# Vitrification of particulated articular cartilage via calculated protocols

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### Protocol calculation

To design our loading protocols, we calculated the spatial and temporal distribution of cryoprotectant concentration, solution freezing point, and vitrifiability, bringing together the work of Abazari et al.28,37 on diffusion coefficients; the work of Elliott et al.26,27,29,30 on the multisolute osmotic virial equation for predicting freezing point; and the work of Weiss et al.25 on solution vitrifiability. We first presented this three-part mathematical approach in a previous paper where we proposed an optimal protocol for preserving articular cartilage dowels23 that was shown to yield high cell viability when implemented experimentally32. Herein, we use our three-part model to develop protocols for articular cartilage cubes.

The first step of developing a vitrification protocol is to choose the cryoprotectant types and concentrations. Protocol E–D–P is based on our previous work on articular cartilage dowels23, and as we did there, here we select EG, DMSO, and PG to load at progressively lower temperatures. In the first loading step at a temperature of 0 °C, we select EG and DMSO because these permeate the quickest and depress the freezing point quickly for the subsequent loading step to take place. In the second loading step, PG is added. In both steps, the concentrations of EG and DMSO are 3 M (the same concentration as we used previously for cartilage dowels23 based on experimental evidence that 3 M solutions of these cryoprotectants are associated with low toxicity35), while the concentration of PG is 2 M (a concentration selected to permit the attainment of a vitrifiable concentration at the end of the loading protocol within a reasonable time period).

Protocol E–D is designed to avoid the use of PG, which has been identified as more toxic than EG and DMSO. For this protocol, we select a loading solution of 3 M EG in the first loading step at a temperature of 0 °C. In the second loading step, we select a solution with DMSO and EG both at 4 M (a concentration selected to expedite the diffusion into the cartilage for the protocol to take a similar amount of time as Protocol E–D–P).

### Cryoprotectant concentration

Fick’s law of diffusion is used in one dimension to calculate the spatial and temporal evolution of cryoprotectant permeation

$$frac{{partial C}}{{partial t}} = Dfrac{{partial ^2C}}{{partial x^2}}$$

(1)

where C is cryoprotectant concentration (mol/L), t is time (s), D is the diffusion coefficient (m2/s), and x is position in the cartilage. The diffusion coefficient is calculated as a function of absolute temperature (T) using the Arrhenius expression

$$D = Aexp left( { – frac{{E_a}}{{RT}}} right)$$

(2)

where A is the pre-exponential factor (m2/s), Ea is the activation energy (kcal/mol), as listed in Table 3, for each cryoprotectant, and R is the ideal gas constant.

Experimentally, condyles are minced into cubes with side lengths of 1 mm. Based on this geometry, we consider a one-dimensional line from the center of one cube face to the center of the cube (length of 0.5 mm) for our calculations, as illustrated in Fig. 1a. We select this dimension for our diffusion calculations because 0.5 mm is the shortest distance from the cartilage–solution boundary to the center of the cube. Using this geometry, the calculated concentration at the center is a lower bound on the expected concentration, given that diffusion also occurs from each side of the exposed cube.

The following boundary and initial conditions are used to solve Eq. (1) for calculating the spatial and temporal distribution of cryoprotectant concentration during loading. First, the concentration of each cryoprotectant at the outer surface of the cube is equal to the concentration in the solution

$$Cleft( {x = 0.5{mathrm{mm}},t} right) = C_{{mathrm{solution}}}$$

(3)

At the center of the cube, there is no flow of cryoprotectant

$$frac{{partial C}}{{partial x}}left( {x = 0,{mathrm{mm}},t} right) = 0$$

(4)

Finally, the initial condition at the beginning of the first loading step is

$$Cleft( {0 ,<, x ,<, 0.5,{mathrm{mm}},t = 0} right) = 0$$

(5)

The concentration profile of each cryoprotectant at the end of the first loading step is used as the initial condition for the second loading step.

### Vitrifiability

Given the distribution of cryoprotectant concentration calculated using Eq. (1), the corresponding spatial distribution of vitrifiability can be determined for the volume and cooling rate expected during the vitrification of cartilage cubes. For our predictions, we use the statistical model of vitrifiability developed by Weiss et al.25, where 5 mL solutions containing between 6 and 9 M of cryoprotectants were placed in 10 mL polypropylene tubes and plunged into liquid nitrogen (a ~60 K/min cooling rate25,31) for 30 min, and then immersed in a 37 °C water bath until they liquified completely, for which an ordinal score was assigned based on visual inspection (on a scale from 0 to 4 outlined in Table 4). The following statistical model was developed with proportional odds logistic regression based on the experimental scores of ordinal vitrifiability for 164 cryoprotectant solutions25

$$mathop {sum }limits_{i = 1}^p left[ {beta _iC_i + mathop {sum }limits_{j = 1}^i beta _{ij}C_iC_j} right] ge left| {alpha _n} right|$$

(6)

where βi and βij are single and interaction (including self-interaction) coefficients for each cryoprotectant i and cryoprotectant pair ij, respectively, as listed in Table 525, and Ci is the molar concentration (mol/L). If the summation calculated over the p cryoprotectants exceeds a threshold value of αn, the solution will reach a vitrifiability score of at least n (Table 4). The coefficients listed in Table 5 are only valid for predicting vitrifiability under the same or more favorable conditions as the experiments in Weiss et al.25, i.e., for 5 mL solutions in 10 mL polypropylene tubes cooled at ~60 K/min and thawed in a 37 °C water bath. Herein, cartilage cubes are placed into a 1.8 mL Cryovial tube for vitrification and warming, which is a smaller volume than that used by Weiss et al.25. A smaller volume increases the rate of cooling and warming and improves the vitrifiability of the cryoprotectant solution within the cartilage matrix. Thus, any protocol that satisfies the vitrifiability criterion determined by Weiss et al.25 is also expected to be vitrifiable under the experimental conditions used herein.

### Freezing point

The distribution of freezing point as a function of position in the cartilage is calculated using26,27,30

$$T_{{mathrm{FP}}}^0 – T_{{mathrm{FP}}} = frac{{left[ {W_1/left( {overline {s_1^{0{mathrm{L}}}} – overline {s_1^{0{mathrm{S}}}} } right)} right]RT_{{mathrm{FP}}}^0pi }}{{1 + left[ {W_1/left( {overline {s_1^{0{mathrm{L}}}} – overline {s_1^{0{mathrm{S}}}} } right)} right]Rpi }}$$

(7)

where (T_{{mathrm{FP}}}^0) is the freezing point of pure water (273.15 K), TFP is the freezing point of the cryoprotectant mixture, π is the osmolality (osmol/kg solvent), W1 is the molar mass of pure water, and (overline {s_1^{0{mathrm{L}}}} – overline {s_1^{0{mathrm{S}}}} = 22.00) J/mol K is the change in molar entropy between pure liquid and pure solid water at (T_{{mathrm{FP}}}^0).

The multisolute osmotic virial equation26,27,29,30 is used to calculate solution osmolality with the fitting coefficients determined by Zielinski et al.26. Only the second-order virial coefficients (B) are needed to accurately describe cryoprotectant solutions containing DMSO, PG, and EG with an isotonic amount of NaCl

$$pi = mathop {sum }limits_{i = 2}^r k_im_i + mathop {sum }limits_{i = 2}^r mathop {sum }limits_{j = 2}^r frac{{B_i + B_j}}{2}k_im_ik_jm_j$$

(8)

where k is the dissociation constant and m is the molality, which is calculated with

$$m_i = frac{{left( {1000frac{{mathrm{L}}}{{{mathrm{m}}^3}}} right)C_i}}{{rho _1left[ {1 – mathop {sum }nolimits_{i = 2}^{r – 1} C_iV_{m,i}} right]}}$$

(9)

where ρ1 is the density of pure water (998 kg/m3 at 22 °C51) and Vm is the molar volume (L/mol) at 22 °C52. Dissociation constants, osmotic virial coefficients, and molar volumes are listed in Table 6 for each cryoprotectant. The volume of mixing and the volumes of NaCl (and other minute additives) are assumed negligible in Eq. (9).

### Porcine articular cartilage cube preparation

Hind legs with joints (n = 23 porcine hind legs) from sexually mature pigs aged over 54 weeks were obtained from a meat-processing plant slaughter house in Wetaskiwin, AB, Canada. No animals were specifically euthanized for this research. The Research Ethics Office at the University of Alberta provided ethical approval for the experimental use of animal tissues and cells. Porcine joints were harvested and immersed in phosphate buffered saline (PBS) immediately, then transported to the research laboratory within 4 h. After joint dissection, articular cartilage was shaved from the condyles, and minced into cubes ~1 mm3 in size using a sterile scalpel blade and cleaned with 50 mL sterile PBS (Ca2+/Mg2+ free) plus antibiotics [100 units/mL penicillin, 100 µg/mL streptomycin, and 0.25 µg/mL amphotericin B (Gibco)] for 15 min under a biological safety cabinet (NuAire, MN, USA).

### Human articular cartilage cube preparation

Healthy knee joints (n = 3 donors) from deceased donors aged 48, 50, and 59 years (mean ± SD: 52.3 ± 5.8 years) were obtained from the Comprehensive Tissue Center in Edmonton, AB, Canada, with consent from patients’ families to use donated cartilage for research. Human research ethics approval was obtained from the University of Alberta Research Ethics Office. After tissue harvesting, knee joints were stored in 500 mL X-VIVO 10 (Lonza, California, USA, a serum-free medium (SFM) that has been approved for clinical use) and transported to the research laboratory within 24 h. Healthy articular cartilage was shaved from the condyles, minced into cubes ~1 mm3 in size using a sterile scalpel blade, and immediately immersed in PBS, then cleaned with 50 mL sterile PBS (Ca2+/Mg2+ free) plus antibiotics [100 units/mL penicillin, 100 µg/mL streptomycin (Gibco)] for 15 min under a biological safety cabinet.

Multicryoprotectant cocktail solutions were made from three cryoprotectants: EG (Fisher), DMSO (Fisher), and PG (Fisher). Fresh cryoprotectant cocktail solutions were prepared in 50 mL final volumes with Dulbecco’s Modified Eagle Medium F12 (DMEM) (Gibco) for porcine cartilage or with X-VIVO 10 SFM for human cartilage on the same day of the experiment, using the following concentrations of cryoprotectants (M = molar): Protocol E–D–P: solution one [3 M EG + 3 M DMSO] and solution two [3 M EG + 3 M DMSO + 2 M PG] and Protocol E–D: solution one [3 M EG] and solution two [4 M EG + 4 M DMSO]. After weighing, cartilage cubes were transferred into the prepared 50 mL cryoprotectant cocktail solutions for cryoprotectant permeation at specific temperatures and times: Protocol E–D–P: solution one at 0 °C for 10 min, followed by solution two at −10 °C for 20 min and Protocol E–D: solution one at 0 °C for 20 min, followed by solution two at −5 °C for 15 min. After the cryoprotectant loading into the cartilage, the particulated cartilage cubes were quickly removed from the Falcon tubes with a mesh strainer and transferred into a sterile 1.8 mL Cryovial tube using a chemical spoon. After closing the vial lid, the Cryovial tube was placed onto a Cryovial cane and quickly plunged into liquid nitrogen for vitrification.

### Cryoprotectant removal from articular cartilage cubes

The Cryovial tube containing vitrified cartilage cubes was quickly removed from the liquid nitrogen and warmed in a 37 °C water bath until the surrounding glass was melted (~0.5 min). The cartilage cubes were extracted with a sterile spatula and washed three times in 25 mL DMEM (for porcine cartilage) or 25 mL X-VIVO 10 SFM (for human cartilage) for 30 min each wash to remove the permeated cryoprotectants from the cartilage cubes.

### Temperature profile of vitrification and rewarming processes

To compare the cooling and warming temperature profiles of Protocol E–D–P and Protocol E–D, a dual thermometer with a thermocouple detector was used to measure the temperatures of 0.5 g of articular cartilage cubes after cryoprotectant permeation within the 1.8 mL Cryovial (n = 5 replicates per group) as a function of time as they were cooled from the step two temperature (−10 or −5 °C) to −196 °C in liquid nitrogen for 10 min, then rewarmed to 37 °C in a water bath for 30 s and transferred to a 4 °C wash media. The temperatures of articular cartilage at the following time points (for cooling, at 0, 10, 20, 30, 40, 50, 60, 90, 120, and 180 s; for rewarming, at 600, 610, 620, 630, 660, 720, 780, 840, and 900 s) were recorded and plotted to show the thermal history regarding the cooling and warming of each protocol.

### Chondrocyte viability by cell membrane integrity stain

Chondrocyte viability was assessed by a cell membrane integrity stain [6.25 µM Syto 13 and 9.0 µM propidium iodide mixed in PBS] using a membrane-permeant nucleic acid stain (Syto 13; Molecular Probes) which fluoresced green, and a membrane-impermeant stain (propidium iodide; Sigma) that penetrates only into cells with disrupted cell membranes fluorescing red. After incubation of cartilage cubes in the dyes for 20 min, cartilage cubes were rinsed in PBS (Ca2+/Mg2+ free) and imaged using a laser scanning confocal fluorescent microscope (model: TCS SP5; Leica). The filters used to image all the cartilage cubes in this study had the following spectra peak maxima wavelengths: excitation/emission: 488 nm/503 nm and 535 nm/617 nm. Three replicate cartilage cubes from one Cryovial were imaged at each time point. Cartilage cubes were imaged at three time points, t1 = positive control before cryoprotectant loading (fresh cartilage cubes after mincing), t2 = after vitrification in LN2 (<24 h, day 0) and tissue warming followed by cryoprotectant removal in medium, and t3 = after vitrification for 180 days (day 180) and tissue warming followed by cryoprotectant removal in medium. A positive control (fresh cartilage cubes after mincing) and a negative control group (freeze/thaw in liquid nitrogen (LN2) without cryoprotectants) from the same condyle were assessed. A minimum 80% absolute chondrocyte viability in the positive (fresh) controls before cryoprotectant exposure (chondrocyte viability at t1) was used to screen out unhealthy cartilage donors.

### Chondrocyte metabolic activity by alamarBlue

Chondrocyte metabolic activity was assessed by an alamarBlue assay (Invitrogen, Burlington). Rewarmed articular cartilage cubes (~0.2 g wet weight) after cryoprotectant removal were washed in 5 mL sterile PBS (Ca2+/Mg2+ free) plus antibiotics for 15 min in a biological safety cabinet. Cartilage cubes were incubated with the alamarBlue assay solution [5 mL X-VIVO 10 medium supplemented with 0.1 mM ascorbic acid, 10 nM dexamesasone, 10 ng/mL transforming growth factor (TGF) beta 1, and mixed with 500 µL alamarBlue] at 37 °C for 48 h. Images of the fluorescence color change of alamarBlue assay solutions of the culture plates were taken at 0, 24, and 48 h using a digital camera (Canon PowerShot ELPH 180). The average of two replicate readings of the blank samples (alamarBlue assay solution without cartilage sample) was subtracted from the average of the experimental samples to yield a value in relative fluorescent units (RFU) divided by gram weight. The RFU were determined by the CytoFluor II software with emission wavelengths of 580/50 nm, excitation wavelengths of 485/20 nm, and a fluorescent intensity gain set to 45.

### Articular cartilage digestion for chondrocyte isolation

After cryoprotectant removal, 0.2 g of porcine cartilage cubes or 0.5 g of human cartilage cubes were weighed and cleaned with 5 mL sterile PBS (Ca2+/Mg2+ free) plus antibiotics [100 units/mL penicillin, 100 µg/mL streptomycin (Gibco)] for 15 min under a biological safety cabinet. The cartilage cubes were then transferred to an empty 50 mL Falcon tube and 5 mL of 0.15% collagenase solution was added under sterile conditions [for 10.5 mL of collagenase solution, prepare: 10 mL DMEM supplemented with antibiotics (PS), 15 mg of 300 units type II collagenase (filtered, Worthington), and 0.5 mL fetal bovine serum (FBS)]. The Falcon tubes containing cartilage cubes were placed in an orbital shaker (250 rpm) at 37 °C for cartilage digestion for 22 h. Once the cartilage digestion was finished, a sterile 100 µm cell strainer was used to filter the digested chondrocytes. The collagenase was neutralized by adding 10 mL of DMEM supplemented with 10% FBS. The chondrocytes were collected by centrifugation for 10 min at 433 × g at 22 °C, followed by two washes in 10 mL sterile PBS (Ca2+/Mg2+ free), and then resuspended in 12 mL of DMEM complete for chondrocyte recovery.

### Chondrocyte recovery and chondrocyte collection

After chondrocyte recovery in an appropriate tissue culture flask (BD, Falcon) in a humidified incubator with 20% O2 and 5% CO2 at 37 °C for 72 h, the chondrocyte monolayer was washed with 5 mL sterile PBS (Ca2+/Mg2+ free) twice. 2 mL 1 × 0.02% trypsin-EDTA solution (Gibco) was added to the tissue culture flask to disassociate chondrocytes for 5 min at 37 °C, and then neutralized with 5 mL of DMEM complete supplemented with 10% FBS. Chondrocytes were collected for cell counting via centrifugation for 10 min at 433 × g at 22 °C.

### Chondrocyte counting by trypan blue

After chondrocytes were resuspended in DMEM complete media, 15 µL cell suspension and 15 µL trypan blue were mixed by pipetting. Ten microliters of this mixture was gently placed in a hematocytometer using a pipette for chondrocyte counting, and the cell count was determined by adding the counted cells in four equally sized areas, dividing by 4, and then multiplying by a dilution factor of 10,000 and by the total volume of chondrocyte suspension solution. Trypan blue is a vital stain used to selectively color dead cells with a blue color, and live cells with intact cell membranes remain unstained. Since live chondrocytes are excluded from staining, this staining method can be used as a dye exclusion method to identify the number of living chondrocytes.

### Scratch wound healing assay and chondrocyte migration quantification

After chondrocyte recovery for 72 h, chondrocytes were counted with trypan blue and seeded onto a 24-well tissue culture plate (Aaka Scientific Inc.) with a density of 105 per well and cultured in a humidified incubator with 20% O2 and 5% CO2 at 37 °C for 168 h. Chondrocytes were grown until they reached over 90% confluence as a monolayer in the culture plate in 2 mL DMEM complete supplemented with 10% FBS with the medium changed twice a week. For the scratch wound healing assay, a sterile 200 µL pipette tip was used to slowly scratch the confluent monolayer (90% or higher) from left to right across the center of the well and introduce a 1 mm wide empty gap in the wells53. The wells were refilled with 2 mL fresh DMEM complete and images of the well were taken at 0, 24, and 48 h to monitor the migration of chondrocytes. Image J software was used to calculate chondrocyte migration percentage every 24 h. Chondrocyte migration was normalized to the initial empty gap width at 0 h and plotted to show the chondrocyte migration speed based on the 24 and 48 h time points.

### Chondrocyte aggregate by pellet culture for 21 days

After isolated chondrocytes were plated for 72 h for cell recovery, chondrocytes were washed with sterile PBS (Ca2+/Mg2+ free) twice. Then, chondrocytes were trypsinized for 5 min at 37 °C and centrifuged at 433 × g for 5 min to collect chondrocytes for making pellets following the procedure below54. After a cell wash and cell counting with trypan blue, 5 × 105 chondrocytes were resuspended in 500 µL defined chondrogenic SFM [high glucose DMEM, HEPES (10 mM), human serum albumin (125 mg/mL), ascorbic acid 2-phosphate (365 lg/mL), dexamethasone (100 nM), and L-proline (40 lg/mL) (Sigma-Aldrich), ITS + 1 premix (5 µL, 100x) (Corning, Discovery Labware, Inc.), 100 units/mL penicillin, 100 µg/mL streptomycin, TGF-b3 10 ng/mL; ProSpec, NJ, USA] in a 1.5 mL sterile conical microtube (Bio Basic Inc, Ontario, Canada). Then, chondrocytes were centrifuged at 433 × g and 22 °C for 5 min to form a pellet at the bottom of the microtube using an Allegra X-22R centrifuge (Beckman Coulter, US). The pellets were cultured in the SFM under 3% O2 and 5% CO2 at 37 °C in a humidified incubator for 21 days, with SFM changes twice a week.

### Wet weight and histology of pellets

After a 21-day culture, pellets were rinsed with sterile PBS (Ca2+/Mg2+ free) and wet weights were measured using an electric balance (Mettler Toledo, Switzerland). Pellets were imaged with a Zeiss camera (AxioCam ERc 5s) for gross morphology and fixed with 10% formalin for 24 h before paraffin embedding. A microtome (Leica) was used to prepare pellet sections with thicknesses of 5 µm, followed by section drying at 37 °C overnight in a dry incubator. Pellet sections were then processed with Safranin O staining to quantify and identify proteoglycan content in the pellets. Stained sections were imaged with a Nikon digital camera (model: DS-Fi2) equipped on a Nikon inverted microscope (model: ECLIPSE Ti-5): exposure time for 100× magnification = 8 ms; exposure time for 200× magnification = 40 ms; gain = 0.

### GAG/DNA measurement

GAG content of pellets was quantified by a dimethylmethylene blue (DMMB) assay. Pellets were weighed and rinsed with PBS and stored in a −80 °C freezer before use. After warming, pellets were digested in 250 µL of 1 mg/mL proteinase K overnight at 56 °C using a dry block heater (Thermo Fisher Scientific). PBE/cysteine buffer (100 mM Na2HPO4, 10 mM Na2EDTA, pH = 6.5, 1.75 mg/mL cysteine, Sigma) and ~0–100 µg/mL chondroitin sulfate A sodium salt (CS, Sigma-Aldrich) were used as controls for a standard curve. The standard curve was prepared in eight Eppendorf tubes with a total volume of 100 µL and an increasing concentration of CS. After protein digestion, a 5 µL digested sample was pipetted into an ultraclear 96-well plate in triplicate (NUNC, Thermo Fisher Scientific). The digested sample in each well was mixed with 5 µL PBE/cysteine buffer and diluted by 1:50 in concentration by adding 250 µL DMMB dye (Sigma-Aldrich). Each plate was read at 525 nm and data were normalized to the blank reading of H2O (260 µL, without DMMB) and the CS standard controls. DNA content was quantified by using the CyQUANTTM proliferation assay kit for cells in culture (Invitrogen, ON, Canada). After cartilage digestion with 1 mg/mL proteinase K, a 5-µL sample was pipetted into a 96-well plate in triplicate. In each well, 195 µL working buffer was added to make the total volume equal to 200 µL. DNA solutions and working buffer were prepared using an assay kit54. For 20 mL working buffer, 50 µL CyQUANT® GR dye and 1 mL cell-lysis buffer were mixed with 19 mL Milli-Q water. The spectra peak maxima for excitation of 450/50 nm and emission of 530/25 nm were used to read the plates, and the supplied λDNA of bacteriophage was used as standard reference.

### Statistical analysis

The numerical data are presented as means ± SD. Based on the Mauchly’s test of sphericity or the Levene’s test of equality, the analysis of variance (ANOVA) with post hoc test (Tukey’s multiple comparison) was performed on the experimental groups, otherwise, the nonparametric test (Kruskal–Wallis with pairwise comparison) was performed to compare experimental variables in multiple groups. Sample size and the p values are reported in the figure legends. All data were analyzed using SPSS 20.0 software for statistical significance and figures were plotted using GraphPad Prism 8 software.

### Reporting summary

Further information on research design is available in the Nature Research Reporting Summary linked to this article.