Factors affecting callus distraction in limb lengthening

Factors affecting the process of callus distraction in limb lengthening include the type of osteotomy, timing and rate of distraction, and stability of fixation. Thirty-two rabbits were studied to evaluate the reliability of transverse osteotomy and delayed distraction and to examine the appropriate rates of distraction. Rabbit tibiae were osteotomized subperiosteally and were subjected to slow distraction using a rigid monolateral external fixator. There was a ten-day waiting period before distraction. The animals were divided into three groups according to the rate of distraction (0.35 mm/12 hours, 0.7 mm/12 hours, 1.4 mm/12 hours). The process of callus formation was monitored by soft x-ray. The reliability of delayed distraction after transverse osteotomy was demonstrated by microangiographic study. Even though intramedullar vessels were interrupted by osteotomy at surgery, blood circulation recovered during the waiting period before distraction. Bone lengthening was successful when distraction was carried out at rates of 0.35 mm/12 hours or 0.7 mm/12 hours. The callus filling a distraction gap showed a characteristic zone structure, i.e., one central radiolucent zone and two adjacent sclerotic zones. Microangiographic study demonstrated the continuity of blood vessels under these rates of distraction. Based on the results of these experiments and clinical experiences on 180 bone lengthenings, the authors believe that a waiting period after osteotomy is more practical than achieving immediate distraction after uncertain corticotomy.     

Biomechanical and physical properties of lengthened bone in a canine model

Reports on the mechanical and physical properties of lengthened bone after completion of the lengthening process remain scarce. Varied results of torsional testing of lengthened bone have been reported. Furthermore, torsional testing provides information on the shear properties of the tissue but does not reflect the elastic properties obtained from tensile, compressive, or bending tests. The present study evaluated the mechanical properties of lengthened bone at various time points, using a uniaxial tension test. Physical properties (density and ash weight) were determined as well. Results indicate that the tensile properties of the lengthened bone increase with time after the completion of lengthening, but they remain significantly weaker than controls (50%) even after 12 weeks. Density and ash weight measurements also increased with time, correlating with the increase in the tensile mechanical properties.     

Regional and temporal changes in the acoustic properties of fracture callus in secondary bone healing

Controlled fractures were created in the right femora of 17 male Sprague-Dawley rats. The fractured limbs were harvested at 2, 4, 6, and 8 weeks after fracture, fixed, and embedded in polymethylmethacrylate. Midsagittal sections from each animal were evaluated with a scanning acoustic microscope, a device that generates an acoustic impedance map of the scanned material. The impedance of the fracture callus was measured in six regions on each specimen. These regions were chosen in an effort to distinguish between the impedance of the callus formed through intramembranous or endochondral ossification, and we found that the time course of increasing impedance differed for the fracture callus formed through the two pathways. Additionally, we found a significant difference in the mean impedance of the callus at each time period (p < or = 0.0013 for all comparisons), which resulted in an extremely linear relationship (r2 = 0.999) between mean callus impedance and healing time. This experimental model has become a popular choice for the investigation of fracture healing. As such, an accurate determination of the mechanical properties of the fracture callus is often sought. We propose that the implementation of scanning acoustic microscopy in the study of fracture healing may determine the changes in the material properties more accurately than conventional testing methods.     

Biomechanical properties of human os calcanei: relationships with bone density and fractal evaluation of bone microarchitecture

The relationship between bone strength and bone mass is well established. The link between trabecular microarchitecture and biomechanical properties has been less extensively explored. To address this question, we have tested the mechanical behaviour of calcaneus bone samples and investigated the correlations between mechanical properties on the one hand, bone density and fractal analysis of microarchitecture on the other hand. Mechanical properties of 43 human os calcanei were determined by uniaxial compression testing of samples from tuber calcanei. Ash density, bulk density and dual energy X-ray absorptiometry of the samples were measured. Fractal analysis of the trabecular bone on calcaneus radiographs was performed by two estimators derived from the fractional Brownian motion model. The mechanical properties of human os calcis were found to correlate with age and density measurements. Fractal parameters derived from the bone texture analysis showed weaker but significant correlations with bone strength. Fractal analysis of texture could account in part for the variations of bone strength, but in this study cannot explain better than density the mechanical properties of trabecular bone. Nevertheless, it provides a non-invasive means of assessing molecular bone microarchitecture.     

Biomechanical and histologic alteration of facial recipient bone after reconstruction with autogenous bone grafts and alloplastic implants: a 1-year study

Potential alteration of the underlying recipient bone resulting from a graft or implant has significant clinical relevance. The present study was designed to evaluate the biomechanical and histologic alteration of facial recipient bone with autogenous bone graft and alloplastic implants over a 1-year period. The bilateral arches of 15 rabbits were randomized between four groups: (1) control (n = 6), subperiosteal exposure of the zygomatic arch was made; (2) onlay (n = 12), bone graft was placed as an onlay to the zygomatic arch; (3) inlay (n = 6), bone graft was placed as an inlay within the zygomatic arch; (4) implant (n = 6), a stainless steel plate was placed as an onlay to the zygomatic arch. Animals were killed 1 year after grafting. In the onlay groups, all steel implants and half of the onlay bone grafts (n = 6) were separated from the zygomatic arch; the remaining onlay bone grafts (n = 6) were left on the zygomatic arch. Three-point breaking strength was measured through the center of the graft/implant site on the zygomatic arch, followed by histologic evaluation and histometric assessment of residual bone density. The findings demonstrated no difference in the breaking strength per unit bone area between the control zygomatic arch group and the onlay group in which the bone graft was left in place. Breaking strength of the zygomatic arch in the former two groups was significantly greater than that in either group in which the onlay bone graft or implant had been removed, and was also greater than the breaking strength in that group in which inlay bone had been placed (p < 0.05). Histologic assessment showed full-thickness conversion in architecture of the zygomatic arch from compact to woven bone beneath onlays of either autogenous bone graft or steel implant; histometric assessment demonstrated an accompanying decrease in bone density in the latter groups relative to the control zygoma (p < 0.05). We conclude that onlay autogenous bone graft and alloplastic implants to the facial skeleton induce transformation of both graft and recipient bone from compact to woven architecture, accompanied by a reduction in bone density. The biomechanical strength of recipient facial bone is significantly weakened if an onlay bone graft or implant is removed. Weakening occurs per unit area of remaining bone, and is therefore independent of any thinning that may occur within the recipient bone because of graft/implant placement. These findings may impact upon decisions to augment stress-bearing regions of the facial skeleton with bone graft or implants, particularly if the graft/implant may eventually require removal.     

Recombinant growth hormone accelerates bone regenerate consolidation in distraction osteogenesis

The purpose of the present study was to prove whether homologous GH has a stimulating effect on bone healing. Therefore, left tibiae of 30 micropigs were osteomized and distracted over an external fixator at the rate of 2 mm/day on each of 10 consecutive days. Animals were killed after a healing period of another 10 days. The treatment group received 100 microg of recombinant porcine growth hormone (rpGH) per kilogram of body weight per day. Serial torsional nondestructive biomechanical tests were performed in vivo using a newly developed measurement device. After killing, destructive torsional strength testing of the sites of distraction was performed. To determine the endocrine response to the administration of rpGH, serum levels of insulin-like growth factor-I (IGF-I) were determined. Nondestructive in vivo testing showed that torsional stiffness of the regenerate was significantly higher in the treatment group than in the control group. Final regenerate torsional failure load was 131% higher and ultimate torsional stiffness was 231% higher in the treatment group than in the control group. The mean serum level of IGF-I increased to 440% of preoperative basal level in the treatment group and remained unchanged in the control group. Our data indicate that systemic administration of recombinant homologous growth hormone greatly accelerates ossification of bone regenerate in distraction osteogenesis.     

Internal calvarial bone distraction in rabbits with delayed-onset coronal suture synostosis

Recent studies have identified a subpopulation of craniosynostotic individuals who exhibit progressive or delayed-onset synostosis and mild craniofacial growth abnormalities. These individuals may be good candidates for nonextirpation, distraction osteogenesis therapy. The present study was designed to test this hypothesis by using internal calvarial bone distraction in a rabbit model with familial delayed-onset craniosynostosis. Data were collected from 159 rabbits: 71 normal controls, 72 with delayed-onset coronal suture synostosis, 8 with delayed-onset coronal suture synostosis and coronal suturectomy, and 8 with delayed-onset coronal suture synostosis and distraction. At 10 days of age, all rabbits had amalgam markers placed on both sides of the frontonasal, coronal, and anterior lambdoidal sutures. At 25 days of age, correction was accomplished through either a 5-mm-wide suturectomy or distraction osteogenesis. An internal distraction appliance was fixed to the frontal and parietal bones and percutaneously and intermittently activated at an average of 0.10 mm/day for 42 days (4.11 mm total). Serial radiographs were taken at 10, 25, 42, and 84 days of age. Results revealed that rabbits with delayed-onset synostosis had significantly (p < 0.01) reduced coronal suture growth rates (0.04 mm/day) compared with the other three groups (0.07 mm/day). Rabbits with suturectomy and rabbits with distraction showed similar coronal suture responses. However, from 42 to 84 days of age, rabbits with distraction showed reduced growth at the vault sutures and abnormal growth patterns in cranial vault width, cranial vault shape, and cranial base angulation compared with the other three groups. Results demonstrated that, although the normal coronal suture growth rate was maintained in rabbits with delayed-onset synostosis using intermittent distraction osteogenesis, normal adult craniofacial structure was not achieved. Such anomalous growth was probably a result of altered growth vectors and compressive forces at adjacent sutures during distraction. These findings suggest that distraction osteogenesis without corticotomy may be a treatment alternative in individuals with progressive, delayed-onset synostosis, but that internal appliances that generate low-level, continuous distractive forces should be investigated and developed.     

Fracture healing and callus innervation after peripheral nerve resection in rats

The effects of femoral and sciatic nerve resection on fracture healing and innervation of the fracture callus were studied using a stable fracture model. In 34 rats the right tibia was subjected to a standardized closed fracture and stabilized with a modular intramedullary nail. In half of the animals, resection of 1 cm of the femoral and sciatic nerves was performed (nerve resection group), whereas the other animals had sham operations (sham group). To avoid unequal load-bearing between the two groups, all fractured hindlimbs were immobilized in a plaster of Paris cast. The trial was terminated after 5 weeks of fracture healing. Callus size was scored radiographically, and bone mineralization was measured by 85-strontium incorporation. Seven rats from each group had immunohistochemical examination for neural regeneration and ingrowth. Antisera for protein gene product 9.5, neurofilaments, neural growth associated protein 43/B-50, calcitonin gene related peptide, and substance P were used. The mechanical properties of the healing fractures were recorded in a three-point cantilever bending test. After 5 weeks, the normally innervated, fractured tibias had regained approximately 50% strength compared with the unfractured side, in comparison with only 20% in the animals that had nerve resection. Although the fracture calluses were mechanically weaker, they were significantly larger in the nerve resection group, indicating defects in tissue composition or organization rendered by the nerve injury. The mineralization rate, as measured by 85-strontium incorporation, was the same in the two groups. However, the nerve resection did not provide complete denervation but changed the innervation pattern of the healing fracture, as the density of sensory nerve fibers immunostaining for substance P and neurofilaments was less in the group with femoral and sciatic nerve resection. The results suggest that intact innervation is essential for normal fracture healing because nerve injury induced a large, but mechanically insufficient, fracture callus.     

Coagulatory response after femoral instrumentation after severe trauma in sheep

Budesonide inhalation powder, available as Pulmicort Turbuhaler, is a corticosteroid with a high ratio of local to systemic effects that is administered to treat persistent asthma. The Turbuhaler achieves lung deposition approximately twice that of a metered-dose inhaler (MDI) with or without a spacer device. Budesonide inhalation powder has clinical efficacy equivalent to that of fluticasone and beclomethasone, but it has lower systemic bioavailability and fewer systemic side effects. As with other inhaled corticosteroids, dysphonia and oral candidiasis are the most frequent adverse effects, and systemic effects are infrequent. The initial starting dosage is 200 microg (1 puff) twice/day and may be increased to 800 microg twice/day in adults or 400 microg twice/day in children. Patients prefer the Turbuhaler to the MDI, Diskhaler, and Rotahaler because it is easier to use and more convenient to carry.     

Regeneration of defects in articular cartilage with callus and cortical bone grafts. An experimental study

Luteal-phase estrogen and progesterone concentrations were measured every other day and used to monitor the corpus luteum activity. The patterns of estrogen and progesterone concentrations were compared relative to the day of endogenous human chorionic gonadotropin (hCG) detection (defined as the day of implantation). The relationship between estrogen and progesterone and hCG concentrations was studied in 71 viable pregnancies, 12 clinical abortions, five preclinical abortions and 84 non-pregnant cycles after IVF/ET. Although all patients received luteal-phase progesterone support (25-50 mg/ml), low late luteal-phase progesterone concentrations of < 30 ng/ml from day + 11 to day + 15 were found in 64 patients (17% of viable pregnancies, 33.3% of clinical abortions, 60% of preclinical abortions and 53.6% of non-pregnant cycles) day + 1 was the day of retrieval). Implantation always occurred before or on day + 13 and 86% of pregnant cycles implanted on day + 8 to day + 11. Viable pregnancies had significantly higher mean progesterone concentrations on day + 3 to day + 7 (pre-implantation) and on day + 9 to day + 15 (postimplantation) than those of non-pregnant cycles or abortions. On the day of implantation, the mean +/- standard of deviation of estrogen (pg/ml) and progesterone (ng/ml) levels for viable pregnancies, clinical abortion and preclinical abortions were 314 +/- 210, 40.5 +/- 25; 226.7 +/- 246, 48.7 +/- 31; and 39.6 +/- 24.5, 28.6 +/- 24.5, respectively. On the same day, 73.2% of viable pregnancies, 41.7% of clinical abortions, and 20% preclinical abortions had a progesterone concentration > 30 ng/ml; 73.2% of viable pregnancies, 41.7% of clinical abortions and 20% of preclinical abortions had an estrogen concentration > 100 pg/ml. Although not precluding implantation completely, late luteal-phase hormonal deficiencies may impair endometrial growth and might ultimately lead to failure or abnormal implantation. A viable pregnancy requires not only a functional corpus luteum in the early luteal phase to develop a receptive endometrium, but also a responsive corpus luteum in the late luteal phase to support pregnancy. The time of implantation is critical. Implantation that occurs before the demise of the corpus luteum will facilitate a normal pregnancy.     

Changes of callus diameter during axial loading and after fixator removal in leg lengthening

We retrospectively reviewed nine tibial lengthenings in seven achondroplastic patients. The callotasis method was used, and a unilateral type lengthener, either the Dynamic Axial Fixator (Orthofix, Italy; eight legs) or the High Functional Fixator (Matsumoto Co., Japan; one leg), was applied. The distracted length averaged 14.6 (range 10-18) cm. The minimum diameter of the callus was measured using a ruler on anteroposterior and lateral radiographs. The callus diameter ratio (%) was calculated as the callus diameter divided by the original diaphysis diameter. For periods during axial loading and after removal of the fixator in each patient, a single regression line was drawn on the callus diameter ratio data using the least squares method, and the diameter change rate (%/day) was evaluated by inclination of this line. The diameter change rates during axial loading were negative in six legs, but those after fixator removal were positive in all legs, and the latter were significantly greater than the former. The diameter change rates after fixator removal on the anteroposterior radiographs were negatively correlated with the callus diameter ratio at the time of fixator removal (r = 0.84, P = 0.0008). Simple axial loading may not be a sufficient mechanial environment for restoration of the physiological shape, and it is important to be aware that we cannot expect the callus diameter to increase by this means alone.     

Changes in bone mass and serum markers of bone metabolism after parathyroidectomy

BACKGROUND: Primary hyperparathyroidism (PHPT) is associated with an increased bone turnover. The simultaneous use of biochemical and bone mass measurements before and after parathyroidectomy is sparsely reported. This study was carried out to evaluate changes in bone mass and markers of bone metabolism in postmenopausal women with PHPT after parathyroidectomy. METHODS: Twelve women, mean age of 63 years, were investigated. Measurements of bone mineral density (total body, spine, hip, and forearm bone mineral density) with dual-energy x-ray absorptiometry were performed before operation and at follow-up at a median of 23 months. Concomitantly, changes in serum intact parathyroid hormone, bone-specific alkaline phosphatase (B-ALP), osteocalcin, carboxyterminal propeptide of type I procollagen, and the immunoactive carboxyterminal telopeptide of type I collagen were recorded. RESULTS: At follow-up a significant increase in bone mineral density of the spine (p < 0.05), femoral neck (p < 0.05), Ward's triangle (p < 0.05), and trochanter (p < 0.01) was observed. No significant changes in the forearm were registered. Levels of parathyroid hormone, B-ALP, and osteocalcin were elevated and intercorrelated before operation. The serum levels of these parameters decreased significantly after operation. Serum levels of carboxyterminal propeptide of type I procollagen and the immunoactive carboxyterminal telopeptide of type I collagen did not significantly differ from a reference population, and no major changes were observed at follow-up. CONCLUSIONS: Bone mineral density in the spine and hip is improved after parathyroidectomy in postmenopausal women with primary hyperparathyrodism. Serum levels of B-ALP and osteocalcin are elevated in PHPT and decrease after operation. The clinical usefulness of serum markers of collagen metabolism in investigating bone metabolism in PHPT seems limited.     

Gender-related differences in the relationship between densitometric values of whole-body bone mineral content and lean body mass in humans between 2 and 87 years of age

BACKGROUND: The role of venovenous bypass (VVB) during orthotopic liver transplantation (OLT) remains controversial. The aims of this study were to evaluate the current role of VVB at all major centers in North America, to examine the results of OLT and complications of VVB between two periods with a strict policy for routine versus selective use of VVB, and to review the literature. STUDY DESIGN: A survey of 50 major liver transplant centers was conducted using mailed questionnaires. A retrospective chart review was performed for 547 OLT patients having transplantation during two distinct periods with a strict policy for routine versus selective use of VVB at the University of Toronto, Canada, and at Duke University Medical Center, Durham, North Carolina. The literature was reviewed with a focus on the benefits and indications for routine versus selective use of VVB. RESULTS: Thirty-eight (76%) of 50 centers responded. Sixteen (42%) of them used VVB routinely, with a reported complication rate of 10-30%. Lymphocele and hematoma were the most common complications, but patients having major vascular injury, air embolism, and death were reported. A recent change to selective use of VVB was reported in 30% of the centers (11 of 38). In the Duke-Toronto series, the complication rates were similar between the two periods, at 13.4% and 18.8%, respectively. The outcome of OLT was not influenced by the policy of routine or selective use of VVB. CONCLUSIONS: There is a trend away from the routine use of VVB during OLT. Intraoperative hemodynamic instability during the hepatectomy and a failed trial of hepatic venous occlusion were the most important criteria for using VVB. We conclude that VVB should be used selectively to avoid associated complications and to decrease operative time and costs.     

Prostaglandin concentrations in intra-uterine tissues from late-pregnant sheep before and after labour

Prostaglandin E (PGE), prostaglandin F (PGF) and 13,14-dihydro-15-keto-prostaglandin F (PGFM) have been measured in cotyledons and myometrium from sheep before and after labour. Fetal cotyledons contained more PGE than maternal cotyledons which in turn contained more than myometrium. The maternal cotyledon contained the highest concentrations of PGF, but the fetal cotyledon was the only tissue exhibiting a statistically significant rise in the concentration of PGF following labour. Concentrations of PGFM were closely correlated with (although usually lower than) those of PGF.     

Calcium elevation in sheep cumulus-oocyte complexes after luteinising hormone stimulation

We investigated Ca2+ levels in intact cumulus-oocyte complexes (COCs) on exposure to peak levels of luteinising hormone (LH). Specific preparations were used where cumulus corona cells were loaded with a membrane-permeant Ca(2+)-sensitive dye (FLUO-3AM), whereas the oocyte was injected directly with the nonpermeant form of the dye (FLUO-3). After exposure to LH, cumulus and corona radiata cells showed distinct rises in intracellular Ca2+ in 50-200 sec. The pattern of Ca2+ response varied in the different cells both for the duration of the transients and for their persistence. Interestingly, Ca2+ elevations were recorded in all the layers of the cumulus mass, including the innermost layer of corona cells, demonstrating the wide diffusion of LH receptors. Following the Ca2+ raise in somatic cells, an intracellular Ca2+ elevation also was recorded within the oocyte with a delay of 100-300 sec. The elevation started at the cortex of the oocyte and then spread all over the ooplasm. The addition of verapamil or manganese chloride did not prevent LH-induced Ca2+ elevation in the COC, whereas mechanical uncoupling of cumulus cells from the oocyte prevented any Ca2+ response within the oocyte. The results indicate that cumulus corona cells are capable of transducing LH message by rising intracellular Ca2+ and show that this signal is rapidly transferred into the oocyte through gap junctions. This may result from the direct diffusion of Ca2+ or its putative releaser IP3 from cumulus cells to the oocyte.     

Immobilisation induced bone loss in the sheep is not modulated by calcitonin treatment

The effect of calcitonin on immobilisation-induced loss of cortical and trabecular bone was studied in adult female sheep. The left calcaneus of 24 adult female Welsh mountain sheep was protected from normal loading by placing an external fixator across the hock joint, from the tibia to the metatarsus. In vivo strain gauge recordings from similar animals showed that this procedure resulted in a 50% reduction in principal strain magnitude in the shaft of the calcaneus during walking. All animals received intramuscular injections three times weekly. Half of the sheep received 100 i.u. of salmon calcitonin while the remainder received vehicle alone. The experiment was conducted blind. Over the 12 week period of the experiment, dual photon absorptiometry was performed at monthly intervals to measure the bone mineral content (BMC) of the calcanei. In all the animals, the loss of bone associated with the functional protection afforded by the fixator was highly significant (p < 0.0001). There was however, no significant difference in either the amount or rate of bone loss between animals which had received calcitonin and those which had not. Post mortem measurement of the cortical thickness of the shaft of the calcaneus revealed a specific pattern of loss which was also not different in the two groups. In this model, calcitonin treatment was ineffective in preventing or retarding loss of bone associated with reduced functional load-bearing over a 12 week period.     

Biomechanical analysis of nonreamed tibial intramedullary nailing after simulated transverse fracture and fibulectomy

PURPOSE: To examine differences between early adolescent girls' and their mothers' perceptions of girls' depressive symptoms. METHODS: 313 daughter-mother dyads completed the Children's Depression Inventory. RESULTS: Low to modest agreement was found for most symptoms, although higher agreement was found for symptoms relating to school performance. The hypothesis that girls would report more ideational symptoms and mothers more behavioral symptoms of depression was tested; girls generally reported more ideational and behavioral symptoms when differences occurred. However, several specific ideational symptoms (feeling like crying; feeling sad; guilt; worrying) tended to be more frequently endorsed by girls and had particularly poor daughter-mother agreement. Examining third variables associated with daughter-mother agreement, girls scoring high on social desirability tended to have smaller daughter-minus-mother difference scores for ideational, but not for behavioral items; therefore, social desirability may be associated with girls underreporting ideational symptoms. CONCLUSIONS: Mothers appear to be reliable raters of symptoms related to school functioning, but may be less aware of certain covert depressive symptoms in their early adolescent daughters.     

Semistructural allografting in bone defects after curettage

Amongst the focal and multifocal neuropathies that are associated with diabetes mellitus one of the most common is a proximal predominantly motor lower limb neuropathy. Recent evidence has indicated that, at least in a proportion of cases, this may have an inflammatory basis. We have examined a consecutive series of 15 cases of proximal diabetic neuropathy (diabetic amyotrophy). These were characterized by proximal pain and asymmetric proximal or generalized lower limb muscle weakness, associated in some cases with radicular sensory involvement. Two-thirds of the patients had an accompanying distal symmetric sensory polyneuropathy. Biopsy of the intermediate cutaneous nerve of the thigh, a sensory branch of the femoral nerve, showed epineurial microvasculitis in 3 patients and nonvasculitic epineurial inflammatory infiltrates in another case. In a further case, microvasculitis was found in both in the sural nerve and a quadriceps muscle biopsy specimen. The detection of inflammatory changes appeared to be correlated with the occurrence of sensory radicular involvement. Whether similar changes are present in muscle nerves in this predominantly motor syndrome requires further study. Nevertheless, the present observations confirm the view that secondary vasculitic or other inflammatory reactions may contribute to some forms of diabetic neuropathy.     

Connectivity and the elastic properties of cancellous bone

The effect of ibuprofen enantiomers on the stereoselective binding of 3-acyloxy-1,4-benzodiazepines to human serum albumin (HSA) was studied using both native and Sepharose-immobilized protein. (S)-Lorazepam acetate exhibited considerably enhanced binding, especially in the presence of (+)-(S)-ibuprofen. The phenomenon is an indication of cooperative allosteric interaction between different binding sites during multiple cobinding of two ligands.