A mathematical model of medial collateral ligament repair: migration,fibroblast proliferation and collagen formation

The partial rupture of ligament fibres leads to an injury known as grade 2 sprain. Wound healing after injury consists of four general stages: swelling, release of platelet-derived growth factor (PDGF), fibroblast migration and proliferation and collagen production. The aim of this paper is to present a mathematical model based on reaction–diffusion equations for describing the repair of the medial collateral ligament when it has suffered a grade 2 sprain. We have used the finite element method to solve the equations of this. The results have simulated the tissue swelling at the time of injury, predicted PDGF influence, the concentration of fibroblasts migrating towards the place of injury and reproduced the random orientation of immature collagen fibres. These results agree with experimental data reported by other authors. The model describes wound healing during the 9 days following such injury.     

A mechanistic damage model for ligaments

PurposeThe accuracy of biomechanical models is predicated on the realism by which they represent their biomechanical tissues. Unfortunately, most models use phenomenological ligament models that neglect the behaviour in the failure region. Therefore, the purpose of this investigation was to test whether a mechanistic model of ligamentous tissue portrays behaviour representative of actual ligament failure tests.ModelThe model tracks the time-evolution of a population of collagen fibres in a theoretical ligament. Each collagen fibre is treated as an independent linear cables with constant stiffness. Model equations were derived by assuming these fibres act as a continuum and applying a conservation law akin to Huxley’s muscle model. A breaking function models the rate of collagen fibre breakage at a given displacement, and was chosen to be a linear function for this preliminary analysis.MethodsThe model was fitted to experimental average curves for the cervical anterior longitudinal ligament. In addition, the model was cyclically loaded to test whether the tissue model behaves similarly.ResultsThe model agreed very well with experiment with an RMS error of 14.23 N and an R² of 0.995. Cyclic loading exhibited a reduction in force similar to experimental data.Discussion and conclusionThe proposed model showcases behaviour reminiscent of actual ligaments being strained to failure and undergoing cyclic load. Future work could incorporate viscous effects, or validate the model further by testing it in various loading conditions. Characterizing the breaking function more accurately would also lead to better results.     

Intrinsic fibroblast-mediated remodeling of damaged collagenous matrices in vivo

Numerous studies have examined wound healing and tissue repair after a complete tissue rupture and reported provisional matrix and scar tissue formation in the injury gap. The initial phases of the repair are largely mediated by the coagulation response and a principally extrinsic inflammatory response followed by type III collagen deposition to form scar tissue that may be later remodeled. In this study, we examine subfailure (Grade II sprain) damage to collagenous matrices in which no gross tissue gap is present and a localized concentration of provisional matrix or scar tissue does not form. This results in extracellular matrix remodeling that relies heavily upon type I collagen, and associated proteoglycans, and less heavily on type III scar tissue collagen. For instance, following subfailure tissue damage, collagen I and III expression was suppressed after 1 day, but by day 7 expression of both genes was significantly increased over controls, with collagen I expression significantly larger than type III expression. Concurrent with increased collagen expression were significantly increased expression of the collagen fibrillogenesis supporting proteoglycans fibromodulin, lumican, decorin, the large aggregating proteoglycan versican, and proteases cathepsin K and L. Interestingly, this remodeling process appears intrinsic with little or no inflammation response as damaged tissues show no changes in macrophage or neutrophils levels following injury and expression of the inflammatory markers, tumor necrosis factor-alpha and tartrate-resistant acid phosphatase were unchanged. Hence, since inflammation plays a large role in wound healing by inducing cell migration and proliferation, and controlling extracellular matrix scar formation, its absence leaves fibroblasts to principally direct tissue remodeling. Therefore, following a Grade II subfailure injury to the collagen matrix, we conclude that tissue remodeling is fibroblast-mediated and occurs without scar tissue formation, but instead with type I collagen fibrillogenesis to repair the tissue. As such, this system provides unique insight into acute tissue damage and offers a potentially powerful model to examine fibroblast behavior.     

Neuropeptides regulate expression of matrix molecule, growth factor and inflammatory mediator mRNA in explants of normal and healing medial collateral ligament

Denervation degrades normal ligament properties and impairs ligament healing. This suggests that secreted neuromediators, such as neuropeptides, could be modulating cell metabolism in ligament and scar tissue. To test this hypothesis we investigated the effect of exogenous substance P (SP), neuropeptide Y (NPY) or calcitonin gene-related peptide (CGRP) on the mRNA levels for proteins associated with inflammation, angiogenesis, and matrix production in tissue-cultured specimens of normal and injured medial collateral ligament. SP and NPY induced increased mRNA levels for several inflammatory mediators in the 2-week post-injury specimens. All three neuropeptides induced decreases in mRNA levels for healing-associated growth factors and matrix molecules, including basic fibroblast growth factor (bFGF), vascular endothelial growth factor (VEGF) and collagen types I and III. The results indicate that neuropeptides strongly influence the metabolic activity of cells in healing ligament, particularly at early time points after injury.     

Deficiency of macrophage migration inhibitory factor gene delays healing of the medial collateral ligament: a biomechanical and biological study

The role played by macrophage migration inhibitory factor (MIF) in the process of wound healing is controversial. Besides, there have been no reports that investigated the expression or the role of MIF in the repair process after ligament injury. In this study, we hypothesized that the deficiency in MIF gene might delay ligament healing in mice. The aim of this study was to clarify this hypothesis using MIF gene-deficient mice (MIFKO) and murine model of injury to the medial collateral ligament (MCL). Biomechanical testing showed that the levels of mechanical properties were significantly lower in MIFKO than in wild-type mice (WT) on day 28 after injury. Levels of matrix metalloproteinase (MMP)-2 and -13 mRNA in the healing tissue were significantly lower in MIFKO than in WT on day 28 and on day 7, respectively. Histologically, healing tissues in MIFKO exhibited prolonged hypertrophy, poor vascularity, and prolonged increase in cell number compared with those in WT. Taken together, it was suggested that MIFKO exhibited delayed healing of the MCL, which might be caused by lower mRNA expression of MMP-2 and -13.     

Potential strain-dependent mechanisms defining matrix alignment in healing tendons

Tendon mechanical function after injury and healing is largely determined by its underlying collagen structure, which in turn is dependent on the degree of mechanical loading experienced during healing. Experimental studies have shown seemingly conflicting outcomes: although collagen content steadily increases with increasing loads, collagen alignment peaks at an intermediate load. Herein, we explored potential collagen remodeling mechanisms that could give rise to this structural divergence in response to strain. We adapted an established agent-based model of collagen remodeling in order to simulate various strain-dependent cell and collagen interactions that govern long-term collagen content and fiber alignment. Our simulation results show two collagen remodeling mechanisms that give rise to divergent collagen content and alignment in healing tendons: (1) strain-induced collagen fiber damage in concert with increased rates of deposition at higher strains, or (2) strain-dependent rates of enzymatic degradation. These model predictions identify critical future experiments needed to isolate each mechanism’s specific contribution to the structure of healing tendons.     

A micromechanically-based, three-dimensional interface finite element for the modelling of the periodontal ligament

Some ideas are presented for the implementation of an interface finite element capable to model in 3-dimensions several mechanical features of the periodontal ligament. Such an element is based on a simple 2-cable micromechanical model, able to reproduce the periodontal ligament stiffness and strength under any loading condition, including the pure torsion of a tooth. A single cable represents a sufficiently populated sample of collagen fibres, each with an initially crimped geometry; a single collagen fibre can provide a mechanical response, in tension, only when it is completely uncoiled. The macroscopic interface behaviour is obtained by statistical integrations over the uncoiled length of each collagen fibre, up to the fibre failure. Such a model can reproduce the periodontal ligament anisotropy due to the variable fibre orientation along the tooth root, its different behaviour in tension/compression/shear, its different behaviour for extrusive/intrusive loading, and so forth. Some numerical examples illustrate the potentialities of this interface element, quite simple in essence but rather complete from an engineering viewpoint.     

Cell Population Kinetics of Collagen Scaffolds in Ex Vivo Oral Wound Repair

Biodegradable collagen scaffolds are used clinically for oral soft tissue augmentation to support wound healing. This study sought to provide a novel ex vivo model for analyzing healing kinetics and gene expression of primary human gingival fibroblasts (hGF) within collagen scaffolds. Sponge type and gel type scaffolds with and without platelet-derived growth factor-BB (PDGF) were assessed in an hGF containing matrix. Morphology was evaluated with scanning electron microscopy, and hGF metabolic activity using MTT. We quantitated the population kinetics within the scaffolds based on cell density and distance from the scaffold border of DiI-labled hGFs over a two-week observation period. Gene expression was evaluated with gene array and qPCR. The sponge type scaffolds showed a porous morphology. Absolute cell number and distance was higher in sponge type scaffolds when compared to gel type scaffolds, in particular during the first week of observation. PDGF incorporated scaffolds increased cell numbers, distance, and formazan formation in the MTT assay. Gene expression dynamics revealed the induction of key genes associated with the generation of oral tissue. DKK1, CYR61, CTGF, TGFBR1 levels were increased and integrin ITGA2 levels were decreased in the sponge type scaffolds compared to the gel type scaffold. The results suggest that this novel model of oral wound healing provides insights into population kinetics and gene expression dynamics of biodegradable scaffolds.     

Omega-3 fatty acids enhance ligament fibroblast collagen formation in association with changes in interleukin-6 production

Altering dietary ratios of n-3 and n-6 polyunsaturated fatty acids (PUFA) represents an effective nonpharmaceutical means to improve systemic inflammatory conditions. An effect of PUFA on cartilage and bone formation has been demonstrated, and the purpose of this study was to determine the potential of PUFA modulation to improve ligament healing. The effects of n-3 and n-6 PUFA on the in vitro healing response of medial collateral ligament (MCL) fibroblasts were investigated by studying the cellular coverage of an in vitro wound and the production of collagen, PGE2, IL-1, IL-6, and TNF. Cells were exposed to a bovine serum albumin (BSA) control or either eicosapentaenoic acid (EPA, 20:5n-3) or arachidonic acid (AA, 20:4n-6) in the form of soaps loaded onto BSA for 4 days and wounded on Day 5. AA and EPA improved the healing of an in vitro wound over 72 hr. EPA increased collagen synthesis and the overall percentage of collagen produced, but AA reduced collagen production and total protein. PGE2 production was increased in the AA-treated group and decreased in the EPA-treated group, but was not affected by wounding. IL-1 was not produced at the time point evaluated, but TNF and IL-6 were both produced, and their levels varied relative to the PUFA or wounding treatment. There was a significant linear correlation (r2 = 0.57, P = 0.0045) between IL-6 level and collagen production. These results demonstrate that n-3 PUFA (represented by EPA in this study) positively affect the healing characteristics of MCL cells and therefore may represent a possible noninvasive treatment to improve ligament healing. Additionally, these results show that MCL fibroblasts produce PGE2, IL-6, and TNF and that IL-6 production is related to MCL collagen synthesis.     

Effects of hepatocyte growth factor and platelet-derived growth factor on the repair of meniscal defects in vitro

Summary Injuries to the avascular region of the meniscus occur frequently and may be difficult to repair. This study was designed to determine whether growth factors could diffuse from a collagen sponge or a collagen gel into meniscal tissue and stimulate healing of defects using an in vitro model. The diffusion of platelet-derived growth factor (PDGF) from the collagen carriers into the medium was rapid with approximately 50% being released from the collagen sponge within the first hour. After 5 d of incubation, 8% of the PDGF was present in the meniscus, 11% in the collagen sponge, and 62% had been released into the medium. Similar results were obtained when a collagen gel was used as a carrier. Histological evaluation of the meniscal explants after 2 wk in culture revealed extensive proteoglycan staining in the areas surrounding defects treated with either hepatocyte growth factor (HGF) or PDGF compared with controls without growth factor. The HGF-PDGF treatment resulted in alignment and migration of meniscal cells toward the defect, which was not observed in untreated controls. At 3–7 d, increased number of cells were observed in defects treated with collagen gels (but not the sponge) with PDGF-HGF. At 4 wk, combined HGF-PDGF treatment resulted in the formation of tissue with birefringence by polarized microscopy, suggestive of organized collagen. The data suggest that use of specific PDGF-HGF may enhance the repair of meniscal injuries.     

The mesenchymal alpha11beta1 integrin attenuates PDGF-BB-stimulated chemotaxis of embryonic fibroblasts on collagens

alpha11beta1 constitutes the most recent addition to the integrin family and has been shown to display a binding preference for interstitial collagens found in mesenchymal tissues. We have previously observed that when alpha11beta1 integrin is expressed in cells lacking endogenous collagen receptors, it can mediate PDGF-BB-dependent chemotaxis on collagen I in vitro. To determine in which cells PDGF and alpha11beta1 might cooperate in regulating cell migration in vivo, we studied in detail the expression and distribution of alpha11 integrin chain in mouse embryos and tested the ability of PDGF isoforms to stimulate the alpha11beta1-mediated cell migration of embryonic fibroblasts. Full-length mouse alpha11 cDNA was sequenced and antibodies were raised to deduced alpha11 integrin amino acid sequence. In the embryonic mouse head, alpha11 protein and RNA were localized to ectomesenchymally derived cells. In the periodontal ligament, alpha11beta1 was expressed as the only detectable collagen-binding integrin, and alpha11beta1 is thus a major receptor for cell migration and matrix organization in this cell population. In the remainder of the embryo, the alpha11 chain was expressed in a subset of mesenchymal cells including tendon/ligament fibroblasts, perichondrial cells, and intestinal villi fibroblasts. Most of the alpha11-expressing cells also expressed the alpha2 integrin chain, but no detectable overlap was found with the alpha1 integrin chain. In cells expressing multiple collagen receptors, these might function to promote a more stable cell adhesion and render the cells more resistant to chemotactic stimuli. Wild-type embryonic fibroblasts activated mainly the PDGF beta receptor in response to PDGF-BB and migrated on collagens I, II, III, IV, V, and XI in response to PDGF-BB in vitro, whereas mutant fibroblasts that lacked alpha11beta1 in their collagen receptor repertoire showed a stronger chemotactic response on collagens when stimulated with PDGF-BB. In the cellular context of embryonic fibroblasts, alpha11beta1 is thus anti-migratory. We speculate that the PDGF BB-dependent cell migration of mesenchymal cells is tightly regulated by the collagen receptor repertoire, and disturbances of this repertoire might lead to unregulated cell migration that could affect normal embryonic development and tissue structure.     

Development of collagen fibril organization and collagen crimp patterns during tendon healing

Normal tendon comprises coaxially aligned bundles of crimped collagen fibres each of which possesses a fibrillar substructure. In acute traumatic injury this level of organization is disrupted and the mechanical function of the tendon impaired. During repair, a degree of recovery of the fibrillar structure takes place. In this tudy we have assessed the re-establishment of tendon organization after injury on the basis of the collagen fibril diameter distribution and the collagen crimp parameters. Crimp became undetectable following injury but one month later was present throughout the tissue. At this time the periodicity was greatly reduced by comparison with that of the normal tendon and normal values were not re-established within 14 months following injury. Collagen fibril diameters remained abnormally small over this same period of time. In particular, fibrils of diameters in excess of 100 nm, commonly found in normal and contralateral tendons, were totally absent from the observed distributions in the healing tendons. Such large diameter fibrils often account for as much as 50% of the total mass of collagen present in the uninjured tissue. Thus the mechanical properties of the healing tendon may remain significantly different from those of normal tendon for a minimum time of 14 months after injury.     

Polarizing analysis of the crimped collagen ligament of the maxillary barbel in Parauchenipterus galeatus, and the functional implications

A polarizing analysis of the crimped collagen ligament in the maxillary barbel of the catfish Parauchenipterus galeatus showed clearly that the maxillo-mandibular ligament of this species is formed by two types of collagen fibres. The first is composed of uncrimped, and the second of crimped collagen fibres. An anatomical examination of the muscular and osteological components which act in the movement of the barbel revealed that abduction of the barbel is performed by the extensor tentaculi muscle and the mechanism of adduction by muscular relaxation of the extensor tentaculi combined with release of the stored elastic energy of the maxillo-mandibular ligament. This ligament has rubber properties and because of this can store energy during abduction (first stage of the cycle of barbel movement). The stored energy is released when the action of the extensor tentaculi muscle ceases. The second half of the locomotory cycle is to return the maxilla to its original position by the antagonistic action of the ligament. The crimping of the ligament permits the take up of slack, allowing greater extension, with less chance of snapping. The connective tissue between the hyomandibular and the maxilla may assist the adduction of the barbel.     

Gene profiling of the rat medial collateral ligament during early healing using microarray analysis

Ligament heals in a synchronized and complex series of events. The remodeling process may last months or years. Experimental evidence suggests the damaged ligament does not recover its normal functional properties. Specific mechanisms to prevent scar formation and to regenerate the original mechanical function remain elusive but likely involve regulation of creeping substitution. Creeping substitution creates a larger hypercellular, hypervascular, and disorganized granulation tissue mass that results in an inefficient and nonregenerative wound healing process for the ligament. Control of creeping substitution may limit the extent of this tissue compromise and reduce the time necessary for healing. The objective of this study is to better understand the mechanism behind scar formation by identifying the extracellular matrix factors and other unique genes of interest differentially expressed during rat ligament healing via microarray. For this study, rat medial collateral ligaments were either surgically transected or left intact. Ligaments were collected at day 3 or 7 postinjury and used for microarray, quantitative PCR, and/or immunohistochemistry. Results were compared with the normal intact ligament. We demonstrate that early ligament healing is characterized by the modulation of several inflammatory and extracellular matrix factors during the first week of injury. Specifically, a number of matrix metalloproteinases and collagens are differentially and significantly expressed during early ligament healing. Additionally, we demonstrate the modulation of three novel genes, periostin, collagen-triple helix repeat containing-1, and serine protease 35 in our ligament healing model. Together, control of granulation tissue creeping substitution and subsequent downstream scar formation is likely to involve these factors.     

Growth factors and extracellular matrix proteins during wound healing promoted with frozen cultured sheets of human epidermal keratinocytes

In a murine model of full-thickness wounds, healing is stimulated by the application of human frozen cultured epidermal sheets. With immunofluorescence techniques, we studied, during this process, the spatial and temporal pattern of expression of: transforming growth factor-alpha (TGF-alpha); transforming growth factor-beta (TGF-beta) isoforms 1, 2, and 3; platelet-derived growth factor (PDGF); and the extracellular matrix proteins fibronectin, collagen IV, and tenascin. The growth factors, with the exception of PDGF, were found to be located in the frozen cultured sheet of keratinocytes before and after its application to the wound, whereas collagen IV and tenascin were deposited in the connective tissue under the frozen cultures. None of these factors were detected in control wound beds. Monoclonal antibodies against collagen IV and tenascin showed that both were of murine origin. We propose that the frozen cultures of human keratinocytes promote faster reepithelialization through the release of growth factors such as TGF-alpha which directly enhance migration and proliferation of murine keratinocytes, and through the stimulation of murine subepithelial cells, by TGF-beta, to secrete basement membrane proteins such as collagen IV, laminin, and tenascin, which provide a provisional substrate that improves migration of the murine epidermal cells.     

Platelet derived growth factor B and epithelial mesenchymal transition of peritoneal mesothelial cells

Platelet derived growth factor (PDGF) is involved in wound healing in various organ systems. Its potential role in the context of peritoneal injury following long-term peritoneal dialysis is unclear. We used an adenovirus expressing the B chain of PDGF (AdPDGF-B) to assess its effect on pro-fibrotic pathways in the peritoneal membrane. To assess the transforming growth factor (TGF) β independent effects of PDGF, we over-expressed PDGF-B in the peritoneum of either wild-type mice (Smad3^+/+) or those with a deletion of the TGFβ signaling protein Smad3 (Smad3^?/?). PDGF-B induced sustained angiogenesis in both Smad3^+/+ and Smad3^?/? mice. Despite increased collagen gene expression, collagen accumulation was transient and fibrogenesis was associated with induction of collagenase activity. We observed epithelial to mesenchymal transition (EMT) involving the peritoneal mesothelial cells, as shown by increased SNAIL and decreased E-Cadherin expression with evidence of mesothelial cells expressing both epithelial and mesenchymal markers. Unlike TGFβ-induced EMT, PDGF-B exposure did not lead to mobilization of the mesothelial cells; they remained as a single monolayer throughout the observation period. This “non-invasive” EMT phenomenon is a novel finding and may have implications concerning the role of EMT in peritoneal fibrosis and injury to other organ systems. The observed effects were similar in Smad3^?/? and Smad3^+/+ animals, suggesting that the PDGF-B effects were independent of TGFβ or Smad signaling.     

Histomorphochemical effects of shortwave diathermy on healing of experimental muscular injury in dogs

The biceps femoris muscle was surgically incised and sutured in 10 clinically healthy mongrel dogs, aged 1-2 yr and weighing 10-15 kg. The surgical wounds of 5 dogs were exposed to shortwave diathermy for 5 min daily for 7 days, starting a day after the creation of trauma. The remaining 5 dogs served as control. After 15 days of healing, the tissues from biceps femoris muscle were collected and subjected to histomorphological and histochemical examination. Mature collagen bundles were seen at healing site in diathermy treated animals while there were immature collagen fibres and more number of fibroblasts in control animals. Normal muscle fibres could be seen on either side of the healing tissue in treated animals whereas in control animals, atrophied and necrosed muscle fibres were encountered. The neutral and acid mucopolysaccharides, lipid droplets in the intermyofibrillar area and the activity of alkaline phosphatase, adenosine triphosphatase and lactate dehydrogenase at the healing site was better in treated as compared to controls.     

Immunohistochemical localization of growth factors in fetal wound healing

Fetal wound healing occurs rapidly, in a regenerative fashion, and without scar formation, by contrast with adult wound healing, where tissue repair results in scar formation which limits tissue function and growth. The extracellular matrix deposited in fetal wounds contains essentially the same structural components as that in the adult wound but there are distinct differences in the spatial and temporal distribution of these components. In particular the organization of collagen in the healed fetal wound is indistinguishable from the normal surrounding tissue. Rapidity of healing, lack of an inflammatory response, and an absence of neovascularization also distinguish fetal from adult wound healing. The mechanisms controlling these differing processes are undefined but growth factors may play a critical role. The distribution of growth factors in healing fetal wounds is unknown. We have studied, by immunohistochemistry, the localization of platelet-derived growth factor (PDGF), transforming growth factor beta (TGF beta), and basic fibroblast growth factor (bFGF), in fetal, neonatal, and adult mouse lip wounds. TGF beta and bFGF were present in neonatal and adult wounds, but were not detected in the fetal wounds, while PDGF was present in fetal, neonatal, and adult wounds. This pattern correlates with the known effects in vitro of these factors, the absence of an inflammatory response and neovascularization in the fetal wound, and the patterns of collagen deposition in both fetal and adult wounds. The results suggest that it may be possible to manipulate the adult wound to produce more fetal-like, scarless, wound healing.