'femur-torque') plus (b) a small torsional-torque about-the-long-axis-of-the-tibia (see graphs, below). There’s a slight amount of torsional tibia torque because the lateral-component of the applied-force entered the ski slightly behind the projected-axis of the tibia. ((The concept of stating "twisting" as a stand-alone term, is meaningless: "twisting" about what?)) Rear-weighting can sometimes arise in this situation, too — and clearly, axial loading of the lower-leg compresses the distal end of the femur on the sloped-surface of the tibial-plateau. When the backward-bending-moment at the distal (bottom) end of the tibia is greater than the lateral-bending-moment at the proximal (top) end of the tibia, the skiing-ACL injury-mechanism converts to become what is called, 'boot-induced-anterior-drawer' (BIAD), a term coined in 1977 by the late orthopedic surgeon, Henry Crane, MD. The slope of the tibial plateau interacts significantly with the BIAD skiing-ACL injury mechanism. Female tibial plateau’s appear to have greater slope than males. All of these forces, torques, moments, valgus-angles, and tibial-plateau-angles mix together to produce large strain across the ACL, across the MCL, and cause the meniscus to become non-uniformly compressed. Depending on the magnitude of the loads, the position of the loads, and the kinematic angles that are involved — the ACL (and/or the MCL) will either become mildly sprained ('Grade-I'), significant-sprained ('Grade II'), or rupture (Grade III).
Skiing technique experts who are also orthopedic-researchers (and some within this group who are also PhD's in mechanical engineering — all 3 disciplines) have rendered a myriad of opinions on these various injury mechanisms for 3 decades ... which opinions are 'interesting'. However, there is no bona fide way to fully-validate and/or quantify these opinions in ways that can be useful from a proper structural engineering perspective in order to arrive at an engineering-solution. The above discussion on ACL injury mechanisms is — from an engineering-perspective — 'conjecture'. Comments about the prevalence of these ACL injury mechanisms are also conjecture. Massive intellectual energy continues to be expended by others attempting to explain ACL injury mechanisms and their underlying causation — only to be disputed by other groups of 'experts'. Here's a possible — perhaps plausible — prevalence-distribution of injury-mechanisms that might be causing skiing ACL injuries, maybe:
Large abduction-moments are involved in the most prevalent skiing-ACL injury mechanisms
The most prevalent mechanism (possibly) representing ~75% of all skiing-ACL injury-mechanisms appears to include Phantom Foot and Slip-Catch injury-mechanisms (maybe). If these 2 types of skiing ACL injury mechanisms are the most prevalent mechanisms — the main the biomechanical loading-component is large abduction-moments (previously — valgus-moments, or 'femur-torque'), which load-component also includes a small amount of torsional-torque about the long-axis of the tibia. Rear-weighting is probably present, too. The problem with this discussion is that it is conjecture. No one knows the prevalence of these various ACL-injury mechanisms.
Engineering go-around on ACL-injury-mechanism conjecture
The unknown nature of the structural-engineering that is involved in skiing-ACL injury mechanisms has led Howell SkiBindings company to deploy a previously proven structural analysis-technique that was first developed by Case Western Reserve University's Biomechanical Engineering Professor, Eugene Bahniuk, PhD, to crack the code in the forensic-analysis of skiing tibia-fractures. This breakthrough technique / approach / involves the use of 'failure envelopes'. By applying a similar 'envelope approach’ to the skiing-ACL-problem — all skiing ACL-loading scenarios are tested by utilizing kinematically-correct surrogates that model: (a) the fracture-limit of the tibia; (b) the theoretical rupture-limit of the ACL; (c) the theoretical rupture-limit of the MCL; (d) the pre-release limit (the lower-limit — found during actual skiing); (e) the release limit of the binding — all, as a function of where the applied-load enters the ski. In this way, 'expert conjecture’ is eliminated, because when each unique binding design's uniquely shaped release-envelope pokes upward through (a) the tibia-fracture-envelope; (b) the ACL-rupture-envelope; or (c) the MCL-rupture-envelope — the tibia will fracture, the ACL will rupture, the MCL will rupture .... OR ... if the binding's uniquely shaped release-envelope pokes downward into the pre-release-envelope — the ski will pre-release. Each musculoskeletal element — tibia, ACL, MCL — has a uniquely shaped biomechanical failure envelope. Each binding design has a uniquely shaped release envelope, which shape is independent of release settings. The non-linear pre-release limit envelope is a defined constraint, too. The binding release envelope should (ideally) operate below the biomechanical-failure-limits of the tibia; below the ACL and MCL rupture limits — including below a margin — and operate above the pre-release envelope, including above a margin. This ‘envelope approach’ seeks to end decades of 'expert conjecture’ about skiing-ACL injury mechanisms that have produced no breakthrough-change in skiing-ACL injuries with the exception of the large and highly positive changes that have been caused in the USA by the Vermont Safety Research 'ACL Awareness Training'; and separately by Maria Weston's 'Proprioceptive Intervention Program' in Sweden. However, again, ACL injuries remain, by far, the most prevalent injury in skiing, followed closely by MCL injuries. Further merit toward deploying the 'envelope approach’ to test and develop the function of ACL-friendly ski-bindings is anchored in the reliance upon the related and established 'knowns' about tibia-fracture characteristics relative to proper ski-binding function (see Part-1, above, about the huge reduction in tibia-fractures, based on ski-binding release-function that was developed through the use of the ‘envelope approach’).
Strength of average male ACL
To test the effect of different applied-forces, torques, bending-moments and kinematic-angles — utilizing the ‘envelope approach — to the structural failure-limits of the tibia, the ACL, the MCL and to the retention-limits involving pre-release in skiing— we utilize the already-established structural-constraints for an average U.S. male as well as our already-known data on the 'skiability pre-release limits'. The torsional fracture-limit of the tibia (about its long axis) = 11.3 daNm (~11.3 DIN). The rupture-limit of the ACL = 20 mm/mm of engineering strain (~20% elongation): this limit is based on the average-value found in the scientific literature. The pre-release limit during aggressive skiing is shown below (8-graphs-below, where there is light-green shading). The already well-established tibia fracture-limit; the theoretical ACL-rupture limit; and the theoretical MCL-rupture limit are 'upper' not-to-exceed-limits. The pre-release limit is a 'lower' not-to-exceed-limit.
But first, here are the combinations of tibia-torques and abduction-moments (‘abduction-moments’ were previously known as 'valgus-moments’) that produce 20% elongation — Grade-III rupture — of an average male's ACL (data for the female ACL still does not exist! Yikes!)
Applying abduction-moments to a surrogate male
Here is how the above ACL rupture algorithm is utilized to produce a response-envelope.
The test-method involves the use of 'Surrogate-2' — an anthropometrically-correct average U.S. male 'metallic dummy' that is kinematically-configured as during a Slip-Catch and/or during a Phantom Foot injury-event — to cause the flow of abduction-forces that are applied to a full-range of positions along the length of the ski to produce tibia-torques and abduction-moments through the point where the surrogate-ACL is located.
The quantification of the structural-limit of the ACL on a ski involves no ski-bindings — so that release is not possible / is not biased by any given type of binding: the ski is rigidly-bolted to the base of the surrogate’s metallic foot. A spacer-block is interposed between the base of the metallic foot and the test-ski to represent the average thickness of a binding and alpine ski boot sole.
(Above) a tensile-force is applied to the lateral (outside) edge of the ski, which tensile-force produces the same vector as snow would produce on the opposite (medial) side of the ski (as in the photo where the skier ruptures the ACL — see the first photo at the top of this 'Section-2', 'ACL-Friendly Release') ... until the surrogate-ACL reaches 20% ACL-elongation as defined by the ACL-rupture-limit algorithm (Surrogate-1) that is shown in the orange-colored graph, above. ACL rupture occurs when the above specified non-linear combination of peak torsional-tibia-torques and peak abduction-moments are reached in Surrogate-1 (the ACL-rupture algorithm, above).
Here's how to read the graph (see below). When an abduction force (blue) enters the medial edge of the ski 20cm behind the projected axis of the tibia producing 4.5 daNm of torsional tibia-torque (red) plus 12 daNm of abduction-moment (green) — ACL-rupture occurs. Those two torques and moments cause the ACL to exceed 20%-elongation, as defined by the upper orange-limit of Surrogate-1. The blue arrow represents the central-position (the centroid) where the abduction-force is applied to the medial-edge of the ski. Shaped-skis produce 2 applied lateral vectors during Slip-Catch or Phantom Foot events — one at the tip and one at the tail — that nature resolves into a single centroid. The blue rectangular-box highlights the resulting combination of tibia-torque and abduction-moment at ACL-rupture ...
If the applied abduction force enters the ski 10cm behind the projected axis of the tibia (see below), producing the combination of 2 daNm of torsional tibia-torque (red) plus 15 daNm of abduction moment (green), ACL-rupture occurs.
If the applied abduction force enters the ski 60cm behind the projected-axis of the tibia (see below) with a magnitude that is greater than 11.3 daNm of tibia-torque (black line) — the tibia will fracture before the ACL-ruptures. Here, when this scenario occurs, the envelopes that represent the combination of the peak abduction-moment and the peak torsional tibia-torque at ACL-rupture — become irrelevant: the tibia fractures before the ACL ruptures. However, in 2018, few skis are long enough to allow loads to develop more than 55cm behind the projected axis of the tibia. See below ...
As can be seen above, the outcome of either tibia fracture OR ACL-rupture is dependent not only on the magnitude of the applied abduction loading — but also and importantly — on the position of the abduction-force on the ski. This is a breakthrough finding. When an abduction force is applied to the medial edge of the ski 55cm (or more) behind the projected-axis of the tibia, the tibia can fracture. 'And based upon the plausible assumptions involved in this biomechanical testing — it appears that when an abduction force is applied to the media edge of the ski between 10cm and 55cm behind the projected-axis-of-the-tibia, the ACL can rupture. This is also a breakthrough finding. The exact quantitative failure limits of the ACL still need refinement — but the 'envelope method' appears to end conjecture and appears to open the real possibility of applying proven structural engineering techniques to crack the code on ACL-friendly skiing, as shown, below ...
Converting the skiing-ACL data to ski-binding application
Each combination of critical torques and moments at ACL-rupture (as a function of their position of application into the ski) have a unique and singular applied-abduction-force that is associated with the critical ACL rupture critical-limit. By recognizing the metric of ‘applied-abduction-force’ as a unifying-metric, the above torque and moment envelopes become simplified and converted, as shown, below. This conversion from critically combined torques and moments at various points along the ski at ACL-rupture — to critical forces at various points along the length of the ski at ACL-rupture — simplifies the the engineering for ski-binding function if critically-tuned lateral heel release is present.
First, the critical biomechanical limits and the critical pre-release limits, expressed in the unified metric of applied abduction force as a function of where along the length of the ski the abduction force is applied:
Testing ski bindings against the above critical biomechanical force-limits:
Ordinary 2-mode ski-binding function — relative to the ACL
Yikes (above)! The above envelopes depict what can occur with an ordinary 2-mode binding when tested at 3 different settings. ACL-rupture can, theoretically, occur. Even if the binding is set at DIN-4 (black release-envelope) ACL-rupture can theoretically occur when an applied abduction force enters the ski between 37cm and 10cm behind the projected axis of the tibia. Double-yikes — because DIN-4 is so low that it is not skiable by an average U.S. male weighing ~170 pounds: pre-release occurs. Notice also the large margin between all of the above ordinary 2-mode binding release-envelopes and the tibia-fracture envelope: these large (good) margins explain why skiing tibia fractures barely exist with ordinary 2-mode ski-bindings. Bravo, 2-mode bindings—for tibias. 'But these envelopes critically illuminate possible adverse 2-mode ski-binding function for the ACL.
The skiing-ACL problem is now, finally, exposed from a structural engineering approach.
🙂 Howell SkiBindings — with additional non-pre-releasing lateral heel release — produce the black release-envelope, below ✅🎯✌️...
Modes of release effect ACL integrity
How do these two different types of bindings produce these vastly different release-envelopes⁉️
Howell SkiBindings uniquely produce a fundamentally different release-response in the presence of applied abduction forces that enter the back half of the ski — below theoretical ACL-rupture — due to lateral heel release.
Settings for lateral heel release
The recommended settings for the lateral heel release function of Howell SkiBinding are based on the unique anti-pre-release function of each mode of release within Howell SkiBindings. Each time the ski flexes — even slightly — the lateral heel release mechanism is forced to re-center the ski to the heel of the boot — unless the above-described critical ACL-injury-limit is approached ... at which point the lateral heel release mechanism provides elastic re-centering to dissipate innocuous abduction forces OR lateral heel release is supplied when the applied abduction force further approaches the critical structural limit of the ACL. Lateral heel release settings vary as a function of the lateral toe release settings. Our derivation of the recommended lateral heel release settings is further backed-up, scientifically, by their relationship to matched-variation in lower-leg length.
To Order by Reservation-Deposit:
Howell 800 Venus — Loaded with ACL-Friendly features for lite & strong women. DIN 2.5—9
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Howell 888 Max — CAUTION: EXTREME SKIERS & RACERS ONLY. DIN 8—20
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It was inevitable.
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Footnote 1: The engineering term, "moment" is applied to structures (such as the tibia) when forces and lever-arms cause the structure to 'bend' about its long axis. The related term, "torque" is applied to a structure (such as the tibia) when forces and lever-arms cause the structure to twist about its long axis. In both cases — 'moment', or 'torque' — the simple engineering equation that applies to the phenomena is, "T = f X r", where "T" can be either 'torque' or 'moment'; "f" is the applied-'force'; and "r" is the 'distance' between the applied-'force' and the point at which the 'torque' or the 'moment' is being resolved, measured or analyzed. In the case of a 'moment', one could select any point along the length of a column (tibia) to analyze the instant bending-'moment' at that point. When the term 'forward bending-moment' is utilized with ski-bindings — it is intended to mean 'forward release' — but the phenomena involves the bending of the tibia, so the correct term is 'forward bending-moment'. (The term 'forward lean release' is an incorrect misnomer: 'forward lean' is the angle of a boot's upper shaft relative to the ski. The person who coined the term, 'forward lean release' is not much of a skier and does not really understand skiing. Besides, Spademan — when it was fully-developed just before its demise — could not really release in the forward-shear direction, so there is no need to differentiate the vernacular between 'forward-lean' and just plain 'forward'.)
Footnote 2: The lay-term 'load' herein means 'torques', 'bending-moments' or 'forces'.
Footnote 3: Biomechanical tibia fracture data: Skiing Safety II; Editor, Jose Figuras, MD; 1978, ISBN 0-8391-1209-2.
Footnote 4: Current anthropometric data: U.S. National Highway Traffic Safety Administration, Research & Data, 2017; and The Measure of Man and Woman: Human Factors in Design, Alvin Tilley, Henry Dreyfuss, ISBN-10: 0471099554.
Footnote 5: 'Ski Binding Settings Based on Anthropometric and Biomechanical Data'; Malcolm Pope, DrMedSci, PhD; Robert Johnson, MD; Human Factors, Vol.18, pp 27-32, 1976.
Footnote 6: 'Discretionary Settings' are allowed by international standard ISO 8061.
Footnote 7: 'The Biomechanics of Contemporary Ski Bindings'; Journal of Safety Research, Vol. 4, pp 160-171, 1972, Eugene Bahniuk; 'Analytical Studies of the Biomechanics of Contemporary Ski Bindings', Mechanics and Sports, The American Society of Mechanical Engineers, pp 221-236, 1975, Eugene Bahniuk; 'Theoretical Estimation of Binding Release Values', Orthopaedic Clinics of North America, Vol. 7, No. 1, pp 117-126, 1976, Eugene Bahniuk; and 'A Method for the Testing and Analysis of Alpine Ski Bindings', Journal of Safety Research, Vol 12, No. 1, pp 4-12, 1980, Eugene Bahniuk et al.
Footnote 8: When the release setting is changed upward or downward, the entire uniquely-shaped release-envelope of any given ski-binding design, shifts upward or downward: the shape of each unique ski-binding's release-envelope does not change. This means that a release setting prescribes only one small aspect of the overall release function. This issue is important to understand and to recognize in terms of a key limitation of all release settings.
Footnote 9: Certification of compliance with ISO 9462 ('release characteristics' and some functions pertaining to 'retention'); ISO 9465 (retention); and ISO 11087 (ski-brakes) — by an independent lab — is mandatory in Germany, Austria, and Switzerland. In Switzerland, non-certified alpine ski-bindings are removed from retail ski shops by the Swiss-BfU.
Footnote 10: References: (1) Dominik Heim, MD; SITEMSH-Japan, 2016. (2) Zorko; Nemec; Matjacic; Olensek; Alpine Skiing Simulations Prove Ski Waist-Width Influences Knee Joint Kinematics; ISSS-Innsbruck, Austria, 2017. (3) Stenroos; Pakarinen; Jalkanen; Mälkiä; Handolin; Tibial Fractures in Alpine Skiing and Snowboarding in Finland: A Retrospective Study on Fracture Types and Injury Mechanisms in 363 patients; Scand J Surg Off Organ Finn Surg Soc Scand Surg Soc., Sept 2015, doi:10.1177/1457496915607410. (4) Improved Short Term Outcomes in Tibial Plateau Fractures of Snow Sports Injuries Treated with Immediate Open Reduction Internal Fixation; Janes, MD; Leonard, MSPH; Phillips, PA-C; Salottolo, MPH; Abbott, MD, Bar-Or, MD; ISSS-Innsbruck, Austria, 2017.