Interactions of Aluminum(III) with Phosphates

In order to obtain information about aluminum(III)-phosphate interactions, potentiometric measurements were carried out to characterize the complex forming properties of Al(III) with organic phosphates, phosphonates, and nucleoside-5'-monophosphates. The aluminum(III)-orthophosphate system is difficult to study due to AlPO(4) precipitation. To overcome this problem, the stability constant logarithms of the 1:1 Al(III) complexes of ligands with the same donor groups (log K(1:1)) were plotted against the basicities of the ligands (log K(PO)3(H)). The resulting linear free energy relation (LFER) indicates that organic phosphates, phosphonates, and uridine-, thymidine-, and guanosine 5'-monophosphates similarly bind Al(III). Adenosine and cytidine 5'-monophosphate fall above the LFER owing to the presence of a second microform with the nucleic base protonated and a hydroxide bound to the Al(III). From the LFER the log stability constant for Al(III) binding to HPO(4)(2-) is estimated as 6.13 +/- 0.05. From the weakness of any soluble orthophosphate complexes of Al(III) we confirm the importance of citrate as the main small molecule Al(3+) binder in the blood serum. The study includes investigation of Al(III) binding to di- and triphosphates, which bind metal ion differently than monophosphates. Structures of the complexes were supported by (31)P NMR measurements.

In vitro fatigue behavior of the equine third metacarpus: remodeling and microcrack damage analysis

We studied remodeling and microcrack damage in specimens of Thoroughbred racehorse third metacarpal bone that had been subjected to monotonic or fatigue failure. We asked three questions. What effects does mechanical loading have on histologically observable microcrack damage? Are there regional variations in remodeling of the equine cannon bone, and do these variations correlate with mechanical properties? To what extent are remodeling and microcrack damage age-dependent? Machined beams from the medial, lateral, and dorsal cortices were loaded to fracture in four-point bending monotonically, or cyclically at a load initially producing 10,000 microstrain. Specimens were then bulk-stained in basic fuchsin, and cross sections were prepared from loaded and load-free regions of each beam. Current and past remodeling, porosity, and microcrack density and length were determined histomorphometrically. Strained and unstained microcracks were observed. Unstained cracks were associated with regions of woven bone and appeared to be damaged Sharpey's fibers. Their density (approximately 30/mm2) did not increase after failure, but their length (approximately 25 microns) did, especially near the surfaces of the beam. Stained cracks were wider and longer than unstained cracks and were located primarily near the fracture surface and on the compressed side of the beam. Stained cracks after failure were more numerous in those beams having a higher elastic modulus, a shorter fatigue life, or greater deformation at failure. The extent of past remodeling increased with age, especially in the medial region; the rate of current remodeling generally declined with age, but not in the dorsal region, which has the best fatigue resistance. In summary, while remodeling varied with age and region, its effects on bone structure did not appear to influence microdamage. Basic fuchsin staining of damage in fractured equine bone was independent of age and region and confined to near the fracture surfaces. Distributed microdamage consisted only of what appeared to be subtle disruptions of Sharpey's fibers.

Calcium buffering is required to maintain bone stiffness in saline solution

This work determined whether mineral dissolution due to prolonged testing or storage of bone specimens in normal saline would alter their elastic modulus. In one experiment, small pieces of equine third metacarpal bone were soaked in normal saline supplemented with varying amounts of CaCl2. Changing Ca ion concentrations in the bath were monitored and the equilibrium concentration was determined. In a second experiment, the elastic moduli of twenty 4 x 10 x 100 mm equine third metacarpal beams were determined non-destructively in four-point bending. Half the beams were then soaked for 10 days in normal saline, and the other half in saline buffered to the bone mineral equilibrium point with Ca ions. Modulus measurements were repeated at 6 and 10 days. The equilibrium Ca ion concentration for bone specimens was found to be 57.5 mg l-1. The modulus of bone specimens soaked in normal saline significantly diminished 2.4%, whereas the modulus of those soaked in calcium-buffered saline did not change significantly.

Osteonal structure in the equine third metacarpus

In studying the flexural fatigue properties of the equine third metacarpal (cannon) bone, we previously found that the dorsal region was weaker monotonically, but more fatigue resistant, than the lateral region. Fatigue resistance was associated with fracture surfaces which demonstrated that secondary osteons had "pulled out" of the surrounding matrix; this never happened in lateral specimens. We therefore became interested in the osteonal structure of this bone, and began to study its birefringence patterns in circularly polarized light. We found that the predominant type of secondary osteon was one in which only the outermost few lamellae were circumferential, with the inner lamellae being longitudinally oriented. This "hoop" pattern had not been described in Ascenzi's classic papers. Using basic fuchsin-stained, undecalcified cross-sections from the dorsal, medial, and lateral midshaft regions of 12 pairs of cannon bones, we classified 360 secondary osteons according to their birefringence patterns, and measured their inner and outer diameters. We found that variants of the hoop category comprised 60% of all osteons, but were significantly less common in the dorsal region, where the predominant types were Ascenzi's "longitudinal" or "alternating" patterns. The dorsal region also had smaller osteons (OD = 156 +/- 19 microns) than the medial (179 +/- 13 microns, p = 0.0004) and lateral (182 +/- 13 microns, p = 0.0001) regions. We postulate that these regional variations in osteonal size and structure, which are obviously produced by regional variations in remodeling, have important mechanical implications.

Noninvasive determination of bone mechanical properties using vibration response: a refined model and validation in vivo

Accurate non-invasive mechanical measurement of long bones is made difficult by the masking effect of surrounding soft tissues. Mechanical response tissue analysis (MRTA) offers a method for separating the effects of the soft tissue and bone; however, a direct validation has been lacking. A theoretical analysis of wave propagation through the compressed tissue revealed a strong mass effect dependent on the relative accelerations of the probe and bone. The previous mathematical model of the bone and overlying tissue system was reconfigured to incorporate the theoretical finding. This newer model (six-parameter) was used to interpret results using MRTA to determine bone cross-sectional bending stiffness, EIMRTA. The relationship between EIMRTA and theoretical EI values for padded aluminum rods was R2 = 0.999. A biological validation followed using monkey tibias. Each bone was tested in vivo with the MRTA instrument. Postmortem, the same tibias were excised and tested to failure in three-point bending to determine EI3-PT and maximum load. Diaphyseal bone mineral density (BMD) measurements were also made. The relationship between EI3-PT and in vivo EIMRTA using the six-parameter model is strong (R2 = 0.947) and better than that using the older model (R2 = 0.645). EIMRTA and BMD are also highly correlated (R2 = 0.853). MRTA measurements in vivo and BMD ex vivo are both good predictors of scaled maximum strength (R2 = 0.915 and R2 = 0.894, respectively). This is the first biological validation of a non-invasive mechanical measurement of bone by comparison to actual values. The MRTA technique has potential clinical value for assessing long-bone mechanical properties.

Fatigue behavior of the equine third metacarpus: mechanical property analysis

This is the first in a series of experiments to study the fatigue properties of equine cannon (third metacarpal) bone specimens from Thoroughbred racehorses. Monotonic and fatigue tests to failure were performed in four-point bending on diaphyseal specimens in a 37 degrees C saline bath to answer three initial questions. (a) Will a linear variable differential transducer yield the same elastic modulus as strain gauges? (b) Will fatigue results depend on whether the periosteal or endosteal side of the beam is in tension? (c) Are there regional variations in the monotonic and fatigue properties of the cannon bone midshaft? Eighteen left-right pairs of specimens from six horses were used. One beam of each pair was fitted with strain gauges. Fatigue tests were conducted on 24 specimens under load control at 2 Hz; an initial range of 0-10,000 microstrain was used so as to produce failure in a reasonable period of time. There were no left-right differences in the fatigue or monotonic properties, and the presence of a gauge had no effect on modulus measured by a linear variable differential transducer. However, gauge-measured moduli were about 1 GPa less than transducer-measured values. Fatigue life was independent of which side of the beam was in tension, and there were significant variations in mechanical properties around the cortex. The lateral region was stiffer than the dorsal region but the latter had a longer fatigue life. The fixed cylindrical supports used in this experiment eventually produced slight wear grooves, causing artifactual stiffening at the end of the load cycle in some specimens. A second experiment using roller supports confirmed the reason for this stiffening. It also showed that fatigue life was shorter when roller supports were used but regional differences were similar.

Involvement and role playing

Three studies focused on involvement as a function of type and content of the role play, experimenter behaviors, and proportion of time in scenario roles. Several measures of involvement were obtained. Generally, there was a low correlation between involvement estimated by observers and self-reported involvement; subjective involvement also was related more consistently to other variables.

On the histologic measurement of osteonal BMU activation frequency

When cortical bone is remodeled by osteonal basic multicellular units (BMUs), activation frequency is defined as the number of new BMUs created per unit volume of cortex per unit time. When osteonal remodeling is histomorphometrically analyzed, a different definition of activation frequency is usually used; it is equivalent to the number of previously activated BMUs reaching the plane of the section per unit area per unit time. Using simple geometric analysis, it is shown that the latter histologic measurement is equal to the former definition multiplied by the mean distance that a BMU tunnels before it ceases its activity.

Citrate as the main small molecule binding Al3+ in serum

A recent proposal (Clin Chem 1992;38:1809-18) that inorganic phosphate is the predominant small molecule binding Al3+ in blood serum is shown to be incorrect. Experiments in which Al3+ is added to solutions containing phosphate and citrate in the same proportions as in serum clearly show that citrate prevents formation of any aluminum phosphate precipitate, and analysis of these data indicates that the assumed binding constants for soluble phosphate are two orders of magnitude too strong. Consideration of the effect of competitive binding of alkaline earth metal ions to citrate on Al3+ binding and of a set of transferrin-Al3+ stability constants leads to the conclusion that the proportions are in close agreement with previously published results. We conclude on the basis of stability constants that, of the Al3+ in blood serum, approximately 89% (+/- 5%) binds to transferrin and approximately 11% (+/- 5%) to citrate.

Citrate as the main small molecule binding Al3+ in serum

A recent proposal (Clin Chem 1992;38:1809-18) that inorganic phosphate is the predominant small molecule binding Al3+ in blood serum is shown to be incorrect. Experiments in which Al3+ is added to solutions containing phosphate and citrate in the same proportions as in serum clearly show that citrate prevents formation of any aluminum phosphate precipitate, and analysis of these data indicates that the assumed binding constants for soluble phosphate are two orders of magnitude too strong. Consideration of the effect of competitive binding of alkaline earth metal ions to citrate on Al3+ binding and of a set of transferrin-Al3+ stability constants leads to the conclusion that the proportions are in close agreement with previously published results. We conclude on the basis of stability constants that, of the Al3+ in blood serum, approximately 89% (+/- 5%) binds to transferrin and approximately 11% (+/- 5%) to citrate.

The relationship between mass and acceleration for impacts on padded surfaces

It is shown analytically that when an object impacts a deformable surface, the acceleration it experiences is inversely proportional to its mass. This is because acceleration is reduced by deformation of the surface, and more massive objects deform the surface more. Since head injury is thought to depend more on acceleration than applied force, this result implies that children may be at greater risk than adults when striking a padded surface. To test the theoretical prediction, 2.69 and 7.40 kg missiles were dropped 31.8 cm onto three deformable surfaces: dry sod, moist sod, and an artificial playing surface. Impact force was measured with a force plate, and divided by missile mass to obtain acceleration. For each test surface, the smaller mass produced a larger acceleration than the larger mass, confirming the theoretical result. Additionally, load-deformation characteristics of the three surfaces were measured, and the results used to predict the effects of mass on acceleration during impact. The predicted results agreed well with the experimental data for the artificial surface (2.3% difference) and moist sod (5.7% difference), but less well for dry sod (21% difference).

The effects of collagen fiber orientation, porosity, density, and mineralization on bovine cortical bone bending properties

The relationship between the mechanical properties of bone in three-point bending and eight histocompositional variables was studied. Ultimate stress, ultimate strain, and elastic modulus were measured in 35 beams of cortical bone from bovine tibias using standard ASTM methods. Four elements of porosity were determined by point counting, mineralization by ashing, and wet and dry apparent density from weight and volume. Collagen fiber orientation was estimated using polarized light, and specimens were categorized as plexiform, mixed, or osteonal. Analysis of variance showed that ultimate stress was similar in the plexiform and osteonal specimens, but elastic modulus was reduced in the latter (18.6 +/- 1.2 vs 21.0 +/- 1.9 GPa), which were significantly less porous (by 24%) and less mineralized (by 3%) than the plexiform group. Stepwise multiple regression analysis showed that collagen fiber orientation ranked highly as a predictor of bending properties. The next best predictors were density and mineralization. In the plexiform group, 77% of the variability in elastic modulus was accounted for by wet and dry density and collagen fiber orientation. In the osteonal group, 88% of modulus variability was accounted for by percentage mineralization and collagen fiber orientation. When all the specimens were pooled, 62% of the variability in elastic modulus was attributable to variations in collagen fiber orientation, density, and porosity due to Haversian canals.

Changes in bone in a model of spinal cord injury

Bone calcium, histomorphometry, and mechanical strength were evaluated in a model of spinal cord injury. Cortical bone area and rates of formation and apposition at the tibiofibular junction (TFJ) and midshaft of the humerus were measured at 35-42, 42-77, and 77-94 days after transection of the spinal cord. All comparisons were between the animals with a spinal lesion and control animals. A 0.34% difference in the length of the tibia of the two groups of animals was observed, the dry weight of the tibia was 28.4% less in rats with a lesion, and there was no significant difference in the amount of calcium per milligram of bone. At 35 days after surgery, the cortical area in the midshaft of the humerus was slightly less (11%) in rats with a lesion, but by 94 days there was no difference in cortical or medullary area. The final (day 94) cortical area at the TFJ in rats with a lesion was less than that in the controls. Bone formation at the TFJ was similar in both groups in the period of 35-42 days and was similar at 77-94 days in the animals with a lesion, and rates of formation and apposition were greater in the humerus of rats with a lesion; the rates did not differ significantly between groups at either site. At 94 days, trabecular bone area in the tibial metaphysis was 41% less in rats with a lesion. Mechanical parameters were significantly less in the femora, but not the humeri, of rats with a lesion.

Bone ingrowth and mechanical properties of coralline hydroxyapatite 1 yr after implantation

A previous study of coralline hydroxyapatite as a bone-graft substitute was extended from 4 to 12 months to determine better the relationships between implantation time, bone ingrowth and mechanical properties. The model consisted of a 10 x 30 mm window defect in the shaft of the canine radius (a cortical site), and a 10 mm diameter cylindrical defect in the head of the humerus (a cancellous site). In the new study, these two defects were made bilaterally in eight dogs, and filled with block-form coralline hydroxyapatite. The radius defects were supported by a metal fixation plate which was removed after 9 months. After 12 months, the dogs were killed and the left-side implants were analyzed histomorphometrically and mechanically. The right-side radius and humerus were reserved for structural analysis. The results were combined with those previously measured after 4, 8, 12 and 16 wk of implantation. In the cortical site, bone ingrowth increased from 52% at 16 wk to 74% at 1 yr. In the cancellous site, bone ingrowth was 38% after 4 wk, then fell monotonically, reaching 17% at 1 yr. Bending and compressive strength and stiffness of the radius implants increased throughout the post-implantation year, but compressive strength and stiffness of the humerus implants did not change after the first 2-4 months. Mechanical properties were strongly correlated to bone ingrowth in the cortical, but not the cancellous, site. The volume fraction of the coralline hydroxyapatite material diminished significantly with time in the cortical, but not the cancellous, site.

Calculating the probability that microcracks initiate resorption spaces

This paper explores the assumptions and limitations of the probability calculation that led to the conclusion by Burr et al. (1985) that microcracks initiate new remodeling events. It also corrects several minor errors in the calculation in the original manuscript. The results show that the probability that cracks and resorption spaces are associated depends heavily on a factor, F, that accounts for the possibility that some osteons that contain both a crack and a resorption space share a cement line with an adjacent osteon to which the crack more properly 'belongs.' F in turn depends on (1) the measurement criteria for cracks and resorption spaces, (2) the osteon population density in the bone, and (3) the mechanism by which cracks initiate remodeling. The theoretical maximum number of osteons that can contain both a crack and a resorption space (nmax) increases as the number of resorption spaces (r), the number of cracks (c), and F increase, but decreases as the osteon population density (d) increases. A larger nmax makes a direct association between cracks and resorption spaces more difficult to demonstrate experimentally.

Emotional crying, depressed mood, and secretory immunoglobulin A

The relationship between emotional crying and secretory immunoglobulin A (S-IgA) in whole saliva was examined. Previous research had indicated that lower S-IgA was associated with crying. Similar results were found in the present study. Depressed mood was not associated with S-IgA.

Histological features of the dorsal cortex of the third metacarpal bone mid-diaphysis during postnatal growth in thoroughbred horses

The dorsal cortex of the equine third metacarpal mid-diaphyseal bone was characterised during growth by the histological and microradiographic examination of specimens from 30 horses ranging in age from 2 months to 8 y. Bone from horses aged less than 6 months was characterised by rapid periosteal apposition of circumferential trabeculae of woven bone that were next connected by radial trabeculae to the parent cortex. Deposition of lamellar bone on the inner trabecular surfaces resulted in rows of primary osteons. Replacement of primary bone occurred only after 4 months of age and preferentially in the woven interstitial bone separating rows of primary osteons formed in the postnatal periosteal cortex. Resorption cavities and incompletely filled secondary osteons characterised bone of 1 and 2-y-old horses. Bone from horses older than 3 y contained several generations of secondary osteons, fewer resorption spaces and incompletely filled osteons, and had a greater portion of circumferentially oriented collagen fibres than bone from younger horses. Bone from horses older than 5 y had large resorption cavities characterised by irregular boundaries. We propose that the process of periosteal bone tissue apposition observed in growing foals be called 'saltatory primary osteonal bone formation' and that this process results in faster cortical expansion and larger total surface area for bone deposition than circumferential lamellar, simple primary osteonal, and plexiform mechanisms of periosteal bone formation. We speculate that bone from 1 and 2-y-old horses would be more susceptible to fatigue microdamage resulting from compressive loads because of high porosity, few completed secondary osteons and low proportion of circumferentially oriented collagen fibres.

A worst-case optimal parameter selection model of cancer chemotherapy

An optimal parameter selection model of cancer chemotherapy in which two system parameters are unknown is formulated as a worst-case optimal parameter selection model. The model assumes that the unknown parameters lie within a known set. The system constraints must be satisfied over this entire set, and the objective function minimized in the worst case. The continuous dependence of the objective function and the system constraints upon the unknown parameters can be removed, making a numerical solution tractable. For the data considered it is proven that a cure is impossible no matter what the values of the unknown parameters in the parameter set. The optimal policy is shown to be relatively low dose intensity for the majority of the treatment, with the remaining drug delivered towards the end of the treatment interval.

Cooperative proton and calcium binding by sarcoplasmic reticulum ATPase

The classic work on binding of calcium to CaATPase is analyzed by an objective non-linear least squares procedure of 74 data points over six pH values. Binding of two calciums to the basic form of the sites occurs with an equilibrium stability constant product of log K1K2 = 13.2. Owing to competition from protons, this value drops in acidic and neutral solutions, becoming, for example, 11.9 at pH 6.8. Binding of the two calciums is so strongly cooperative that its extent is difficult to estimate reliably; there is very little of the one calcium species. Two protons are also bound cooperatively to the calcium sites. In solutions of calcium free protein, at pH less than 7.6 the predominant species holds two protons at the calcium sites, while at greater pH the dominant species bears no protons; there is very little of the intermediate one proton species. The analysis also reveals the likely presence of a small, less than statistical, amount of a ternary complex bearing one calcium and one proton.

Optimal control of tumor size used to maximize survival time when cells are resistant to chemotherapy

The high failure rates encountered in the chemotherapy of some cancers suggest that drug resistance is a common phenomenon. In the current study, the tumor burden during therapy is used to slow the growth of the drug-resistant cells, thereby maximizing the survival time of the host. Three types of tumor growth model are investigated--Gompertz, logistic, and exponential. For each model, feedback controls are constructed that specify the optimal tumor mass as a function of the size of the resistant subpopulation. For exponential and logistic tumor growth, the tumor burden during therapy is shown to have little impact upon survival time. When the tumor is in Gompertz growth, therapies maintaining a large tumor burden double and sometimes triple the survival time under aggressive therapies. Aggressive therapies aim for a rapid reduction in the sensitive cell subpopulation. These conclusions are not dependent upon the values of the model constants that determine the mass of resistant cells. Since treatments maintaining a high tumor burden are optimal for Gompertz tumor growth and close to optimal for exponential and logistic tumor growth, it may no longer be necessary to know the growth characteristics of a tumor to schedule anticancer drugs.