SPINOPELVICUNIT — TECHNICAL AND CLINICAL EVIDENCE APPENDIX
Release 1.2 (4) | implementation and literature audit: 7 November 2026
Anatomical V2 and preserved Legacy V1

A. PURPOSE, EVIDENCE AND IMPLEMENTATION BOUNDARY

This appendix defines what the current source calculates, how each result is signed and attributed, why some fields remain unavailable, and how the clinical literature should be read. It describes two deliberately separate methods. Anatomical V2 introduces the specified lateral-radiograph geometry. Legacy V1 retains historical formulas and thresholds for existing cases. A shared abbreviation does not make those methods equivalent.

The formulas are engineering realizations of cited anatomical definitions and explicitly named app conventions. There is no supplied independently adjudicated clinical accuracy dataset, observer-reliability study, phantom validation report, clinical outcome trial or validated TKA decision rule for this app. Agreement with a paper's definition and success on synthetic coordinates do not constitute clinical validation. A clinical study's own validation or outcome finding cannot be transferred to the application through citation. [1–16,21–24]

Principal source responsibilities:
• MeasurementModels.swift: method identity, anatomical image direction, posture state, optional per-value method attribution and geometry-review state.
• AnatomicalMeasurementEngine.swift and AnatomicalMeasurementCatalog.swift: explicit V2 geometry, availability, named anatomy and no inherited legacy reference bands.
• LandmarkMeasurementEngine.swift and MeasurementCatalog.swift: dispatch plus the preserved V1 engine/catalog.
• MeasurementConstruction.swift and the anatomical construction helper: visual construction lines/arcs; a displayed construction is not an independent measurement.
• MeasurementWorkflowSupport.swift: accepted manual/adjusted composition, dependent fields and posture subtraction order.
• SpinopelvicClassification.swift and CupOrientationPlan.swift: method-aware grouping, research-screen availability and cup-candidate behavior.
• PatientAvatarState.swift and scene/view code: a separate schematic display and control layer.
• CaseReportGenerator.swift and annotated-image export: disclosure of values, method and review state.
• MotionData.swift and the bundled motion JSON: authored anatomy/movement and illustrative mass/activation assumptions.

This is a description of this release, not a promise that every later build is identical. The complete bibliography is numbered 1–24. Original studies and methods were favored. The bibliography is curated rather than exhaustive, and no third-party article PDF or figure is part of the intended app artwork.

B. RECORDS, COMPATIBILITY AND ATTRIBUTION

B.1 Method identity

MeasurementMethod has legacyV1 and anatomicalV2. New empty cases explicitly select anatomicalV2. Historical JSON without a posture method decodes as legacyV1. The low-level PostureRecord initializer retains a legacy default for compatibility; creating a new V2 case is a deliberate application operation. Existing cases are not converted in place. A new V2 assessment requires a separate case and the appropriate image/landmark review; do not overwrite the historical meaning of saved data.

ImageAnteriorDirection is unspecified, left or right. PostureRecord includes imageAspectRatio and geometryReviewRequired. Snapshots carry the method and review state. MeasurementValue can carry an optional method tag. A nonnil tag explicitly conflicting with the posture method is rejected in both calculation paths. A nil tag inherits the containing posture's declared method; that attribution does not verify which external technique produced a manual value. Old nil-tag values in old records remain in V1 because their containing posture defaults to V1.

Provenance remains distinct: derived, retained/manual measured, adjusted, illustrative or unavailable. The new method does not turn illustrative content into measured data. Raw manual/adjusted information is retained for review rather than silently relabelled as an independent anatomical observation.

B.2 Image review is a workflow state

Replacing a source image can retain points, calibration and overrides. A review flag identifies that retained geometry needs rechecking; changing anatomical direction also demands explicit review of signed geometry. Automatic V2 geometry stops while geometryReviewRequired is true. Paired calculations also reject review-required snapshots. This is not an automatic validation of every imported/manual datum: nil per-value tags do not by themselves cause the flag, and acknowledgement is a user review action, not a scientific accuracy test.

C. IMAGE COORDINATES, SCALE AND ANATOMICAL FRAME

C.1 Stored points

Stored u,v are normalized image coordinates in [0,1]. With image width W and height H after display orientation, a=W/H. For an upright lateral image with isotropic source pixels, V2 uses:
  x = s×a×u; y = −v.
  s=+1 if anterior is image right; s=−1 if anterior is image left.
The result is an anterior-positive x axis and cranial-positive y axis, in a common image-height scale. Translation is immaterial. Both coordinates must be finite and within the accepted normalized image bounds before transformation.

V2 requires a finite positive a, a selected anterior direction and a reviewed record. It does not guess left/right from point positions. It does not correct arbitrary image rotation, anisotropic source pixels, stretching, projection distortion or transverse patient rotation. Horizontal/vertical refer to the correctly positioned source image. The still-image workflow does not establish DICOM row/column spacing or radiographic magnification.

V1 uses q=(a×u,v) when valid aspect metadata exist, preserving screen-positive-y. A nil aspect retains q=(u,v) with a review diagnostic; an explicitly invalid aspect cannot provide valid automatic geometry. For example, 100 image pixels in each direction on a 1000×2000 image are (0.1,0.05) in separately normalized storage, but become (0.05,0.05) in the restored common scale. The respective angles 26.565° and 45° illustrate why a scalar length calibration cannot generally repair missing anisotropic normalization. This arithmetic example is not a clinical accuracy estimate.

C.2 Physical distances and dimensionless ratio

Given reference length L>0 and two distinct reference endpoints in the same restored metric frame:
  k = L / hypot(ΔxReference,ΔyReference).
V2 signed horizontal displacement is k×Δx. The calibration helper converts the absolute magnitude and reapplies the offset sign. Finite zero offsets remain zero. A missing/invalid scale, nonpositive L, coincident reference points or non-finite result yields unavailable mm, not an assumed zero. V1 distance constructions retain absolute horizontal offsets.

The V2 ratio divides two same-image horizontal offsets, so k cancels. No mm calibration is required for the geometric ratio. A valid override of either distance changes the problem: the ratio then uses matching effective mm values, or is unavailable if they are not both available with positive SFD. An explicit ratio override takes precedence. A marker's placement and projection must still be assessed clinically for every reported mm result.

D. ANATOMY, VECTOR OPERATIONS AND ACCEPTED BRANCHES

D.1 Named landmarks

A and P are respectively anterior and posterior-superior S1 endplate corners; S=(A+P)/2. H is the explicit bicoxofemoral midpoint, or the mean of both projected femoral-head centres. The explicit point takes precedence; an invalid explicit point is not silently replaced by the paired alternative. The old single-head point is not a V2 substitute. C is the C7 vertebral-body centre.

L1A/L1P identify the superior L1 endplate. T1 and T12 identify the superior T1 and inferior T12 endplates. Fprox/Fdist are two diaphyseal centre points ordered proximal to distal. Cup rim point1/point2 identify the projected opening ellipse's long axis; the separate cup-opening direction point chooses its visibly open side. Its distance does not determine cup size. S1 promontory, pubic symphysis, generic APP points, cup centre and old cup-axis tip remain historical identifiers; V2 does not use them as substitutes. [1,14,21–24]

D.2 Helpers

For finite nonzero vectors p,q:
  dot(p,q)=p.x×q.x+p.y×q.y.
  cross(p,q)=p.x×q.y−p.y×q.x.
  signedAngle(p,q)=atan2(cross(p,q),dot(p,q))×180/π.
The implementation normalizes the two vectors before the cross/dot operation. Zero-length or non-finite vectors are rejected. θ(e)=atan2(e.y,e.x)×180/π. An anterior-directed endplate requires e.x>0; a reversed or exactly vertical declared tangent is unavailable rather than silently reordered. These are explicit geometric acceptance rules, not inferred diagnoses.

The sacral tangent is e=A−P. S1 descends anteriorly for positive SS. The cranial S1 normal is n=(−e.y,e.x). For the pelvic vector v=S−H, the upright protocol requires v.y>0. PT=atan2(−v.x,v.y) preserves negative PT. PI is the signed angle n→v on the nonnegative branch: below −1e−9° is unavailable, and absolute angle below 1e−9° is normalized to zero. On that accepted branch PI=PT+SS. Do not replace a rejected negative branch with its absolute value or complementary angle merely to restore a plausible result. [1,21,24]

LL is θ(L1 tangent)−θ(S1 tangent), positive lordosis and negative net kyphosis. TK is θ(T12 tangent)−θ(T1 tangent), using the specified fixed span. These signed differences are not acos magnitudes. SSA is the absolute signed angle from the anterior S1 tangent to C−S; it keeps the obtuse anatomical branch. Anterior-positive SVA uses C−P, and SFD uses H−P in the horizontal direction. [14,22]

D.3 Directed PFA and cup normal

Let d=Fdist−Fprox. PFA is the counterclockwise angle d→v mapped to [0°,360°); a near-zero signed angle below 1e−9° in magnitude is normalized to zero. Values above 180° are necessary, not errors to fold away. On the usual branch, FI=atan2(d.x,−d.y) and PFA=180°+PT−FI. Thus vertical femur with PT 15° gives PFA 195°, while PT 40° with femur inclined 75° anteriorly gives PFA 145°. The primary triangle illustrates this distinction. [23]

For rim vector r=point2−point1 and midpoint M, choose unit candidate normal nCup=(−r.y,r.x)/|r|. Let w=openingPoint−M. If dot(nCup,w)<0, reverse the normal. If w is zero or |dot(nCup,w)|≤|w|×1e−8, the open side is geometrically ambiguous and the result is unavailable. This relative tolerance resolves numerical collinearity; it is not an estimate of clinical precision. Reversing rim endpoint order alone does not change the final outward normal.

AI=atan2(nCup.x,−nCup.y)×180/π, signed from caudal vertical, in approximately [−180°,180°]. Negative AI and AI>90° remain visible with a review diagnostic. The rim-to-horizontal representation corresponds to the normal-to-caudal-vertical definition; measuring the normal from horizontal creates the wrong complement. CSI is the unwrapped sum PFA+AI for the same hip/posture/method. The opening-side construction is an implementation derivation of the published axis definition, not a separately validated novel measurement technique. [13,14]

E. COMPLETE TWO-METHOD FORMULA REGISTER

All 32 catalog fields remain addressable and searchable. V2 has 14 single-posture automatic outputs, including dependent/alias fields, five named comparisons composed from compatible records, and 13 manual/external/additional-view/model fields. A catalog identifier alone does not mean the lateral engine measures it. V1 retains 20 single-posture constructions, six comparison fields and six other fields.

The notation in each V2 entry refers to the canonical frame above. The V1 expression refers to the restored screen frame or historical nil-aspect fallback; angle(a,b) is its unsigned acos-based angle. V1 source point names, clinical distinctions and retained bands are reproduced for interpretability, not endorsed as standard definitions.

E.01. thoracicKyphosis
Unit: degrees.
Anatomical V2 equation: θ(T12 inferior, posterior→anterior) − θ(T1 superior, posterior→anterior).
V2 interpretation/availability: Positive denotes the declared kyphotic direction. The fixed T1–T12 span is not automatically equivalent to T4–T12 or another study span. Both endplates and image orientation are required. [2,3,17]
Legacy V1 equation: angle(T1 anterior→posterior, T12 anterior→posterior).
V1 actual construction: Unsigned angle between the selected T1 superior-endplate line and T12 inferior-endplate line.
V1 band: Standing: 10 ≤ TK ≤ 40. Retained legacy range.

E.02. lumbarLordosis
Unit: degrees.
Anatomical V2 equation: θ(L1 superior, posterior→anterior) − θ(S1 superior, posterior→anterior).
V2 interpretation/availability: This is L1–S1, not the legacy L1–L5 construction. Preserve a negative angle. Projection, vertebral rotation and endpoint selection remain sources of error. [1,4,5,14,21]
Legacy V1 equation: angle(L1 anterior→posterior, L5 anterior→posterior).
V1 actual construction: Unsigned angle between the selected L1 superior-endplate line and L5 inferior-endplate line.
V1 band: No configured band.

E.03. totalLumbarLordosis
Unit: degrees.
Anatomical V2 equation: No separate automatic construction; external method/manual only.
V2 interpretation/availability: Do not assume TLL is another automatic LL result or an independent confirmation of it. [2,3]
Legacy V1 equation: unavailable in LandmarkMeasurementEngine.
V1 actual construction: No automatic calculation is implemented in the landmark engine; it remains unavailable unless a value is entered or imported.
V1 band: No configured band.

E.04. sacralSlope
Unit: degrees.
Anatomical V2 equation: −θ(e) = atan2(−e.y,e.x) ×180/π, e=A−P.
V2 interpretation/availability: The image must be upright and anterior side explicitly selected. A genuine negative angle is retained rather than reflected. Sacral change alone does not diagnose lumbar stiffness. [1,10,15,20,21,24]
Legacy V1 equation: atan2(S1post.y−S1ant.y, S1post.x−S1ant.x) in degrees.
V1 actual construction: Signed screen-plane line angle from the anterior to the posterior S1 endplate point, measured with atan2.
V1 band: No per-posture band.

E.05. sacralTilt
Unit: degrees.
Anatomical V2 equation: Manual/external only; do not reuse the V1 three-point ST construction.
V2 interpretation/availability: Some authors use sacral tilt as a synonym for SS. State whether that is intended; a separate ST field is not evidence of another measured degree of freedom. [1,20,23]
Legacy V1 equation: angle(S1ant→S1post, S1post→promontory).
V1 actual construction: Unsigned angle between the S1 anterior→posterior line and the S1 posterior→sacral-promontory line.
V1 band: Standing: 30 ≤ ST ≤ 50. Relaxed seated: 11 ≤ ST ≤ 29. Legacy ranges.

E.06. pelvicTilt
Unit: degrees.
Anatomical V2 equation: atan2(−v.x,v.y) ×180/π, v=S−H, requiring v.y>0.
V2 interpretation/availability: Posterior displacement of S1 relative to the hip axis is positive; anterior is negative. S1 must be cranial to the hip axis. Use the explicit bicoxofemoral midpoint or both head centres, not one arbitrary hip point. [1,5,6,21,24]
Legacy V1 equation: angle(hip→promontory, hip→(hip.x, hip.y+1)).
V1 actual construction: Unsigned angle from the femoral-head-centre→sacral-promontory line to the positive-y vertical at the hip point.
V1 band: Standing: 0 ≤ PT < 20. The retained threshold does not validate this construction.

E.07. spinopelvicTilt
Unit: degrees.
Anatomical V2 equation: Manual/external only; no PT alias and no automatic flexed research screen.
V2 interpretation/availability: SPT terminology and signs vary. Aubert assigns anterior rotation a positive sign, unlike conventional positive-retroversion PT. V2 does not generate the legacy SPT research flag. [11,15,16]
Legacy V1 equation: atan2(promontory.y−hip.y, promontory.x−hip.x) in degrees.
V1 actual construction: Signed screen-plane angle of the femoral-head-centre→sacral-promontory line.
V1 band: No configured band.

E.08. totalPelvicTilt
Unit: degrees.
Anatomical V2 equation: Manual/external only; no duplicate of PT or SPT.
V2 interpretation/availability: The label alone does not identify a unique anatomical method. Record landmarks, reference axis, sign, posture and source. [1,17,21]
Legacy V1 equation: same calculation as SPT.
V1 actual construction: The same signed hip-centre→sacral-promontory line angle as SPT.
V1 band: No configured band.

E.09. pelvicIncidence
Unit: degrees.
Anatomical V2 equation: signedAngle(n,v) on its accepted nonnegative branch, n=(−e.y,e.x), v=S−H; reject angle<−1e−9°, normalize |angle|<1e−9° to 0.
V2 interpretation/availability: Uses the midpoint and perpendicular, not the promontory or sacral tangent. PI = PT + SS on the declared branch. A failed branch or reversed anatomy is unavailable, not replaced by a complement. This geometric identity is not clinical validation. [1,21,24]
Legacy V1 equation: angle(S1ant→S1post, hip→promontory).
V1 actual construction: Unsigned angle between the S1 anterior→posterior endplate vector and the femoral-head-centre→sacral-promontory vector.
V1 band: All postures: 48 ≤ PI ≤ 53. Legacy population-like range, not a universal normal interval.

E.10. pelvicIncidenceMinusLumbarLordosis
Unit: degrees.
Anatomical V2 equation: PI − signed L1–S1 LL, using effective constituents unless explicitly overridden.
V2 interpretation/availability: The V2 group uses signed standing mismatch. A large negative result is not converted to positive flatback or treated as proof of normal anatomy. Inspect any explicit composite override. [3,7,9,15,21]
Legacy V1 equation: PI − LL; category alignment input = abs(PI−LL).
V1 actual construction: Signed arithmetic difference of the engine PI and engine LL values. The category routine separately uses its absolute value.
V1 band: Standing display band: 0 ≤ PI−LL < 10. Category uses |PI−LL| < 10 instead.

E.11. appTilt
Unit: degrees.
Anatomical V2 equation: Manual/external only; generic APP image points do not reconstruct an anatomical plane.
V2 interpretation/availability: A true APP requires defined ASIS and pubic references; two arbitrary image points do not reconstruct that three-dimensional plane. PT is not silently substituted. [13,14]
Legacy V1 equation: atan2(APPpost.y−APPant.y, APPpost.x−APPant.x) in degrees.
V1 actual construction: Signed angle of the selected APP anterior→posterior line in the image.
V1 band: No configured band.

E.12. sagittalVerticalAxis
Unit: mm.
Anatomical V2 equation: k×(C.x−P.x); signed, zero allowed.
V2 interpretation/availability: A valid zero is 0 mm. Correct C7 centre, posterior S1 reference, upright image and same-image calibration are required. This is not the patient gravity line or a force-plate result. [3,5,17,22]
Legacy V1 equation: abs(C7.x−promontory.x) × calibration factor.
V1 actual construction: Absolute horizontal separation between the selected C7 point and sacral-promontory point, converted through calibration.
V1 band: Standing: 0 ≤ SVA < 40. Do not transfer the adult-deformity threshold to this altered construction.

E.13. c7PlumbLineDistance
Unit: mm.
Anatomical V2 equation: Alias of V2 SVA; same posterior-superior S1 reference.
V2 interpretation/availability: It is not a second independent balance measurement. Review inconsistent separately entered alias values; do not count them as corroboration. [17,22]
Legacy V1 equation: same calculation as SVA.
V1 actual construction: The same calibrated absolute C7-to-sacral-promontory horizontal separation as SVA.
V1 band: No configured band.

E.14. spinosacralAngle
Unit: degrees.
Anatomical V2 equation: abs(signedAngle(e,C−S)), yielding0…180° with the obtuse branch preserved.
V2 interpretation/availability: Use the S1 midpoint and correct ray direction. With SS 45° and C7 directly cranial to the midpoint, SSA is 135°, not 45°. It is not an independent gravity measurement. [22]
Legacy V1 equation: angle(C7→promontory, S1ant→S1post).
V1 actual construction: Unsigned angle between C7→sacral-promontory and S1 anterior→posterior vectors.
V1 band: Standing: 127 ≤ SSA ≤ 143. Legacy range.

E.15. sagittalFemoralDistance
Unit: mm.
Anatomical V2 equation: k×(H.x−P.x); signed distance including zero/negative raw separation.
V2 interpretation/availability: This replaces the legacy C7-to-hip construction only in V2. Negative or zero separation is retained for review; the conventional ratio requires a strictly positive denominator. [22]
Legacy V1 equation: abs(C7.x−hip.x) × calibration factor.
V1 actual construction: Absolute horizontal separation between the selected femoral-head centre and C7, after calibration.
V1 band: No configured band.

E.16. c7PlumbLineToSfdRatio
Unit: ratio.
Anatomical V2 equation: (C.x−P.x)/(H.x−P.x), requiring denominator>0; scale-free unless constituent override requires effective mm composition.
V2 interpretation/availability: Scale cancels for image geometry. The denominator must be positive. If a distance is overridden, the ratio requires matching effective mm offsets or an explicit ratio override; stale geometry is not substituted. [22]
Legacy V1 equation: SVA / SFD.
V1 actual construction: The computed SVA value divided by the computed SFD value, with a nonzero denominator required.
V1 band: Standing: −1.9 ≤ ratio ≤ 0.1. Legacy range; negative values cannot arise from the current automatic nonnegative distances.

E.17. pelvicRetroversionAngle
Unit: degrees.
Anatomical V2 equation: Manual/external only; no independent PRA angle invented from PT.
V2 interpretation/availability: Posterior pelvic rotation is represented by increasing conventional PT, but the PRA name does not supply another validated angle or permit a promontory-based substitute. [1,21,24]
Legacy V1 equation: same calculation as PT.
V1 actual construction: The same unsigned hip→promontory versus positive-y vertical angle as PT.
V1 band: No configured band.

E.18. pelvicFemoralAngle
Unit: degrees.
Anatomical V2 equation: wrap360(signedAngle(d,v)); d=Fdist−Fprox, v=S−H. Values>180° retained; near-zero signed result |angle|<1e−9° becomes0.
V2 interpretation/availability: Two shaft-centre points are essential. Pubic symphysis is not a substitute. Values above 180° are expected in the defined standing branch; a smaller unsigned angle would discard extension. [11,12,14,23]
Legacy V1 equation: angle(hip→promontory, hip→pubicSymphysis).
V1 actual construction: Unsigned angle between hip→sacral-promontory and hip→pubic-symphysis vectors.
V1 band: Standing: 165 ≤ PFA ≤ 195. Relaxed seated: 113 ≤ PFA ≤ 137. Legacy ranges.

E.19. acetabularInclination
Unit: degrees.
Anatomical V2 equation: atan2(nCup.x,−nCup.y) ×180/π, with outward unit normal selected by rim endpoints and opening-side point.
V2 interpretation/availability: This is not AP radiographic inclination or anteversion. Negative and >90° results are retained with a review diagnostic. Ambiguous opening side is unavailable. The old cup-centre/axis-tip line is not substituted. [13,14,23]
Legacy V1 equation: abs(atan2(cupTip.y−cupCentre.y, cupTip.x−cupCentre.x)) in degrees.
V1 actual construction: Absolute signed-line angle of cup centre→cup axis tip relative to the screen horizontal.
V1 band: Standing: 25 ≤ AI ≤ 45. Relaxed seated: 42 ≤ AI ≤ 62. Legacy ranges.

E.20. sagittalAcetabularAngle
Unit: degrees.
Anatomical V2 equation: Manual/external only; historical SAA identifier is not silently changed to SS+AI.
V2 interpretation/availability: Published SAA can mean sacroacetabular angle = SS + AI; that is different from the legacy label and construction. V2 does not rename or substitute it silently. [13,14,23]
Legacy V1 equation: angle(APPant→APPpost, cupCentre→cupTip).
V1 actual construction: Unsigned angle between the selected APP line and cup-centre→cup-axis-tip line.
V1 band: All postures: 60 ≤ SAA ≤ 90. Legacy range.

E.21. cupSpineIndex
Unit: degrees.
Anatomical V2 equation: PFA + signed sagittal AI, same posture/hip/method; unwrapped sum, recomputed unless explicitly overridden.
V2 interpretation/availability: Recomputed after compatible constituent overrides unless CSI itself is explicitly overridden. A numeric CSI is not an automatically safe zone, instability probability or TKA component target. [12–14,23]
Legacy V1 equation: SAA + SS; not published PFA + ante-inclination.
V1 actual construction: The sum of the engine SAA and SS values.
V1 band: Standing: 217 ≤ CSI ≤ 243. Relaxed seated: CSI ≥ 152. Legacy ranges.

E.22. deltaSS
Unit: degrees.
Anatomical V2 equation: SSstanding − SSrelaxed.
V2 interpretation/availability: Positive commonly represents posterior pelvic rotation on sitting. Negative change is shown as direction information but cannot enter the V2 category. It is not continuously measured motion or a direct lumbar-stiffness test. [9,10,15,20]
Legacy V1 equation: SSrelaxed − SSstanding.
V1 actual construction: Relaxed-seated SS minus standing SS.
V1 band: Standing-tagged comparison: ΔSS > 10; exactly 10 is outside the band.

E.23. deltaPT
Unit: degrees.
Anatomical V2 equation: PTrelaxed − PTstanding.
V2 interpretation/availability: This order differs from the SS reduction because their anatomical signs differ. Preserve the posture names and review the PI/SS/PT relationship. [5,6,20,21]
Legacy V1 equation: PTrelaxed − PTstanding.
V1 actual construction: Relaxed-seated PT minus standing PT.
V1 band: No configured band.

E.24. deltaSPT
Unit: degrees.
Anatomical V2 equation: No automatic V2 comparison/screen. An explicitly entered ΔSPT remains an external/raw audit value.
V2 interpretation/availability: A manually retained SPT cannot be assumed to reproduce Aubert’s measurement, direction or threshold. V2 does not turn it into the ≥20° research screen. [11,15,16]
Legacy V1 equation: SPTflexed − SPTstanding.
V1 actual construction: Flexed-seated SPT minus standing SPT.
V1 band: No display band; research-screen threshold ≥20°.

E.25. deltaLL
Unit: degrees.
Anatomical V2 equation: LLstanding − LLrelaxed in the main comparison; an explicitly named flexed pair remains a separate protocol.
V2 interpretation/availability: The default relaxed comparison is not the flexed-seated lumbar-flexion research protocol. Do not relabel a posture or infer spinal stiffness from a different pair. [10,15,20]
Legacy V1 equation: LLrelaxed − LLstanding.
V1 actual construction: Relaxed-seated LL minus standing LL.
V1 band: No configured band.

E.26. deltaPFA
Unit: degrees.
Anatomical V2 equation: PFAstanding − PFAflexed; no abs or modulo correction of the difference.
V2 interpretation/availability: A numeric change remains available when valid, but V2 does not issue the legacy ≥95° research flag. Matching a research threshold requires its complete protocol, not only this subtraction. [11,23]
Legacy V1 equation: PFAflexed − PFAstanding.
V1 actual construction: Flexed-seated PFA minus standing PFA.
V1 band: No display band; research-screen threshold ≥95°.

E.27. deltaAI
Unit: degrees.
Anatomical V2 equation: AIrelaxed − AIstanding in the main comparison. A supplementary flexed AI difference is separately labelled AIflexed − AIstanding.
V2 interpretation/availability: Use the same hip, opening-side convention and method. Do not substitute AP cup angles or interpret the change as a knee implant measurement. [13,14,23]
Legacy V1 equation: AIselected − AIstanding in workspace/PNG; report comparisons separately use AIrelaxed − AIstanding and AIflexed − AIstanding.
V1 actual construction: In the legacy workspace/PNG, selected-posture AI minus standing AI, including zero on the standing view. The text report separately lists relaxed−standing and flexed−standing AI.
V1 band: No configured band.

E.28. pelvicObliquity
Unit: degrees.
Anatomical V2 equation: No automatic result from the lateral engine; a separate coronal method is required.
V2 interpretation/availability: Projected left/right head centres on a lateral view do not provide the missing coronal information. [17]
Legacy V1 equation: unavailable in LandmarkMeasurementEngine.
V1 actual construction: No automatic measurement is supplied by the single lateral-image engine.
V1 band: No configured band.

E.29. pelvicRotation
Unit: degrees.
Anatomical V2 equation: No automatic result from the lateral engine; a separate axial/3D method is required.
V2 interpretation/availability: Do not infer a missing view or axial anatomy from an apparently rotated avatar. [13,17]
Legacy V1 equation: unavailable in LandmarkMeasurementEngine.
V1 actual construction: No automatic measurement is supplied by the lateral-image engine.
V1 band: No configured band.

E.30. modelCenterOfMassOffset
Unit: offset (model frame; not a patient mm unit).
Anatomical V2 equation: No patient-image COM solver; model/external data require their own frame and units.
V2 interpretation/availability: It is not measured patient COM, centre of pressure, muscle force, joint load or fall risk. The catalog offset is not a guaranteed patient millimetre unit. [17,18]
Legacy V1 equation: model-only; no patient COM solver in the landmark engine.
V1 actual construction: Not a patient radiograph calculation; authored scene/animation data may display model COM coordinates.
V1 band: No configured band.

E.31. gravityVectorOffset
Unit: offset (model frame; not a patient mm unit).
Anatomical V2 equation: No patient gravity-line, force or centre-of-pressure solver.
V2 interpretation/availability: A rendered vector does not measure ground reaction, joint moment or patient balance. C7 plumb offset is a different construct. [17,18]
Legacy V1 equation: model-only; no force-plate or patient gravity-line measurement.
V1 actual construction: Not a patient radiograph calculation; the scene displays a model gravity reference.
V1 band: No configured band.

E.32. theoreticalReference
Unit: none.
Anatomical V2 equation: Reference-only; no automatic patient measurement.
V2 interpretation/availability: State the source, population, coordinate frame and assumptions. A theoretical value is not an individual treatment target. [1,2,17]
Legacy V1 equation: unavailable in LandmarkMeasurementEngine.
V1 actual construction: A reference-only catalog field with no automatic patient calculation.
V1 band: No configured band.

F. EFFECTIVE VALUES AND DEPENDENCIES

F.1 Composition order

The workflow calculates the method-specific landmark snapshot, applies accepted retained/manual values, then accepted adjusted values. An explicit conflicting nonnil method tag is ignored with a diagnostic in either method; historical nil tags remain attributable to their containing posture. For V2, override acceptance also requires a finite numeric value, matching unit, applicable or unspecified posture, and provenance other than unavailable/illustrative. Acceptance is a data-consistency check, not confirmation of a clinician's external measurement technique.

In V2, dependent composites are recomputed after accepted inputs at each composition stage unless the composite has an explicit accepted override:
• PI−LL = effective PI − effective signed LL.
• CSI = effective PFA + effective sagittal AI.
• A sole SVA/C7PLD alias override updates the other alias unless it too is explicitly overridden.
• A relevant SVA/C7PLD/SFD override recomputes the ratio from effective calibrated SVA divided by strictly positive SFD, unless the ratio is explicitly overridden. If the required effective mm pair is unavailable, the ratio becomes unavailable rather than falling back to stale geometry.
Without those distance overrides, keep the scale-free geometric ratio even if no scale is available. A dependent value is adjusted when the effective constituent adjustment propagates; raw and adjusted provenance remain reviewable.

An explicit composite override has priority and can intentionally differ from its components. Both aliases can also be explicitly entered inconsistently. The app does not hide those entries or prove their clinical consistency. Users must inspect their methods and reasons.

V1 retains its original per-field composition behavior. PI−LL is not automatically rebuilt after independent PI/LL overrides, and CSI is not rebuilt from effective SAA/SS overrides. This is a historical-method limitation, not a global claim about V2.

F.2 Comparison order and gate

The compared snapshots must identify the required distinct postures, have the same method, have no pending geometry review, and contain finite required values. V2 SS, LL and PFA comparisons use first minus second. V2 PT and AI use second minus first. The default displayed rows are:
  ΔSS = SSstanding−SSrelaxed.
  ΔPT = PTrelaxed−PTstanding.
  ΔLL = LLstanding−LLrelaxed.
  ΔPFA = PFAstanding−PFAflexed.
  ΔAI = AIrelaxed−AIstanding.
The supplementary flexed AI difference, where shown, is separately labelled AIflexed−AIstanding. The default LL row must not be represented as flexed-seated lumbar flexion. No absolute value or automatic modulo wrapping is applied to these differences.

V2 ΔSPT is manual/external only in comparison presentation. Even separately entered manual SPT values do not create the automatic ΔSPT research screen. An explicitly entered ΔSPT can remain in raw/audit entries with its protocol. V1 preserves second-minus-first comparison direction. SS/PT/LL use relaxed seated, and SPT/PFA use flexed seated. Legacy workspace/PNG ΔAI uses the currently selected posture minus standing, including zero on the standing view; the text report separately lists relaxed−standing and flexed−standing AI.

G. EXACT CLASSIFICATION AND CUP BEHAVIOR

G.1 Anatomical V2 profile

The four labels describe signed standing PI−LL and standing-to-relaxed sacral-slope change under the explicit Fontalis 2026 Table 2 equality convention, within the original THA hip–spine framework. They are not the SRS–Schwab or Roussouly classifications, and not a TKA decision rule. Published equality choices vary; the named profile makes this implementation reproducible. [2,3,9,15]

A=standing signed PI−LL, M=SSstanding−SSrelaxed.
1A: A≤10°, M≥10°.
1B: A≤10°, 0≤M<10°.
2A: A>10°, M≥10°.
2B: A>10°, 0≤M<10°.

At exact 10°, the mismatch branch is type 1 and the mobility branch is mobile. The classifier uses unrounded values, so a formatted 10.0 can lie on either side. It does not apply abs to mismatch. A negative mismatch belongs to the no-positive-mismatch branch of this rule, not a guarantee of normal overall alignment. Negative M is unavailable under an explicit extra app direction-review guard; do not attribute that restriction to the paper. Mixed methods, pending review and missing/non-finite required inputs also prevent a category.

The group describes a posture-pair observation, not an individualized dislocation probability or proof of lumbar stiffness. Low relaxed-seated sacral change and limited lumbar flexion are different observations; the literature specifically cautions against treating one as the other. [10,15]

V2 returns no automatic legacy flexed-seated research flags and no automatic cup-candidate range. This does not remove manual cup orientation/visualization controls. It avoids turning the corrected numerical group into an unsupported automatic surgical recommendation. Actual compatible PFA change remains displayed.

G.2 Preserved Legacy V1 profile

A=abs(standing PI−LL), M=SSrelaxed−SSstanding. Require finite A,M and M≥0.
1A: A<10°, M>10°.
1B: A<10°, 0≤M≤10°.
2A: A≥10°, M>10°.
2B: A≥10°, 0≤M≤10°.
Exactly 10° therefore has the opposite equality assignment from V2 at both branches. V1 flexed screens remain SPTflexed−SPTstanding≥20° and PFAflexed−PFAstanding≥95°, review only. Their geometry and signs must not be represented as replication of the Aubert protocol. [11]

V1 cup candidates preserve inclusive inclination/anteversion constants:
1A [40,45]°/[20,25]°.
1B [45,45]°/[25,30]°.
2A [40,45]°/[20,25]°.
2B [40,45]°/[25,35]°.
No available group means no range. These THA teaching constants are not universal safe zones, patient-specific optimization or knee-component targets. Selecting or overriding a model value does not validate it. [9,12–16]

H. REFERENCE BANDS AND PROVENANCE DISPLAY

V2 descriptor reference-band arrays are empty. No legacy green/red numerical band is transferred to the corrected definition. This does not suppress the separately named classifier or provenance; a neutral result still needs interpretation. Adjusted, illustrative and unavailable states remain distinct.

V1 retains these bands, where applicable: standing TK 10–40; standing ST 30–50 and relaxed ST 11–29; standing 0≤PT<20; PI 48–53 across postures; standing 0≤PI−LL<10; standing SVA 0≤value<40mm; standing SSA 127–143; standing C7PL/SFD −1.9–0.1; standing PFA 165–195 and relaxed 113–137; standing AI 25–45 and relaxed 42–62; SAA 60–90 across postures; standing CSI 217–243 and relaxed CSI≥152; and the standing-tagged ΔSS>10 display rule. Endpoints are inclusive unless an explicit < or > is written. Fields not listed have no applicable configured band.

These intervals are historical display behavior, not claims of validated normality for altered V1 constructions. V1 classification also differs from its displayed mismatch band by taking abs. No color or band membership independently establishes disease, clinical safety or treatment need.

I. AVATAR, PRESENTATION GESTURES AND AUTHORING ASSUMPTIONS

I.1 Scalar controls and method awareness

PatientAvatarState starts from the method-specific measured snapshot, including accepted retained/manual fields. Its own controls form a separate layer from stored case adjustments. V2 uses sagittal AI as the cup scalar; V1 uses the historical SAA field. The avatar's PT, LL, SS and cup adjustments do not overwrite saved radiographic landmarks or calibration. Pelvis, lumbar and hip controls drive the skeletal pose; SS and cup controls are numerical scalar references and do not independently rotate their anatomical meshes. V2 reuses the audited composition rules for resulting dependent values; a preserved explicit composite override remains explicit.

Display height defaults to 1.70 m and is limited to 1.20–2.20 m. Display scale equals height/1.70. PT, LL, SS and cup control deltas are limited to −30°…+30°; the separate illustrative hip-flexion adjustment to −45°…+45°; phase to 0…1. Those are interface/control limits, not physiological normal ranges or clinical measurement validation.

With c=sin(2π×phase), the authored activity offsets are:
Standing: pelvic 0°, hip 0°, lumbar 0°.
Sitting: pelvic +20°, hip +80°, lumbar −18°.
Walking: pelvic 4c°, hip 25c°, lumbar 3c°.
Transfer: t=clamp(2×phase,0,1); pelvic (1−t)×20°, hip (1−t)×80°, lumbar (1−t)×(−18)°.
The transfer scalar reaches its standing endpoint at phase 0.5 and remains there afterward. This is an authored display function, not a recorded transition. V2 preserves signed lumbar pose input plus activity offset; V1 retains its historical nonnegative lumbar pose floor. The visible pose can differ from the raw measurement because of activity and display adjustments. Missing inputs can use a neutral visual default while the measurement remains unavailable.

I.2 Gestures are display transforms

Supported drag, pinch/magnification and rotation gestures, together with visible controls, translate, scale and rotate the avatar/AR presentation. iOS AR uses pan/pinch/rotation on placed content; visionOS provides supported targeted spatial gestures. Hardware capability, permission and anchoring affect the available path. These transformations do not alter the measurement coordinate frame, reference length or saved point positions. A world-space model metre or a visually enlarged skeleton is not proof of patient registration, anatomical reconstruction or surgical navigation.

I.3 Bundled motion and muscle display

The asset describes CT-derived partial anatomy with explicitly schematic completion and illustrative kinematics. It is not patient motion capture. Authored mode data are walking 1.1 seconds / 67 samples; standing 8 seconds / 121 samples; sitting 8 seconds / 121 samples; transfer 12 seconds / 241 samples. Transfer uses prescribed ankle targets and a geometric two-link inverse-kinematics construction. These stored animation samples differ from the simpler scalar activity offsets above.

The asset contains 146 muscle definitions. Activation parameters are normalized 0…1 and carry authored timing metadata. They are visual phase emphasis, not EMG, motor-unit recording, percent MVC, measured strength, tendon force or a physiological inverse-dynamics estimate. An empirical gait paper supplies context, not validation of unrelated authored animation. [19]

I.4 Model centre of mass and gravity

The illustrative total mass is 75 kg. Reference mass fractions are HAT 0.6028, each thigh 0.1416, each shank 0.0433 and each foot 0.0137, summing to 1. Segment COM fractions are hip-to-knee 0.4095, knee-to-ankle 0.4395 and heel-to-toe 0.4415. The authored HAT COM position is 0.65×T12+0.25×C7+0.10×Head, plus 25 mm local-anterior offset at T12. Aggregate COM is the mass-weighted model position under those assumptions.

The reference fractions cite de Leva's anthropometric work, while the chosen HAT position and schematic completion are authored assumptions. They are not the patient's measured mass distribution or recorded body weight. The motion decoder checks finite/ordered values, quaternions, activation bounds, mass and a world-Y-down gravity convention; passing those schema checks does not establish clinical validity. [18]

Radiographic C7 offset, whole-body COM, a gravity line, centre of pressure, support-polygon geometry and ground reaction are distinct constructs. The app does not acquire force-plate data or solve patient-specific muscle forces, joint moments or a validated fall-risk score. Dedicated whole-body/gravity studies illustrate why those measurements must not be conflated. [17–19]

J. WHY THIS INFORMATION IS USEFUL TO A TKA SURGEON

The direct TKA evidence supports considering knee extension, lumbar alignment, back symptoms, previous fusion and compensatory posture together. Murata describes knee–spine association; Kitagawa examines alignment and low-back symptoms around TKA; Shichman studies a fusion-related subgroup; Sheppard examines spondylolisthesis/mismatch; Li examines pelvic incidence and femoral-component sagittal relationships. These are study-specific associations, not a universal causal or surgical algorithm. [4–8]

V2 makes the selected observations easier to communicate because the anatomy, direction and posture pair are explicit. A surgeon can explain whether a number represents pelvic morphology, pelvic orientation, lumbar curvature, global offset, femur-to-pelvis angle, cup orientation or a change between two images. Those categories answer different questions. They cannot establish which structure caused a patient's pain or prescribe a distal femoral resection, tibial slope, rotation, mechanical axis, ligament balance or operation sequence.

THA studies explain functional hip orientation and why spinal/pelvic posture may matter in a patient with coexisting hip pathology. They do not validate a TKA risk category. A corrected formula is a measurement-method improvement; outcome claims still need independent study. Roussouly and SRS–Schwab background references do not mean those full classification systems are implemented. [2,3,9–16]

K. SYNTHETIC EXAMPLES AND RELEASE LIMITS

K.1 Examples with stated assumptions

In canonical isotropic coordinates choose H=(0,0), S=(−25.8819045103,96.5925826289), S1P=(−40.0240401340,110.7347182526), S1A=(−11.7397688865,82.4504470052). S1 descends 45° anteriorly, while the pelvic vector is 15° posterior to cranial vertical. Therefore SS 45°, PT 15°, PI 60°. Add an L1 anterior-directed tangent at +15° to get LL 60° and mismatch 0°. A vertical distal femoral shaft gives PFA 195°. A cup outward normal (sin30°,−cos30°) gives AI 30° and CSI 225°. C7 directly 300 coordinate units cranial to S gives SSA 135°; with k=1, SVA14.1421356237mm, SFD40.0240401340mm and ratio0.35334103145.

A second constructed posture with SS 20°, PT 40°, fixed PI 60°, horizontal L1 superior endplate and femoral inclination 75° gives LL 20° and PFA 145°. AI 55° gives CSI 200°. The paired changes are SS reduction 25°, PT increase 25°, LL reduction 40°, PFA reduction 50° and AI increase 25°. Core angular values illustrate the geometry in Heckmann's primary figure; auxiliary L1/C7 coordinates are original synthetic software fixtures. They are not patient data or normal ranges. [23]

Other diagnostic examples: PT −10° with SS 40° gives PI 30° on the accepted branch and vertical-shaft PFA 170°. LL −20° with PI 30° gives mismatch 50°, not 10°. AI −15° with PFA 195° gives CSI 180°. C7 aligned with posterior S1 gives SVA 0, not unavailable. SFD 0 makes the ratio unavailable. Mirroring an image while also reversing the declared anterior side should preserve all anatomical results. Changing pixel aspect requires the same physical geometry restoration before testing invariance.

K.2 Required review boundaries

Unidentified anatomy, wrong posture, incorrect endplate span, incomplete hips/shaft, reversed landmarks, bad image aspect, wrong anterior side, nonupright acquisition, poor scale/magnification, stale image annotations, contradictory aliases, unsupported manual methods, mismatched postures and hidden explicit composite overrides all remain possible sources of error. Finite arithmetic does not exclude them. Negative/zero values must be distinguished from unavailable states; additional-view and model fields must not be synthesized from missing anatomy.

Meaningful verification includes independently constructed geometry, both anterior directions, image resizing/aspect, signed negative and exact-zero results, degenerate vectors, PFA above 180°, cup opening-side reversal/ambiguity, scale-free ratios, accepted and rejected overrides, both sides/equality of thresholds, mixed methods, review-required records and export disclosure. Synthetic checks test the equations and branches. Repeated-observer, calibrated reference and clinical outcome studies would be needed for broader clinical claims.

Native Swift/Xcode compilation, iOS/visionOS execution and physical-device AR/immersive tests were unavailable in this environment and were not claimed as completed. Code/content review and numerical examples do not prove a successful device build, App Store acceptance, regulatory status or clinical validation. Device/account release gates are documented separately in the release handoff.

K.3 Exact export scope

The interactive image canvas and supported schematic measurement display show the selected construction lines/arcs. The annotated PNG exporter draws the source image or background, landmark dots/labels and numeric result/method panels. It does not draw the MeasurementConstructionBuilder line/arc primitives. A PNG therefore is not an exact capture of every on-screen measurement construction. The plain-text report records values, method, provenance and review status; it does not embed source radiograph pixels. Neither format proves clinical accuracy or certifies a surgical plan.

L. NUMBERED REFERENCES

The same 1–24 numbering appears in the in-app help and full help. Entries 1–20 are retained; 21–24 are appended primary anatomical/methodological sources. No citation establishes that this application was used in or validated by the cited study.

[1] Legaye J, Duval-Beaupère G, Hecquet J, Marty C.
Pelvic incidence: a fundamental pelvic parameter for three-dimensional regulation of spinal sagittal curves.
Eur Spine J. 1998;7(2):99–103.
DOI: https://doi.org/10.1007/s005860050038
PMID: 9629932 — https://pubmed.ncbi.nlm.nih.gov/9629932/
Use and limit: Original anatomical/radiographic study. Defines PI and its relationship to pelvic and lumbar geometry; does not validate this application.

[2] Roussouly P, Gollogly S, Berthonnaud E, Dimnet J.
Classification of the normal variation in the sagittal alignment of the human lumbar spine and pelvis in the standing position.
Spine (Phila Pa 1976). 2005;30(3):346–353.
DOI: https://doi.org/10.1097/01.brs.0000152379.54463.65
PMID: 15682018 — https://pubmed.ncbi.nlm.nih.gov/15682018/
Use and limit: Original descriptive study of normal sagittal shape variation. A population description is not a universal individual target. The app does not implement the Roussouly classification.

[3] Schwab F, Ungar B, Blondel B, et al.
Scoliosis Research Society-Schwab adult spinal deformity classification: a validation study.
Spine (Phila Pa 1976). 2012;37(12):1077–1082.
DOI: https://doi.org/10.1097/BRS.0b013e31823e15e2
PMID: 22045006 — https://pubmed.ncbi.nlm.nih.gov/22045006/
Use and limit: Original adult spinal deformity classification validation. Its alignment modifiers are not TKA implant alignment rules or validation of the app measurements.

[4] Murata Y, Takahashi K, Yamagata M, Hanaoka E, Moriya H.
The knee-spine syndrome. Association between lumbar lordosis and extension of the knee.
J Bone Joint Surg Br. 2003;85(1):95–99.
DOI: https://doi.org/10.1302/0301-620X.85B1.13389
PMID: 12585585 — https://pubmed.ncbi.nlm.nih.gov/12585585/
Use and limit: Original study supporting an association between knee extension and lumbar alignment. Association does not establish which joint should be operated on first.

[5] Kitagawa A, Yamamoto J, Toda M, Hashimoto Y.
Spinopelvic Alignment and Low Back Pain before and after Total Knee Arthroplasty.
Asian Spine J. 2021;15(1):9–16.
DOI: https://doi.org/10.31616/asj.2019.0359
PMID: 32693445 — https://pubmed.ncbi.nlm.nih.gov/32693445/
Use and limit: Prospective observational TKA cohort. Provides direct knee–spine context; relief of knee flexion contracture does not guarantee restoration of global sagittal alignment.

[6] Shichman I, Ben-Ari E, Sissman E, Singh V, Hepinstall M, Schwarzkopf R.
Total knee arthroplasty in patients with lumbar spinal fusion leads to significant changes in pelvic tilt and sacral slope.
Arch Orthop Trauma Surg. 2023;143(4):2103–2110. Online publication 2022.
DOI: https://doi.org/10.1007/s00402-022-04462-w
PMID: 35536355 — https://pubmed.ncbi.nlm.nih.gov/35536355/
Use and limit: Retrospective TKA cohort with a prior lumbar fusion subgroup. Supports considering spinal history and postoperative posture changes; not an individual outcome predictor. A correction is indexed separately at PMID 35674822.

[7] Sheppard WL, Chiou D, Upfill-Brown A, et al.
Spondylolisthesis and mismatch deformity affect outcomes after total knee arthroplasty.
J Orthop Surg Res. 2023;18:157.
DOI: https://doi.org/10.1186/s13018-023-03605-y
PMID: 36864440 — https://pubmed.ncbi.nlm.nih.gov/36864440/
Use and limit: Retrospective TKA study linking spinal features with postoperative motion-related outcomes. Selection, confounding and sample size limit causal and treatment conclusions.

[8] Li H, Zhu F, Liao S, et al.
Higher Pelvic Incidence Was Associated with a Higher Risk of Sagittal Malposition of Femoral Component and Poor Outcomes of Primary Total Knee Arthroplasty: A Retrospective Cohort Analysis.
J Knee Surg. 2023;36(8):806–813. Online publication 2022.
DOI: https://doi.org/10.1055/s-0042-1743494
PMID: 35405755 — https://pubmed.ncbi.nlm.nih.gov/35405755/
Use and limit: Retrospective TKA cohort examining pelvic and femoral sagittal relationships. Its reported component-angle associations do not authorize an app-generated implant target.

[9] Vigdorchik JM, Sharma AK, Buckland AJ, et al.
2021 Otto Aufranc Award: A simple Hip-Spine Classification for total hip arthroplasty: validation and a large multicentre series.
Bone Joint J. 2021;103-B(7 Supple B):17–24.
DOI: https://doi.org/10.1302/0301-620X.103B7.BJJ-2020-2448.R2
PMID: 34192913 — https://pubmed.ncbi.nlm.nih.gov/34192913/
Use and limit: Original multicentre THA series. Source of the hip–spine framework; its clinical validation belongs to that study and protocol, not to the app or TKA.

[10] Sharma AK, Grammatopoulos G, Pierrepont JW, Madurawe CS, Innmann MM, Vigdorchik JM, Shimmin AJ.
Sacral Slope Change From Standing to Relaxed-Seated Grossly Overpredicts the Presence of a Stiff Spine.
J Arthroplasty. 2023;38(4):713–718.e1. Epub 2022 May 16.
DOI: https://doi.org/10.1016/j.arth.2022.05.020
PMID: 35588904 — https://pubmed.ncbi.nlm.nih.gov/35588904/
Use and limit: Prospective multicentre THA cohort questioning use of relaxed-seated ΔSS alone to diagnose lumbar stiffness.

[11] Aubert T, Halle A, Gerard P, Riouallon G, Auberger G, Lhotellier L.
Adverse spinopelvic mobility in patients undergoing total hip arthroplasty is associated with high mobility of the hip in a flexed seated position.
Hip Int. 2025;35(1):47–53. Online publication 2024.
DOI: https://doi.org/10.1177/11207000241284260
PMID: 39618092 — https://pubmed.ncbi.nlm.nih.gov/39618092/
Use and limit: Original THA research linking protocol-specific ΔPFA and ΔSPT. A research threshold is not a general diagnosis or TKA decision rule.

[12] Tezuka T, Heckmann ND, Bodner RJ, Dorr LD.
Functional Safe Zone Is Superior to the Lewinnek Safe Zone for Total Hip Arthroplasty: Why the Lewinnek Safe Zone Is Not Always Predictive of Stability.
J Arthroplasty. 2019;34(1):3–8.
DOI: https://doi.org/10.1016/j.arth.2018.10.034
PMID: 30454867 — https://pubmed.ncbi.nlm.nih.gov/30454867/
Use and limit: Original THA functional alignment study. Supports considering femoral and pelvic posture together; it does not establish a universally safe cup position.

[13] Murray DW.
The definition and measurement of acetabular orientation.
J Bone Joint Surg Br. 1993;75(2):228–232.
DOI: https://doi.org/10.1302/0301-620X.75B2.8444942
PMID: 8444942 — https://pubmed.ncbi.nlm.nih.gov/8444942/
Use and limit: Foundational geometric definitions distinguishing anatomical, operative and radiographic cup orientation.

[14] Innmann MM, Merle C, Ratra A, Speirs A, Adamczyk A, Murray D, Gill HS, Grammatopoulos G.
The Relationship of Cup Inclination and Anteversion in the Coronal Plane with Ante-Inclination in the Sagittal Plane: Exposing the Fallacy of Cup Safe Zones.
JB JS Open Access. 2024;9(3):e23.00120.
DOI: https://doi.org/10.2106/JBJS.OA.23.00120
PMID: 38994529 — https://pubmed.ncbi.nlm.nih.gov/38994529/
Use and limit: Geometric and clinical THA study. Shows why cup angles in different planes require an explicit convention rather than interchangeable labels.

[15] Fontalis A, Osmani HT, Guerra-Perron M, Mancino F, Wignadasan W, Putzeys P, Haddad FS.
Comparative Analysis of Relaxed- and Flexed-Seated Radiographs for Assessing Spino-Pelvic Mobility in Total Hip Arthroplasty.
J Arthroplasty. 2026;41(9S1):S197–S202. Epub 2026 May 4.
DOI: https://doi.org/10.1016/j.arth.2026.04.101
PMID: 42092467 — https://pubmed.ncbi.nlm.nih.gov/42092467/
Use and limit: Original comparison of seated radiographic protocols in THA. Supports preserving the identity of relaxed and flexed postures.

[16] Gilbertson B, Babazadeh S, van Bavel D.
Variations in pelvic tilt between relaxed-seated and flexed-seated positions affect stability assessment in 3D modelling in total hip replacement.
ANZ J Surg. 2025;95(1–2):175–179.
DOI: https://doi.org/10.1111/ans.19317
PMID: 39887822 — https://pubmed.ncbi.nlm.nih.gov/39887822/
Use and limit: THR radiographic and modelling study. Impingement findings from a model are not observed dislocation probabilities or TKA predictions.

[17] Hasegawa K, Okamoto M, Hatsushikano S, Shimoda H, Ono M, Homma T, Watanabe K.
Standing sagittal alignment of the whole axial skeleton with reference to the gravity line in humans.
J Anat. 2017;230(5):619–630.
DOI: https://doi.org/10.1111/joa.12586
PMID: 28127750 — https://pubmed.ncbi.nlm.nih.gov/28127750/
Use and limit: Original whole-body EOS and force-plate study. Distinguishes radiographic spinal alignment from a measured gravity line.

[18] de Leva P.
Adjustments to Zatsiorsky-Seluyanov's segment inertia parameters.
J Biomech. 1996;29(9):1223–1230.
DOI: https://doi.org/10.1016/0021-9290(95)00178-6
PMID: 8872282 — https://pubmed.ncbi.nlm.nih.gov/8872282/
Use and limit: Anthropometric reference work for segment mass and centre-of-mass estimates. Population coefficients are not measured patient mass distribution.

[19] Fukuchi CA, Fukuchi RK, Duarte M.
A public dataset of overground and treadmill walking kinematics and kinetics in healthy individuals.
PeerJ. 2018;6:e4640.
DOI: https://doi.org/10.7717/peerj.4640
PMID: 29707431 — https://pubmed.ncbi.nlm.nih.gov/29707431/
Use and limit: Original measured gait dataset. Background for gait education; the app's bundled trajectories are authored illustrations, not a replay or validation of this dataset.

[20] Endo K, Suzuki H, Nishimura H, Tanaka H, Shishido T, Yamamoto K.
Sagittal lumbar and pelvic alignment in the standing and sitting positions.
J Orthop Sci. 2012;17(6):682–686.
DOI: https://doi.org/10.1007/s00776-012-0281-1
PMID: 22915074 — https://pubmed.ncbi.nlm.nih.gov/22915074/
Use and limit: Original radiographic standing/sitting study in healthy adults. Supports posture-specific interpretation, not a universal target for arthritic knees.

[21] Boulay C, Tardieu C, Hecquet J, Benaim C, Mouilleseaux B, Marty C, Prat-Pradal D, Legaye J, Duval-Beaupère G, Pélissier J.
Sagittal alignment of spine and pelvis regulated by pelvic incidence: standard values and prediction of lordosis.
Eur Spine J. 2006;15(4):415–422. Online publication 2005.
DOI: https://doi.org/10.1007/s00586-005-0984-5
PMID: 16179995 — https://pubmed.ncbi.nlm.nih.gov/16179995/
Full text: https://pmc.ncbi.nlm.nih.gov/articles/PMC3489325/
Use and limit: Original radiographic study supporting S1-midpoint/hip-axis definitions, the PI = PT + SS relationship and positive-posterior PT convention. Its population observations are not individual targets or app validation.

[22] Barrey C, Jund J, Noseda O, Roussouly P.
Sagittal balance of the pelvis-spine complex and lumbar degenerative diseases. A comparative study about 85 cases.
Eur Spine J. 2007;16(9):1459–1467.
DOI: https://doi.org/10.1007/s00586-006-0294-6
PMID: 17211522 — https://pubmed.ncbi.nlm.nih.gov/17211522/
Full text: https://pmc.ncbi.nlm.nih.gov/articles/PMC2200735/
Use and limit: Original comparative study defining the posterior-sacral reference for signed C7 offset, sacrofemoral distance and their ratio, and the S1-midpoint construction for SSA. These geometric definitions do not turn the app into a validated balance or gravity-line test.

[23] Heckmann N, Tezuka T, Bodner RJ, Dorr LD.
Functional Anatomy of the Hip Joint.
J Arthroplasty. 2021;36(1):374–378. Epub 2020 July 31.
DOI: https://doi.org/10.1016/j.arth.2020.07.065
PMID: 32839062 — https://pubmed.ncbi.nlm.nih.gov/32839062/
Use and limit: Original clinical and geometric THA work illustrating femoral-shaft PFA, including a standing angle above 180°, and coordinated pelvic/cup posture. Its sacroacetabular SAA terminology is distinct from the historical app field. No TKA target or app clinical validation follows.

[24] Legaye J, Duval-Beaupère G.
Sagittal plane alignment of the spine and gravity: a radiological and clinical evaluation.
Acta Orthop Belg. 2005;71(2):213–220.
PMID: 16152857 — https://pubmed.ncbi.nlm.nih.gov/16152857/
Publisher full text: https://www.actaorthopaedica.be/assets/1135/13-Legaye_et_al.pdf
Use and limit: Original radiological/clinical study. Its pelvic-parameter diagram supports the S1 slope and midpoint/perpendicular conventions. Spinal alignment and measured gravity remain distinct concepts. No DOI was identified for this record; the verified PMID and publisher link identify it.