The probe tip's contact force is modelled as F = kΒ·(x β c), where x is how far the trainee has pushed past first contact c, and k is the vessel wall's stiffness. In haptic-feedback VR, that force is rendered back into the hand controller as resistance: past a comfortable push capacity the lever visibly stalls, so the trainee's hand naturally stops before the tear threshold β exactly like a real force-reflecting surgical console. In visual-only VR, the lever tracks the hand 1:1 with zero resistance: nothing in the headset conveys how hard the probe is actually pressing, so the same push that felt fine a moment ago can silently cross into vessel-damaging territory.
F = k Β· max(0, x β c)
haptic: |Ξx| β€ v_maxΒ·dtΒ·(1 β F/P) (hand physically resisted)
visual: x = controller position (no cap β force invisible)
- Push force β how hard the trainee drives the probe forward against tissue resistance.
- Safe range β the force window that keeps the vessel wall intact; shown live only in haptic mode.
- Tear threshold β the force above which the fragile vessel ruptures; identical in both modes, but only felt (not seen) as a hard stop in haptic mode.
Real-world relevance: this is why force-reflecting haptic consoles are considered essential for delicate procedures such as vascular or neurosurgical training β a millisecond-scale force channel back to the trainee's hand prevents tissue injuries that a video feed alone cannot warn against, and lets skill transfer safely from simulator to operating room.