High-Speed Dynamic Biomechanical Test Frame
Applies rapid ramp-and-hold displacement (rise time < 100 ms) with closed-loop servohydraulic control.
Biomedical Engineering / Ligament Viscoelastic Relaxation
FREE TO EXPLORELABORATORY 24 · BIOMEDICAL ENGINEERING
Viscoelastic Ligament Stress Relaxation & Reduced Relaxation Function
Determine the continuous relaxation spectrum parameter c_r of an anterior cruciate ligament (ACL) specimen under tensile stress relaxation using Fung's quasi-linear viscoelastic (QLV) theory. Explore interactive physiological instrumentation simulation, biomechanics, and biomedical engineering telemetry.
BIOINSTRUMENTATION · BIOSIGNALS · BIOMECHANICS · IMAGING
Your virtual biomedical engineering laboratory.
NORMALIZED STRESS Σ(T)/Σ₀—
PHYSIOLOGICAL & TEST CELL TELEMETRY
Ready to sample with Time t = 30.0 s.
Adjust Time t, then execute biomedical trial.
Biomedical engineering telemetry and physiological states are evaluated rigorously using 64-bit IEEE 754 precision. Residuals reflect ordinary least-squares regression across successive observations. Continuous data structures support high-fidelity biological and physiological modeling.
Biomedical assumptions and boundary condition limits
The linear semi-logarithmic relation applies over the intermediate time window (τ_1 ≪ t ≪ τ_2); it deviates at very short (< 1 s) and very long (> 10⁴ s) times. Evaluated on porcine bone-ACL-bone complexes mounted in anatomical tensile grips in 37.0 °C saline. Subjected to a rapid ramp-and-hold tensile strain (ε_0 = 0.05 applied in 0.1 s) and held for 300 s. Semi-logarithmic slope c_r = 0.0450 ratio/ln(s) evaluated across times from 5 s to 300 s.
Biomedical apparatus & physiological sensors.
Anatomical Bone-Block Clamping Fixtures
Rigidly grips femoral and tibial bone blocks preserving natural anatomical ligament insertion angles.
High-Frequency Piezoelectric Load Cell (0–2 kN)
Captures instantaneous peak tensile force and subtle millinewton relaxation decay without drift.
Submerged Physiological Bio-Chamber (37.0 °C)
Maintains ligament in continuous 37 °C phosphate buffered saline preventing tissue desiccation.
Non-Contact Video Tracking Extensometer
Verifies that grip displacement holds mid-substance ligament strain strictly constant during relaxation.
High-Speed Synchronous Data Acquisition System
Logs time and force channels at 1 kHz during ramp and logarithmically decimate during 300 s hold.
FOLLOW THE METHOD
A reason behind every step.
Determine the continuous relaxation spectrum parameter c_r of an anterior cruciate ligament (ACL) specimen under tensile stress relaxation using Fung's quasi-linear viscoelastic (QLV) theory. Standardized parameter settings: 5.0, 15.0, 30.0, 60.0, 120.0, 300.0 s.
01
Specimen Dissection and Anatomical Mounting
Dissect knee joint leaving intact femur-ACL-tibia complex, pot bone blocks in polymethylmethacrylate (PMMA) cylinders, and clamp in aligned tensile fixtures.
02
Saline Bio-Chamber Equilibration
Submerge the mounted ligament complex in 37.0 °C PBS bath and allow 20 minutes for thermal and osmotic equilibration.
03
Preconditioning Cyclic Protocol
Apply 10 cycles of triangular preconditioning from 0 to 2% strain at 0.5 Hz to achieve repeatable, steady-state viscoelastic cycling.
04
Ramp-and-Hold Step Strain Execution
Apply a rapid tensile displacement step to 5% mid-substance strain within 100 ms, triggering high-speed data acquisition at peak load σ_0.
05
Isometric Relaxation Data Collection
Hold displacement strictly constant for 300 seconds, logging decaying load at standardized intervals: 5, 15, 30, 60, 120, and 300 seconds.
06
Fung QLV Semi-Logarithmic Regression
Normalize stress σ(t)/σ_0, plot against natural logarithm of time ln(t), and extract Fung's relaxation spectrum parameter c_r from the linear slope.
YOUR NOTEBOOK · 0 OBSERVATIONS
Turn measurements into biomedical engineering insight.
Points are your recorded observations. The solid regression line validates Ligament Viscoelastic Relaxation mathematical scaling.
LINEAR REGRESSION FIT · y = mx + b
σ(t)/σ₀ = -c_r · ln(t) + G_0 = -0.0450 · ln(t) + 0.9800
| # | Relaxation Time t (s) | Normalized Stress σ(t)/σ₀ (ratio) | Log relaxation time ln(t) [ln(s)] | Normalized stress σ(t)/σ₀ (ratio) | Remove |
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