2.1.

Cartilage Ex Vivo Irradiation

Hip joint articular cartilage was taken from a 6-month-old piglet and was irradiated within 1-h postmortem. We employed an erbium-doped glass fiber laser with the wavelength $1.56\mu \mathrm{m}$ (IPG Photonics). The radiation was delivered by applying a fiber with the diameter $600\mu \mathrm{m}$ in the contact with the cartilage surface. The spotspacing was 2 to 3 mm. The pulse duration was 100 ms, the pulse repetition rate was 1 Hz. The laser power was 0.9 W, and the exposure time was 10 s (10 pulses). These laser parameters were chosen on the basis of the results of preceding publications.^15,22 The irradiated fragments ($\sim 1{\mathrm{mm}}^3$) and the nonirradiated control samples were extracted using the cylindrical cutting tool, fixed in 10% formalin for histology and in 2.5% glutartaldehyde for transmission electron microscopy (TEM) and processed for the further analysis (48 irradiated fragments and 6 controls).

2.2.

Cartilage In Vivo Irradiation

Ten 6-month-old miniature pigs were tested in the in vivo experiment. The aim of this study was to create minimally traumatic injury of cartilage to allow animals to continue moving. The artificial defects of the size of $2\times 11\mathrm{mm}$ were introduced surgically into the hip articular cartilage using a cutter (two defects for each animal on the right and left joint). The depth of the defect was 300 to $400\mu \mathrm{m}$, with care taken not to approach the bone. After 2 months, the defective joints were reopened. The visual observation showed that new, superficial secondary defects (200 to $300\text{-}\mu \mathrm{m}$ deep) occurred in neighboring areas (10 to 15 mm from the primary defect) on the cartilage surface due to abnormal movement of the animals’ legs during the preceding 2 months. These secondary defects were examined histologically and considered as a model for degenerated cartilage (OA). The detailed description of such defect modeling is provided in our previous work.²³ In the course of this (secondary) surgery, all defects were irradiated by the laser with the wavelength of $1.56\mu \mathrm{m}$ using the parameters described in the cartilage ex vivo section. Half of the defects (right or left) were left intact. At 2 and 3 months after irradiation, the joints were opened and the cartilage from the experimental area was extracted for further analysis.

2.3.

Tissue Sampling

Microscopic investigation using atomic force microscopy (AFM), structural illuminating microscopy (SIM), and TEM methods has been carried out on the tissue sections having 200- to $300\text{-}\mu \mathrm{m}$ depth and 250- to $500\text{-}\mu \mathrm{m}$ radius counted from the symmetry axis of the laser beam.

2.4.

Atomic Force Microscopy

Cartilage samples for AFM analysis were prepared as described elsewhere.²⁴ In brief, cartilage fragments were embedded in Tissue-Tek (Tissue-Tek, 4583 Compound, Sakura Finetek Europe, Zoeterwoude, Netherlands) and sectioned on Leica CM3050 S (Nussloch, Germany) cryotome to $20\mu \mathrm{m}$ slices and placed onto the glass substrates. Using phosphate-buffered saline (PBS) solution, the samples were washed from the remaining embedding medium and dried at room temperature to constant mass. The images were obtained using the scanning tunnel microscope Nanoscope IIIa (Digital Instruments, Santa Barbara, California). The height profiles were obtained on the air in the tapping mode using the silicon nitride AFM probe (Nanosensors, tip radius $<30\mathrm{nm}$, scanning rate 1.5 Hz, and resonant frequency 90 to 170 kHz. The collected data were analyzed using Gwyddion 2.03 software (courtesy of David Neĉas and Petr Klapetek).

2.5.

Transmission Electron Microscopy

The cartilage samples were fixed in the 2.5% glutaraldehyde solution in the phosphate buffer and stored at 48°C for 24 h. Then, the samples were immersed into the phosphate buffer two times for 10 to 15 min, dehydrated with the mixture of the absolute alcohol and acetone and embed in the araldite resin. The blocks were cut on ultramicrotome LKB model 3 (Sweden) to obtain the slices of 20- to 30-nm in thickness. The slices were stained with the uranyl acetate, put on the formvar film in the center of a copper grid, and analyzed with the Jeol JEM-1011 transmission electron microscope (Japan) at 80-kV accelerating voltage.

2.6.

Structural Illuminating Microscopy

The slices of tissues 4- to $5\text{-}\mu \mathrm{m}$ thick were made parallel to the surface (at a distance of 100 to 150 μm from the surface) using Cryomicrothome Leica CM1900 (Leica Microsystems Nussloch GmbH, Germany) at $-15°\mathrm{C}$ with refrigerant Jung tissue freezing medium. The marker Fluo-4 Ca dye (Molecular Probes, Inc.) was applied to manifest ${\mathrm{Ca}}^{2+}\text{ions}$. Images were obtained with the super-resolution microscope, the Optical Microscopy eXperimental (OMX) system v3.0 (Applied Precision, Inc., the GE Healthcare Company). The $60\times$, 1.45 numerical aperture oil immersion objective was used. The 532-nm laser was used for the fluorescence excitation and the objective immersion oil with the refractive index of 1.514. Super-resolution fluorescence images were reconstructed using softWoRx 2.0 (Applied Precision, Inc.) with the raw data collected with OMX. Reconstructed images were postprocessed and displayed using ImageJ.

2.7.

Histochemistry and Histology

The samples were fixed in the 10% formalin, stained with the paraffin, and cut on the microtome to obtain the slices of 4- to $5\text{-}\mu \mathrm{m}$ thick. The groups of slices were stained with (a) hematoxylin and eosin, to manifest general structure including cells, (b) picrofuchsin according to van Giesone’s protocol for collagen fibrils visualizing, and (c) toluidine blue for acid glycosaminoglycans. The preparations were analyzed using the optical microscope Longway LCX-121S (China). The microphotographs were obtained using the camera model DEM200 MiniSee (China) and processed with the Scope Photo software.

2.8.

Temperature Calculations and Measurements

Temperature field was calculated on the basis of the solution of thermoconductivity problem for two media (cartilage and quartz optical fiber) described in detail in Ref. 14

Here, $a$ is the thermal diffusivity, $G(\mathrm{x},\mathrm{y},\mathrm{z},\tau )$ is the heat source, which is zero for optical fiber

The boundary conditions for the equality of heat fluxes and temperatures at the surface $S$ between optical fiber and cartilage²⁵

The heat conductivity problem Eqs. (1) to (4) is solved using the finite difference method in an explicit scheme (temperature on the following time-step can be expressed through the temperatures on the previous time steps). The parameters used for calculations are as follows:²⁵ $\kappa =51/\mathrm{cm}$, $r_0=250\mu \mathrm{m}$, the laser power is 0.9 W, the exposure time is 10 s (pulse duration 100 ms, pulse repetition rate 1 Hz), $\lambda$ is $0.006\mathrm{W}/\mathrm{cm}$ $K$, and $a$ is $0.0014{\mathrm{cm}}^2/\mathrm{s}$.

Surface temperature of cartilage slab in the course of laser irradiation was measured using IR radiometer (Testo 865, Testo SE & Co. KGaA, Lenzkirch, Germany).

3.1.

Ex Vivo Experimental Results

Laser-induced pores of micron and submicron size in ex vivo obtained articular cartilage of the pigs revealed by AFM are shown in Figs. 1(a) and 1(b). The images display the submicron size pores in the tissue matrix with intact periodic collagen fibrils. The green line in Figs. 1(a) and 1(b) corresponds to surface topography presented in graphs [Figs. 1(c) and 1(d)]. The pore size distribution function of the nonirradiated cartilage obtained from the quantitative analysis of its topography shows the maximum at $\sim 40\mathrm{nm}$ [Fig. 1(e)]. The pore size distribution of the laser-irradiated cartilage demonstrates significantly wider distribution than that for the pristine cartilage, with the maximum at the size of 150 nm [Fig. 1(f)]. These structural peculiarities identified as pores are revealed by SIM [Figs. 1(g), 1(h), and 1(i)]. The nonirradiated cartilage sample, see Fig. 1(g), does not show any pores. For the irradiated cartilage, the size and concentration of the pores depend on the position of the imaged area: the sample taken from the area of the maximal temperature gradient, Fig. 1(i), demonstrates high-porous structure, which is less prominent in the center of the laser beam, Fig. 1(h).

Fig. 1

Laser-induced pores in porcine cartilage. (a) and (b) AFM images of cartilage structure: submicron size pores in cartilage matrix. The bar is $2\mu \mathrm{m}$. (a) Nonirradiated cartilage. The colorimetric scale on the right specifies the correlation between the profile height and the color of the image. The periodic collagen fibrils with the diameter from 50 to 150 nm and the mean period of $62\pm 7\mathrm{nm}$ are seen. The structure is smooth and the height changes are small. (b) Laser-irradiated cartilage topography. The collagen structure is comparable to that of the pristine one. The presence of dark-colored regions reveals the extended pores (marked with arrows). (c) The texture profile of the nonirradiated cartilage obtained along the green line in nonirradiated cartilage (a). $X$-and $Y$-axes are the coordinate and the texture height value correspondingly. The observed height changes do not exceed tens of nm. (d) The texture profile of the irradiated cartilage. The observed height changes are hundreds of nm that reveals the porous structure. (e) Pore size distribution (arbitrary units) of the nonirradiated cartilage obtained from the quantitative analysis of its topography. The maximum is $\sim 40\mathrm{nm}$. (f) Pore size distribution (arbitrary units) of the laser-irradiated cartilage obtained from the quantitative analysis of its topography. The width of the size distribution is substantially wider than that for the intact cartilage. The maximum is $\sim 150\mathrm{nm}$. (g) SIM image of the nonirradiated cartilage, the bar is $3\mu \mathrm{m}$. (h) SIM image of the irradiated cartilage in the center of laser spot (temperature maximum), the bar is $3\mu \mathrm{m}$. (i) SIM image of the irradiated cartilage near the maximum of temperature gradient, the bar is $3\mu \mathrm{m}$.

The pores in the laser-irradiated tissue are shown with higher magnification in Fig. 2. The TEM microphotograph of the laser-irradiated cartilage with a pore (the electronically more transparent area) between the chondrocyte (on the right) and the pericellular matrix (PM) (on the left) is shown in Fig. 2(a). The whitish spheroids visualizing a completely transparent area with the diameter from 50 to 150 nm probably can be identified as laser-induced gas bubbles. Figure 2(b) shows two isogenic chondrocytes of the irradiated cartilage surrounded by the pores containing gas bubbles (light spheroids) with diameters from 50 to 180 nm. Figure 2(c) shows such spheroids (gas bubbles) with the diameter from 20 to 200 nm inside the devitalized cell. The nonirradiated control sample contains a minimum of electronically transparent areas and spheroids, see Fig. 2(d).

Fig. 2

TEM microphotograph of micropores and gas bubbles in laser-irradiated cartilage. (a) A pore (the electronically transparent area, marked with dashed line) between the chondrocyte (C, on the right) and PM (on the left). The light (white) spheroids with the diameter from 50 to 150 nm probably are the signs of laser-induced gas bubbles, the bar is $1\mu \mathrm{m}$. (b) The two isogenic chondrocytes (C) of the irradiated cartilage surrounded by the pores (marked with the dashed lines) containing light spheroids (gas bubbles) with the diameter from 50 to 180 nm, the bar is $2\mu \mathrm{m}$. (c) Light spheroids (gas bubbles) with the diameter from 20 to 200 nm inside the devitalized cell (marked with dashed line). The disturbed remains of the chondrocytes (C) are on the right, the bar is $2\mu \mathrm{m}$. (d) The representative view of the intact cartilage chondrocyte (C) surrounded by the ECM of small-grained substance, the bar is $1\mu \mathrm{m}$.

Although the performed experiments do not allow for the direct monitoring of the dynamics of gas bubble formation, growth, and collapse, we can observe them in the tissue after laser irradiation probably due to their stability.

3.2.

In Vivo Experimental Results

In the control group, when the animals were not exposed to laser irradiation, the fibrous connective tissue (FT) was revealed histologically in the defect area [Fig. 3(a)]. Sometimes, the fibrous cartilage (FC) was forming under the FT [Fig. 3(a)]. In the laser-irradiated group, the pronounced chondrocyte proliferation in the defect zone was shown in Fig. 3(b). On the defect periphery and in the nearby surroundings outside the defect, numerous large, multicellular clones were forming [Fig. 3(b)]. Figures 3(c)–3(f) shows laser-induced structural alterations that lead to the development of hyaline-type cartilage in miniature pig joints 2 and 3 months after laser treatment. Transformations of the multicellular clones of chondrocytes into the separate, mature chondrocytes that are capable of generating new matrix of the hyaline type are presented in Fig. 3(c). The next sequential steps toward cartilage repair, e.g., the various stages of cartilaginous matrix transformation from the fibrous to fibrous-hyaline and eventually to HC (in 2 months after the laser irradiation), are presented in Figs. 3(d), 3(e). Figure 3(d) shows the FC (bottom right), which transforms into the fibrous-HC (center), and then into the HC (upper left). Figure 3(e) shows fibrous-HC with the typical chondrocytes of HC and matrix looking like the FC. Figure 3(f) shows the final stage of the development of the HC completely filling a cartilage defect of a miniature pig joint 3 months after the laser treatment with the specialized laser settings controlling the formation of the micropores containing transparent spheroids (stable gas bubbles).

Fig. 3

(a) View of control nonirradiated defect. The defect is filled with FT and FC; residuary HC is under defect; toluidine blue stain, $400\times$. (b) The common view of the laser-irradiated defect (between the arrows) and surrounding tissues after 2 months. In the center of the defect, there is a noticeable chondrocyte proliferation. On the periphery of the defect, there are large multicellular clones. Under the cartilage plate, there is subchondral bone, toluidine blue stain, $100\times$. (c)–(e) The images taken 2 months after the laser treatment. (c) Transformation of chondrocytes: isogenous groups IG (multicellular clones) transforms to separate chondrocytes (in the central zone), restoration of lamina splendens (on the top, marked with the arrow), van Gieson stain, $400\times$, the bar is $50\mu \mathrm{m}$. (d) Growing HC substitutes FC, hematoxylin, and eosin stain, $400\times$, the bar is $100\mu \mathrm{m}$. (e) Intermediate fibro-HC (in the centum), toluidine blue stain, $400\times$, the bar is $50\mu \mathrm{m}$. (f) Completely recovered HC and lamina splendens (marked with the arrow) in 3 months after laser treatment of articular cartilage defect, van Gieson stain, $200\times$, the bar is $100\mu \mathrm{m}$.

3.3.

Theoretical Modeling of the Temperature Effects

Temperature fields on the surfaces of the cartilage calculated for laser settings used in the experiments are presented in Figs. 4(a) and 4(b). The evolution of the temperature change $\mathrm{\Delta }T$ at the center of the laser spot following the laser pulse repetition is presented in Fig. 4(a). The spatial distribution of average temperature is shown in Fig. 4(b). The resulting laser heating of the irradiated tissue volume of 1 mm in diameter is nonhomogeneous with the spatial temperature variations of 3°C to 12°C.

Fig. 4

Numerical simulations of the temperature field and pore formation. (a) Calculated dynamics of the temperature in the center of the laser spot on the surface of the tissue specimen under pulsating irradiation (solid line), average temperature (dashed line), and measured surface temperature (black squares). (b) Spatial distribution of the average temperature in cartilage for the wavelength being $1.56\mu \mathrm{m}$, the Gaussian radius ($1/e$) $250\mu \mathrm{m}$, laser power 0.9 W, time of irradiation 10 s, pulse 100 ms, 1 Hz. (c)–(e) Time evolution of the pores configuration under the permanent heating. (c) Initial distribution of the bond density. (d) Further formation of pores accompanied with the stress relaxation. (e) Final nearly equilibrium pore texture defined by the original cartilage inhomogeneity. (f) Pore-related part of the cartilage free energy at different heating temperatures as function of time. The legend for panels (g)–(h) is given in panel (h). (g) Average pore size as function of time. (h) The relative fraction of the volume occupied by pores as function of time. One sees that under the excessive heating, $T=50.0°\mathrm{C}$, the full burning off of the cartilage occurs during the finite time and the corresponding pore-related free energy relaxes to zero, evidencing the self-consistency of the model.

3.4.

Thermomechanical Model of the Pore Formation

Pore formation under laser irradiation is governed by the interplay between the tissue heating and relaxing of its internal and external stresses. To formulate a treatable model for pore formation accounting for both, we consider the tissue as a nonlinear quasi-elastic medium and assume that the thermal destruction of the material can be described as thermally activated breakdown of the chemical bonds.

Here, we select the simplest, two-dimensional version of the problem formulation, which allows us to demonstrate the approach and its main outcomes in the clearest manner. At this stage, it does not take into account important self-healing processes, which may dramatically suppress pore growth. To formulate the model illustrating the pore formation, we will consider cartilage as a nonlinear, practically incompressible elastic medium with a relatively small shear modulus. Cartilage is incompressible because of the practical incompressibility of water, its main constituent. The cartilage stiffness is ensured by its skeleton, comprising macromolecules connected by chemical bonds. Under moderate stress, the probability of the bond breaking is small, and the bond breaking rate is negligible. We quantify the probability of the bond breaking by introducing the corresponding potential barrier so that the probability $p$ of the breaking (per unit time) is defined by the Arrhenius law²⁶

It is known that the bond-breaking energy would depend not only on what particular chemical bond is involved but also—due to a random environment—upon the bond’s spatial position. However, the fact that dynamics of a complex systems governed by the thermally activated behavior is controlled by locally weakest bonds while the neighboring ones are released by avalanche processes, allows to simplify the model taking for $U$ a single typical value.

The natural assumption that the deformation reduces the bond-breaking barrier²⁷ implies that the pore develops at the spots of the increased mechanical stress. Then, the bond breaking decreases the local stiffness of the matrix, and the system relaxes into a new elastic equilibrium with the new stress distribution.

The deformation of the cartilage and thus the related strain reduces the barrier, $U\to U-\mathrm{\Delta }U$, easing the formation of pores.²⁷ We assume that the difference $\mathrm{\Delta }U$ is proportional to the elastic energy released as a result of the breaking of one bond

The Euler equations and corresponding boundary conditions are not given explicitly since both theoretical study and the numerical solution of the problem are based on the variational formulation.²⁸ We also do not adopt the usual assumption about the smallness of deformations. The problem reduces to solving the self-consistent system of the elastic equations, including the Arrhenius rate of relaxation and thermal conductivity equations. The obtained closed system of equations and the variation problems defining the behavior of the cartilage under the laser irradiation are further solved numerically using the finite-elements method.

The experimentally observed laser-induced pores and nanobubbles in the cartilage correspond to moderate laser heating over 10 deg to 12 deg; the temperature time evolution and spatial distribution for the temperature and its gradient are presented in Figs. 4(a) and 4(b). As shown in Fig. 4(a), temperature measurements data confirm the calculation results.

The exemplary initial, nonhomogeneous bond density adopted for calculations is shown in Fig. 4(c). This defines the local elasticity of the cartilage corresponding to the spatially varying stiffnesses of the ECM and chondrons.¹⁶ Applying spatially uniform heating, we arrive at the characteristic pore dynamics shown in Figs. 4(d) and 4(e). In the first stage shown in Fig. 4(d), small pores appear at spots of maximal stress followed by pore growth accompanied by relaxation of the local stresses. At the final stage, we get a pore texture resulting from a relatively long heating of the initially nonuniform matrix, see Fig. 4(e).

To gain an insight into the dynamics of the development of the pore structure, we inspect the temperature evolution of the physical parameters characterizing pores. Figure 4(f) shows the incremental decrease of the pore-related part of the elastic free energy upon the pore formation and the corresponding relaxing stress. Figure 4(g) shows the evolution of the average pore size with the time of heating, and Fig. 4(h) shows the temporal dynamics of the volume fraction occupied by the pores.