The maths, in the open.
Every value Laminitis Tool returns traces to a published equation and a named constant. There is no black box. This page walks the model from the horse's bodyweight all the way to the millimetres you mark on the shoe — with the formula, the reasoning, and the reference behind each step.
The model was first set out in full in the peer-reviewed paper A Centre-of-Rotation Referenced Biomechanical Model for Prescriptive Farriery in Equine Laminitis (Caldwell, Madden & Yxklinten, Journal of Equine Veterinary Science, 2026), and is developed at length in The Equine Foot, Volumes 1–2. It is, to our knowledge, the first published model to derive patient-specific shoe-placement parameters from an integrated framework of ground reaction force, tendon mechanics, joint geometry, and hoof-horn material science. Every constant below carries its source.
1 · From bodyweight to force
The whole model scales with the horse. The tool is calibrated at a 500 kg reference horse and scales every force to the patient's actual weight.
Scaling factor
Every force output is proportional to bodyweight. Dividing actual bodyweight by the 500 kg reference gives a multiplier applied throughout.
Standard biomechanics scaling; Caldwell & Madden 2025.
Force on one front foot
In bilateral front-foot laminitis each front limb bears about 30% of bodyweight at the stance. Multiplying kilograms by gravity (9.81 m/s²) converts to Newtons.
Forelimb weight share, Clayton 2012; converted to SI units. Caldwell & Madden 2025.
2 · The force that keeps pulling: DDFT loading
Rotation of the pedal bone (P3) is not a static finding — the deep digital flexor tendon (DDFT) keeps pulling on the rotated bone, driving continued lamellar shear. The tool quantifies that excess pull.
Excess tendon tension from rotation
Each degree of P3 rotation adds approximately 87.5 N of DDFT tension at 500 kg. This is the central rate constant of the model. When a deep digital flexor tenotomy has been performed, this term is set to zero.
McGuigan et al. 2005, Equine Vet J 37(2):161–165, scaled to light-horse weight. [attribution under review — McGuigan vs O'Grady & Steward 2007]
Why walk only
At trot, dynamic loading raises ground reaction force — and therefore DDFT tension — by about 1.65×. This is the mechanical basis for restricting acute and sub-acute laminitics to walk only.
Trot multiplier, Merkens et al. 1993; Ratzlaff & Grant 1986; Caldwell & Madden 2025.
A 500 kg horse with 10° of rotation: dDDFT = 1.0 × 10 × 87.5 = 875 N of excess tendon tension — roughly 60% of the horse's bodyweight, pulling the tip of P3 down and back, every step.
3 · The headline number: F9 heel elevation
Raising the heel to a target palmar angle unloads the DDFT and reduces the rotational force on P3. The F9 protocol turns the radiographic findings into a precise heel-elevation figure in millimetres.
Elevation from rotation
The required vertical rise at the heel, capped at 6 mm per shoeing cycle — the maximum safe increment for a single visit.
O'Grady & Steward, AAEP 2007 (the F9 procedure).
The model's key insight
When the palmar angle exceeds 5° alongside rotation, the standard F9 formula under-corrects, because it addresses only the rotational component. The excess palmar angle (PA above 5°) represents additional tendon deformation that needs additional elevation. Adding it to the rotation gives the effective correction angle. This compound model is the contribution of Caldwell & Madden — it is not in the original F9 literature.
Caldwell & Madden 2025, derived from DDFT mechanics; O'Grady 2007 (foundation).
A horse with 8° rotation and a 9° palmar angle, at 130 mm sagittal length: the compound model prescribes 27.1 mm of elevation. A model addressing rotation alone would prescribe 18.1 mm — an under-correction of about 33%. Same radiograph, materially different shoe.
After a tenotomy, the target changes
Once the DDFT has been cut, the objective shifts from correcting rotation to reaching a target palmar angle (typically 3°). Elevation is then set by the difference between current and target PA.
O'Grady 2009 — DDFT tenotomy protocol; Caldwell & Madden 2025.
4 · Centre-of-rotation referenced placement
The pivot of the coffin joint — the centre of rotation (CoR) — is the one stable datum that does not move with conformation. Every shoe-placement distance is referenced to it, not to the toe or the heel.
Where the foot pivots
The CoR of the coffin joint lies at a fixed 49.2% of sagittal length from the heel bulb. This ratio was statistically constant across conformation types (p>0.05) in the Caldwell & Madden dataset, and validated against MRI-confirmed joint position.
Caldwell & Madden 2025, The Equine Foot Vol.2; Caldwell PhD 2017 (blinded MRI trial, n=155 feet).
Where the toe of the shoe ends
P3 is rotated, so its horizontal reach is the bone length projected onto the ground. The fixed 22 mm anterior margin places breakover far enough ahead of the P3 apex to avoid loading it at toe-off, close enough to keep the tendon moment arm short.
O'Grady & Steward AAEP 2007; Caldwell & Madden 2025.
The moment arm loading the lamellae
The distance from the centre of pressure to the toe — the full moment arm bending the dorsal lamellar interface. Shortening it (by moving the centre of pressure palmarly through correct trim and placement) is the biomechanical purpose of the trimming protocol. Beyond 55 mm, a hoof cast is indicated.
Caldwell & Madden 2025.
5 · Mediolateral balance — the dual-vector model
Medial-lateral correction has to resolve a conflict: what the limb needs and what the hoof capsule needs are not always the same direction. The dual-vector model allocates the shoe extension between the two.
Two measurements, one requirement
Physical wall-height difference reflects current capsule asymmetry; the radiographic P3 offset reflects actual bone position. The P3 offset is weighted at half because it is a structural finding that may not be fully correctable within one shoeing cycle. A wall-distortion score then splits the prescription between capsule bracing and limb correction.
Caldwell & Madden 2025 — Dual-Vector ML Model.
6 · Sizing the support: the Turner ratio
Is the foot big enough for the horse?
Bodyweight per unit of solar bearing area, treating the hoof outline as an ellipse. Above 5.5 kg/cm² the foot is overloaded and needs firmer support material to stop P3 bottoming through the pad — relevant for draft breeds and overweight horses with relatively small feet. This drives the Shore-A hardness recommendation.
Turner 1986; threshold confirmed Ogbanya 2017; Caldwell & Madden 2025.
7 · Safety gates — what the maths refuses to do
The model is not one equation but a set of clinical rules. Several thresholds change the prescription or stop farriery altogether.
Sole-depth gates
| Sole depth | Action | Source |
|---|---|---|
| ≥ 15 mm | Standard protocol. No rim pad required. | O'Grady 2007 |
| 12–15 mm | 4 mm EVA rim pad. Conservative trim, no toe reduction. | O'Grady 2007 |
| 8–12 mm | 6 mm EVA + leather. No toe trim; proximal dorsal wall only. | Redden; Caldwell & Madden 2025 |
| < 8 mm | Emergency. 8 mm rim pad. No trim. Vet assessment first. | Redden; Ogbanya 2017 |
| < 6 mm | Penetration risk. Rim pad + hospital plate mandatory. No walking. | Pollitt 1999; Redden |
| < 4 mm | Imminent penetration. Emergency referral. | Cripps & Eustace 1999 |
Cast indication
When the estimated tensile force at the lamellar interface exceeds what a passive shoe can resist, cast immobilisation is indicated. A cast is triggered if any of: rotation > 12°, lamellar lever > 55 mm, or fTensile > 200 N.
Caldwell & Madden 2025.
Red-flag thresholds
| Finding | Threshold | Meaning |
|---|---|---|
| Rotation | > 18° | High risk; sinking likely |
| Palmar angle | negative | Reversed sole — never lower the heels |
| Sole depth | < 4 mm | Imminent penetration |
| Founder distance | > 15 mm | Significant distal displacement (sinking) |
8 · Prognosis from published outcome data
The prognosis the tool reports is not opinion. Return-to-work and survival percentages are mapped from this horse's rotation, sole depth, and degree of sinking onto published outcome datasets.
| Finding | Return to work | Survival |
|---|---|---|
| Mild rotation, good sole depth | ~83% | ~72% |
| Moderate rotation | ~57% | ~62% |
| Severe rotation | ~27% | ~44% |
| Any sinking (distal displacement) | ~27% | ~44% |
Cripps & Eustace 1999, Equine Vet J 31(5):433–442; French et al. 2007.
9 · How we keep it honest
Every constant and equation on this page is implemented in the engine and frozen against a reference. On every release a maths-gate compares fifteen calculation and rendering functions against that frozen reference; if a single byte drifts, the release is blocked. The complete formula reference (F-01 to F-28, with derivations and sources) is maintained as a standalone document for clinical and academic audit. The current state is fifteen of fifteen functions byte-identical, ten of ten clinical scenarios passing.
References
- Caldwell, M.N., Madden, N. & Yxklinten, U. (2026). A Centre-of-Rotation Referenced Biomechanical Model for Prescriptive Farriery in Equine Laminitis. Journal of Equine Veterinary Science. [publication status & DOI to confirm]
- Caldwell, M. & Madden, N. (2025). The Equine Foot: Science, Craft and Clinical Reasoning in Farriery and Podiatry, Vols 1–2. Scientific Horseshoeing Limited.
- Caldwell, M.N. (2017). PhD thesis, University of Liverpool — blinded MRI trial of the centre-of-rotation datum (n=155 feet).
- McGuigan, M.P. et al. (2005). Deep digital flexor tendon force in normal and laminitic ponies. Equine Veterinary Journal, 37(2), 161–165.
- O'Grady, S.E. & Steward, M.L. (2007). Wooden shoe / F9 heel-elevation procedure. Proc. AAEP, 53, 423–429.
- O'Grady, S.E. & Steward, M.L. (2009/2011). DDFT tenotomy and realignment shoeing. Proc. AAEP / J. Equine Vet Sci.
- Cripps, P.J. & Eustace, R.A. (1999). Factors associated with the prognosis for laminitis. Equine Veterinary Journal, 31(5), 433–442.
- French, K.R., Pollitt, C.C. et al. (2007). Equine laminitis: survival to discharge. Equine Veterinary Journal.
- Pollitt, C.C. (1999, 2004). Equine laminitis pathophysiology and the lamellar interface. Proc. AAEP / Clin. Tech. Equine Pract.
- Redden, R.F. (2004). Sole depth and contralateral-limb support. Clin. Tech. Equine Pract., 3(1), 57–63.
- Turner, T.A. (1986). Hoof size, body weight and the foot index. JAVMA, 189(3), 298–301.
- Merkens, H.W. et al. (1993); Clayton, H.M. (2012). Ground reaction force distribution and dynamic loading.
- Obel, N. (1948). Studies on the histopathology of acute laminitis. Uppsala — the original Obel grade.
Citations and attributions marked [under review] are awaiting Mark's final confirmation of source, page, and publication status. The clinical implementation is verified against the source procedure on every release regardless of formatting.