Stress-vs-time signals allow the prediction of structurally catastrophic events during fracturing of immature cartilage and predetermine the biomechanical, biochemical, and structural impairment

Abstract

Objective: Trauma-associated cartilage fractures occur in children and adolescents with clinically significant incidence. Several studies investigated biomechanical injury by compressive forces but the injury-related stress has not been investigated extensively. In this study, we hypothesized that the biomechanical stress occurring during compressive injury predetermines the biomechanical, biochemical, and structural consequences. We specifically investigated whether the stress-vs-time signal correlated with the injurious damage and may allow prediction of cartilage matrix fracturing.

Methods: Superficial and deeper zones disks (SZDs, DZDs; immature bovine cartilage) were biomechanically characterized, injured (50% compression, 100%/s strain-rate), and re-characterized. Correlations of the quantified functional, biochemical and histological damage with biomechanical parameters were zonally investigated.

Results: Injured SZDs exhibited decreased dynamic stiffness (by 93.04±1.72%), unresolvable equilibrium moduli, structural damage (2.0±0.5 on a 5-point-damage-scale), and 1.78-fold increased sGAG loss. DZDs remained intact. Measured stress-vs-time-curves during injury displayed 4 distinct shapes, which correlated with histological damage (p<0.001), loss of dynamic stiffness and sGAG (p<0.05). Damage prediction in a blinded experiment using stress-vs-time grades was 100%-correct and sensitive to differentiate single/complex matrix disruptions. Correlations of the dissipated energy and maximum stress rise with the extent of biomechanical and biochemical damage reached significance when SZDs and DZDs were analyzed as zonal composites but not separately.

Conclusions: The biomechanical stress that occurs during compressive injury predetermines the biomechanical, biochemical, and structural consequences and, thus, the structural and functional damage during cartilage fracturing. A novel biomechanical method based on the interpretation of compressive yielding allows the accurate prediction of the extent of structural damage.

Keywords: Articular cartilage; Bilayer composite; Bio-mechanics; Cartilage; Cartilage fracture; Compressive injury; Damage prediction; Functional damage; GAG loss; Histology; Immature; Immature cartilage; Impact injury; Injury; Peak stress; Post-traumatic osteoarthritis; Stress; Stress time signal; Stress-vs-time; Structural damage; Zonal damage; Zonal function; Zone.

Figure 1. Calculation of the depth-position & biomechanical characterization of cartilage disks before injury

(A) The depth position (distance from the articular surface) was calculated for each disk (superficial zone disk: SZD (n=32); deeper zones disk: DZD (n=32)) to assess the distance of each disk center (x and y) from the articular surface (AS). x and y were calculated as follows: x = 1/2*SZ disk thickness; y = SZ disk thickness + 1/2*DZ disk thickness. (B) Dynamic stiffness and equilibrium modulus vs. depth position (distance from the articular surface to the center of a SZD (x) or DZD (y)) as scatter plot with regression lines. For both frequencies 0.1 and 1Hz, the non-linear regression reached significant levels when both SZDs and DZDs were statistically analyzed as one data set (as shown) and when the DZDs but not the SZDs were analyzed separately. For the equilibrium modulus vs. depth position, linear regression reached significant levels when both SZDs and DZDs were statistically analyzed as one data set (as shown).

Figure 2. Typical Stress-vs-time signals, their time-derivatives (to identify the maximum stress rise), and the corresponding histology

(A) Representative stress-vs-time signal of a Grade 0 SZD (negative stress indicates compression). Its derivative was characterized by 1 critical (C) and 2 inflection (I) points. S: sample stress-vs-time point, for which the derivative was determined from the slope of the tangent line (t). The corresponding histology of an injured SZD that remained undamaged is shown in (E). (B) Representative stress-vs-time signal of a Grade 1 SZD. The derivative revealed a lower magnitude stress rise over time, though still characterized by 1 critical and 2 inflection points. The corresponding histology of an injured SZD that remained undamaged is shown in (F). (C) SZD Grade 2 stress-vs-time signal whose derivative showed a local decrease with time during the compression phase and was characterized by 1 critical point and 4 inflection points. The corresponding histology of an injured SZDE (superficial zone damaged explant) that suffered compaction is shown in (G). (D) Grade 3 stress-vs-time signal with the presence of a double tip instead of a single tip at the transition from compression to relaxation indicating a pronounced stress loss during the final stage of injurious compression. The derivative was characterized by 3 critical points and 4 inflection points. The corresponding histology of an injured SZDE that suffered extensive structural damage is shown in (G).

Figure 3. Peak stress and maximum stress rise of the occurring stress during injury

(A) Scatter plot and non-linear regression of the peak stress (measured during injury) vs. equilibrium modulus (white markers) and dynamic stiffness at f=1Hz (black markers); (B) Scatter plot and non-linear regression of the maximum stress rise vs. depth position (distance from the articular surface; positive values: compression, negative values: relaxation; SZD: superficial zone disk).

Figure 4. Biomechanical impairment after injury

(A) Scatter plot and non-linear regression of the loss of dynamic stiffness vs. depth position and (B) the loss of dynamic stiffness vs. the stress derivative during injury ; SZDE: superficial zone disk.

Figure 5. Biochemical impairment after injury

(A) Scatter plot and non-linear regression of the loss of sGAG vs. depth position and (B) the loss of sGAG vs. stress derivative during injury; SZDE: superficial zone disk.

Figure 6. Histological analysis and correlation with stress-vs-time signals

Representative images of (A) an uninjured control disk without damage, (B) an injured disk with slight compaction but without structural damage, and (C) an injured disk with slight compaction and structural damage such as matrix disruption. (D) The damage score and stress-vs-time signal characterization of injured and structurally damaged disks. In injured disks, the presence of histological damage correlated with the presence of 4 inflection points, 3 critical points, and the presence of a split at the signal tip (see Fig. 2). Damage score grade 0=normal appearing cartilage with proper staining in each zone except the intact superficial zone with the surface showing no signs of damage; grade 1=minimal surface damage with isolated disruptions; grade 2=moderate surface damage with widespread disruption; grade 3=minimal permanent compression; grade 4=permanent compression to approximately ≥ 30% of the original disk thickness.

Figure 7. Histological analysis for damage prediction of injured disks

Representative images of serial sections of (A) an uninjured control disk without damage, (B) an injured disk with a single horizontal matrix disruption, whose corresponding stress-vs-time signal contained a double tip (stress-vs-time grade 3; see Fig. 3D), (C) an injured disk with a horizontal matrix disruption pervading the disk in a y-shape whose corresponding stress-vs-time signal contained a triple tip (stress-vs-time grade 3), (D) an injured disk whose stress-vs-time signal was graded as 1 (Fig. 2B).

Figure 8. Effects of disk thickness and zonal origin on peak stress and stress-vs-time grades

Three additional sets of disks with retained superficial zone (rSZ; n=28) were prepared with thicknesses ranging from 250-420μm, 420-600μm, and 600-1000μm and compared to 3 sets of DZDs with comparable thickness ranges. The differences in the peak stress (A) between each set of rSZ and the corresponding DZD set indicated a zonal effect on peak stress. When comparing the 3 rSZ sets with each other, the peak stress of the set with 600-1000μm thickness was significantly higher than the other 2 sets having lower thickness. The same was true for the DZD sets which, together, suggest an effect of thickness on peak stress. (B) There were no significant differences in the stress-vs-time grades between each set of rSZ and the corresponding DZD set, suggesting that there was no zonal effect on the stress-vs-time grades. When comparing the 3 rSZ sets with each other, the stress-vs-time grades were not significantly different. The same was true for the DZD sets which, together, suggest that there was no effect of thickness on the stress-vs-time grades.