Biomechanical Measurement Error Can Be Caused by Fujifilm Thickness: A Theoretical, Experimental, and Computational Analysis
Bibliographic record
Abstract
This is the first study to quantify the measurement error due to the physical thickness of Fujifilm for several material combinations relevant to orthopaedics. Theoretical and experimental analyses were conducted for cylinder-on-flat indentation over a series of forces (750 and 3000 N), cylinder diameters (0 to 80 mm), and material combinations (metal-on-metal, MOM; metal-on-polymer, MOP; metal-on-bone, MOB). For the scenario without Fujifilm, classic Hertzian theory predicted the true line-type contact width as <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:msub><mml:mrow><mml:mi>W</mml:mi></mml:mrow><mml:mrow><mml:mi>O</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mo stretchy="false">{</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mn fontstyle="italic">8</mml:mn><mml:msub><mml:mrow><mml:mi mathvariant="normal">F</mml:mi><mml:mi mathvariant="normal">D</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">c</mml:mi><mml:mi mathvariant="normal">y</mml:mi><mml:mi mathvariant="normal">l</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo><mml:mo>/</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mi>π</mml:mi><mml:msub><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">c</mml:mi><mml:mi mathvariant="normal">y</mml:mi><mml:mi mathvariant="normal">l</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo><mml:mo stretchy="false">[</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mn fontstyle="italic">1</mml:mn><mml:mo>-</mml:mo><mml:msup><mml:mrow><mml:msub><mml:mrow><mml:mi>ν</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">c</mml:mi><mml:mi mathvariant="normal">y</mml:mi><mml:mi mathvariant="normal">l</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mn fontstyle="italic">2</mml:mn></mml:mrow></mml:msup><mml:mo stretchy="false">)</mml:mo><mml:mo>/</mml:mo><mml:msub><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">c</mml:mi><mml:mi mathvariant="normal">y</mml:mi><mml:mi mathvariant="normal">l</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mn fontstyle="italic">1</mml:mn><mml:mo>-</mml:mo><mml:msup><mml:mrow><mml:msub><mml:mrow><mml:mi>ν</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">f</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">a</mml:mi><mml:mi mathvariant="normal">t</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mn fontstyle="italic">2</mml:mn></mml:mrow></mml:msup><mml:mo stretchy="false">)</mml:mo><mml:mo>/</mml:mo><mml:msub><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">f</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">a</mml:mi><mml:mi mathvariant="normal">t</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">]</mml:mo><mml:msup><mml:mrow><mml:mo stretchy="false">}</mml:mo></mml:mrow><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>/</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math>, where <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:mi>F</mml:mi></mml:mrow></mml:math> is compressive force, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mml:mrow><mml:msub><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">c</mml:mi><mml:mi mathvariant="normal">y</mml:mi><mml:mi mathvariant="normal">l</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math> is cylinder diameter, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M4"><mml:mrow><mml:msub><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">c</mml:mi><mml:mi mathvariant="normal">y</mml:mi><mml:mi mathvariant="normal">l</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math> is cylinder length, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M5"><mml:mrow><mml:msub><mml:mrow><mml:mi>ν</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">c</mml:mi><mml:mi mathvariant="normal">y</mml:mi><mml:mi mathvariant="normal">l</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M6"><mml:mrow><mml:msub><mml:mrow><mml:mi>ν</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">f</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">a</mml:mi><mml:mi mathvariant="normal">t</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math> are cylinder and flat Poisson’s ratios, and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M7"><mml:mrow><mml:msub><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">c</mml:mi><mml:mi mathvariant="normal">y</mml:mi><mml:mi mathvariant="normal">l</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M8"><mml:mrow><mml:msub><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">f</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">a</mml:mi><mml:mi mathvariant="normal">t</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math> are cylinder and flat elastic moduli. For the scenario with Fujifilm, experimental measurements resulted in contact widths of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M9"><mml:msub><mml:mrow><mml:mi>W</mml:mi></mml:mrow><mml:mrow><mml:mi>F</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn fontstyle="italic">0.1778</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mn fontstyle="italic">0.2273</mml:mn></mml:mrow></mml:msup><mml:mo>×</mml:mo><mml:msup><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mn fontstyle="italic">0.2936</mml:mn></mml:mrow></mml:msup></mml:math> for MOM tests, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M10"><mml:msub><mml:mrow><mml:mi>W</mml:mi></mml:mrow><mml:mrow><mml:mi>F</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn fontstyle="italic">0.0449</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mn fontstyle="italic">0.4664</mml:mn></mml:mrow></mml:msup><mml:mo>×</mml:mo><mml:msup><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mn fontstyle="italic">0.4201</mml:mn></mml:mrow></mml:msup></mml:math> for MOP tests, and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M11"><mml:msub><mml:mrow><mml:mi>W</mml:mi></mml:mrow><mml:mrow><mml:mi>F</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn fontstyle="italic">0.1647</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mn fontstyle="italic">0.2397</mml:mn></mml:mrow></mml:msup><mml:mo>×</mml:mo><mml:msup><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mn fontstyle="italic">0.3394</mml:mn></mml:mrow></mml:msup></mml:math> for MOB tests, where <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M12"><mml:mrow><mml:mi>F</mml:mi></mml:mrow></mml:math> is compressive force and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M13"><mml:mrow><mml:mi>D</mml:mi></mml:mrow></mml:math> is cylinder diameter. Fujifilm thickness error ratio <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M14"><mml:msub><mml:mrow><mml:mi>W</mml:mi></mml:mrow><mml:mrow><mml:mi>F</mml:mi></mml:mrow></mml:msub><mml:mo>/</mml:mo><mml:msub><mml:mrow><mml:mi>W</mml:mi></mml:mrow><mml:mrow><mml:mi>O</mml:mi></mml:mrow></mml:msub></mml:math> showed a nonlinear decrease versus cylinder diameter, whilst error graphs shifted down as force increased. Computational finite element analysis for several test cases agreed with theoretical and experimental data, respectively, to within 3.3% and 1.4%. Despite its wide use, Fujifilm’s measurement errors must be kept in mind when employed in orthopaedic biomechanics research.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".