A Framework for Program Development Based on Schematic Proof

Often, calculi for manipulating and reasoning about programs can be recast as calculi for synthesizing programs. The difference involves often only a slight shift of perspective: admitting metavariables into proofs. We propose that such calculi should be implemented in logical frameworks that support this kind of proof construction and that such an implementation can unify program verification and synthesis. Our proposal is illustrated with a worked example developed in Paulson's Isabelle system. We also give examples of existent calculi that are closely related to the methodology we are proposing and others that can be profitably recast using our approach

Obesity and kidney stone disease. A systematic review

INTRODUCTION: Currently, abdominal obesity has reached an epidemic stage and obesity represents an important challenge for worldwide health authorities. Epidemiologic studies have demonstrated that the stone risk incidence increases with Body Mass Index, through multiple pathways. Metabolic syndrome and diabetes are associated with an increased renal stones disease incidence. The aim of this systematic review was to investigate the prevalence, morbidity, risk factors involved in the association between obesity and urolithiasis. EVIDENCE ACQUISITION: The search involved finding relevant studies from MEDLINE, EMBASE, Ovid, the Cochrane Central Register of Controlled Trials, CINAHL, Google Scholar, and individual urological journals between January 2001 and May 2017. The inclusion criteria were for studies written in the English language, reporting on the association between obesity and urinary stones. EVIDENCE SYNTHESIS: The underlying pathophysiology of stone formation in obese patients is thought to be related to insulin resistance, dietary factors, and a lithogenic urinary profile. Uric acid stones and calcium oxalate stones are observed frequently in these patients. Insulin resistance is thought to alter the renal acid-base metabolism, resulting in a lower urine pH, and increasing the risk of uric acid stone disease. Obesity is also associated with excess nutritional intake of lithogenic substances and with an increase in urinary tract infection incidence. Recent studies highlighted that renal stone disease increases the risk of myocardial infarction, progression of chronic kidney disease, and diabetes. Contemporary, bariatric surgery has been shown to be associated with hyperoxaluria and oxalate nephropathy. Certainly, the many health risks of obesity, including nephrolithiasis, will add more burden on urologists and nephrologists. CONCLUSIONS: Obesity related nephrolithiasis seems to necessitate weight loss as primary treatment, but the recognition of the associated complications is necessary to prevent induction of new and equally severe medical problems. The optimal approach to obesity control that minimizes stone risk needs to be determined in order to manage obesity-induced renal stones disease

Physiochemical modifications to bone mineral

Bone is a complex composite material consisting of three main components: a mineral phase structurally similar to calcium hydroxyapatite (HAp), an organic matrix containing collagenous and non-collagenous proteins and, water. The complexity of bone has led to an abundance of literature across a wide range of disciplines, which have endeavoured to provide a greater understanding of this material. In particular, heated bone studies are prevalent in biomedicine where heat treatment is often used to sterilise bone material required for xeno– and allo- grafts, in forensic science where species differentiation of unknown heated bone specimens would prove invaluable and in archaeology, where heated bone material often provides information about the cooking and funeral practices of our ancestors. Unfortunately, many of these studies are largely observational and some of the processes and mechanisms associated with heated bone are largely assumed and in some instances ambiguous. Over 1000 biological and synthetic HAp specimens were utilised during this research to investigate the fundamental processes and mechanisms associated with unheated and heated bone. In particular, three controversial areas of bone research were considered: - in vivo HAp crystal size control, the relationship between the organic and mineral components of bone during heat treatment and the confounding effects of cooling on bone mineral during heat treatment. This was achieved by considering the chemical composition of unheated biological and synthetic HAp specimens, and heated bone specimens from various species including human. The results of this thesis demonstrate that an intrinsic rather than extrinsic source may be responsible for in vivo biological HAp crystal size control, a concept which has not previously be considered. The results have also shown bone mineral crystallisation during heat treatment is promoted by the organic matrix and, cooling has an impact on both crystallisation and thermal decomposition of HAp during heat treatment. This research has also questioned the use of current X-ray diffraction (XRD) refinement techniques with nanocrystalline materials such as bone, to determine crystalline size and strain. Further interpretation of the results questioned whether heated bone data is comparable between research groups, whether it was possible to create a time and temperature predictive model for heated bone and whether human bone is statistically different from other bone types when dynamically heated. Due to the fundamental nature of this research, it is expected the results will have an impact across a wide range of disciplines including biomedicine, forensic science and archaeology

The effect of O-Carboxyphenyl-β-D-Gluco-pyranosiduronic acid upon the water dissolution of chemical compounds in urinary calculi

Thesis (M.A.)--Boston UniversityPrien and Walker^39 have treated chronic kidney stone formers with aspirin. They obtained clinical evidence showing no new stone growth and inhibition of the growth of existing stones. The rationale behind such therapy is that aspirin is excreted as a glucuronide conjugate in the urine, and the glucuronide increases dissolution of calcium phosphate stones. Previous laboratory studies^39,10 have shown glucuronides (a concentrate of mixed urinary glucuronides, or o-aminophenol glucuronide) to increase the dissolution of tricalcium phosphate. Tricalcium phosphate is neither a major nor even common component of urinary calculi. The purpose of this investigation is to demonstrate the effect of a glucuronide of salicylates on the dissolution of urinary calculi and their major component compounds. The diffuse pharmacological action of salicylates makes critical, in vitro experiments imperative. The ether glucuronide conjugate of salicylic acid, o-carboxyphenyl-β-D-glucopyranosiduronic acid (o-CPG), a known metabolic product of salicylates found in urine^40 and stones of known composition or synthetic components of stones should be used in these experiments. In the course of this investigation evidence of increased dissolution warranted further experimentation into the possible cause of such effects. Aspirin therapy as initiated by Prien and Walker derived from the qualitative experiments of Neuberg, Mandl and Grauer^33,29,30. In these experiments the authors attempted to either dissolve calcium salts or to inhibit their precipitation by addition of naturally occurring organic and inorganic acids. They showed that 1-menthol-Dglucuronic acid solubilizes both calcium carbonate and calcium phosphate salts, that it functions in this way much better than non conjugated glucuronic acid and that incubation of such a mixture with β-glucuronidase leads to precipitation of the salt. The work of Cessi^10 followed in which the solubilizing effect of a glucuronide was observed during the synthesis of the glucuronide by an in vitro biological system. p^32 in the supernatant fluid resulting from dissolution of a solid phase of tricalcium phosphate containing p^32 (placed in the flask with the liver slices) was measured by counting the activity. The increase of p^32 over a control flask was found to vary directly with the glucuronide concentration. Salicylates have been shown to be excreted as the phenolic glucuronide ^40,25,2. Smith^42 has shown that acetylsalicylic acid is probably hydrolyzed in plasma to form salicylic acid. An increase of urinary glucuronides could then be made to occur by the ingestion of various "glucurongenins" (Teague). Prien and Walker^39 have reported an increase of 200 - 400 per cent over the basal level of urinary glucuronides in man during a 2 gm dose of aspirin / day. Glucuronides are manufactured largely by the liver, kidney and mucosa of the alimentary tract^15,23,24. The biosynthesis requires a coenzyme, uridine diphosphate which is thought to react with glucose to produce uridine diphosphoglucose which then may be oxidized to uridine diphosphoglucuronic acid in the presence of DPN^+45. The uridine diphosphoglucuronic acid will then transfer the glucuronic acid to a proper acceptor such as a phenol. The role of ingested glucuronic acid in this metabolic scheme seems to be negligible. Only a small percentage is recovered in the urine^20. Douglas and King using labeled glucurone found the glucuronic acid in the urine to be labeled in such a way as to support the theory that the glucurone breaks to three-carbon fragments. These fragments probably form a six-carbon precursor of glucuronic acid. Urinary tract calculi have been shown by Prien^37 to contain calcium in 90 per cent of 1000 calculi studied. Thirty-three per cent were pure calcium oxalate, 3.4 per cent pure hydroxy apatite and 34 per cent were mixtures of calcium oxalate and hydroxy apatite. Hydroxy apatite is considered to be the main inorganic component of animal bone. The chemical structure of a unit cell is Ca10(PO4)6(OH)2^34,9,4. This crystal is the most common phosphate crystal found in urinary calculi. It is this component of urinary calculi with which this investigation is mainly concerned. EXPERIMENTAL The first series of experiments were designed to find the effect of o-CPG on the dissolution of a urinary tract stone composed chiefly of hydroxy apatite. The degree of dissolution was followed with phosphate determinations, using the colorometric procedure of Fiske and Subbarow.^21 Since uric acid, salicylic acid, salicyluric acid and o-CPG are all found in the urine in increased amounts following ingestion of salicylates, these compounds were examined for their dissolutive effect. The test flask contained 100 mg of a powdered urinary stone composed mainly of hydroxy apatite, and 0.1 mMoles of the test compound. The mixture was placed in a small dialysis bag along with 4-5 glass beads and 10 ml of buffer. This bag was placed in a 50 ml Erlenmeyer flask containing 30 ml of the buffer and a few glass beads. Several drops of toluene were added to prevent bacterial contamination. The buffer used was Michaelis universal veronal buffer, pH 7.8. This pH was chosen because Prien and Walker^39 had found it to be optimal for dissolution of calcium phosphate in their early experiments. The o-CPG was synthesized in this laboratory using the method of Lunsford and Murphey.^28 The flasks were placed in a shaking water bath at 38°C. and aliquots of the external phase in the flasks were analysed at 5 hours and 10 hours. Duplicate flasks were set up for each substance in question and for the control flask which contained hydroxy apatite only. At the end of 5 hours the o-CPG flask showed an increase in the phosphate concentration of 85 per cent over the control. The other substances showed little or no increase. After 10 hours the o-CPG showed an increase of 36 per cent over the control. We conclude that o-CPG increases the dissolution of urinary tract calculi composed mainly of hydroxy apatite. Furthermore, it is suggested from the decreasing per cent of increased dissolution over time that the o-CPG also hastens the equilibrium of dissolution. The experiment was repeated substituting synthetic hydroxy apatite, prepared in this laboratory, for the powdered stone. Estradiol glucuronide was examined as well as o-CPG. After 5.75 hours both glucuronides increased dissolution; the estradiol glucuronide increased the dissolution by 87 per cent and in this case the o-CPG produced a 555 per cent increase. It can be concluded that o-CPG increases dissolution of hydroxy apatite and that it works better on pure hydroxy apatite than on other forms of calcium and phosphate. Other investigators^39,10 have found an increase of about 40 per cent using calcium phosphate. The first possible explanation for these results, which occurred to us was that o-CPG was complexing calcium ion. In order to determine if complex formation with calcium were taking place, conductometric titrations were performed. The titration curves of sodium hydroxide and of calcium hydroxide with o-CPG, glucuronolactone and salicylic acid, were compared. If the sodium hydroxide titration fits well to the calcium hydroxide titration curve, one concludes that no highly conductive ions are produced and complex formation is absent. The results showed that there is a possibility that a slight amount of complex formation may have occurred with glucuronolactone but certainly not with salicylic acid or o-CPG. Further proof that no complexing of calcium was taking place was obtained by measuring conductivity of separate solutions of calcium lactate and o-CPG at different concentrations. They were then combined, each at one half their original concentration and the resultant conductivity compared with the theoretical conductivity which we calculated. Results show that the combined conductivity is about the same as the theoretical and therefore complex formation is absent. This type of experiment was repeated using calcium chloride instead of calcium lactate and the same results were obtained. The only conclusion we can draw is that o-CPG does not complex calcium. It was thought that perhaps o-CPG complexes calcium and phosphate together. To test this hypothesis another dissolution experiment was designed similar to the first ones reported. However, the o-CPG was incubated in one case with phosphate and in another case with barium and phosphate before being added to the synthetic hydroxy apatite. The only test flask which showed a significant difference from the controls was that one in which o-CPG was incubated first with barium and phosphate. Here, the dissolution effect of o-CPG was decreased by 30 per cent. We conclude that calcium and phosphate may be complexed together by o-CPG. In summary we may state that o-CPG increases the dissolution of urinary tract calculi containing hydroxy apatite; it increases the dissolution of synthetic hydroxy apatite; it does not form a complex with calcium but it may form a complex with calcium and phosphate. The results also suggest that it may increase the dissolution of hydroxy apatite by acting at the surface of the crystal. This question requires further investigation

The effect of O-Carboxyphenyl-β-D-Gluco-pyranosiduronic acid upon the water dissolution of chemical compounds in urinary calculi

Thesis (M.A.)--Boston UniversityPrien and Walker^39 have treated chronic kidney stone formers with aspirin. They obtained clinical evidence showing no new stone growth and inhibition of the growth of existing stones. The rationale behind such therapy is that aspirin is excreted as a glucuronide conjugate in the urine, and the glucuronide increases dissolution of calcium phosphate stones. Previous laboratory studies^39,10 have shown glucuronides (a concentrate of mixed urinary glucuronides, or o-aminophenol glucuronide) to increase the dissolution of tricalcium phosphate. Tricalcium phosphate is neither a major nor even common component of urinary calculi. The purpose of this investigation is to demonstrate the effect of a glucuronide of salicylates on the dissolution of urinary calculi and their major component compounds. The diffuse pharmacological action of salicylates makes critical, in vitro experiments imperative. The ether glucuronide conjugate of salicylic acid, o-carboxyphenyl-β-D-glucopyranosiduronic acid (o-CPG), a known metabolic product of salicylates found in urine^40 and stones of known composition or synthetic components of stones should be used in these experiments. In the course of this investigation evidence of increased dissolution warranted further experimentation into the possible cause of such effects. Aspirin therapy as initiated by Prien and Walker derived from the qualitative experiments of Neuberg, Mandl and Grauer^33,29,30. In these experiments the authors attempted to either dissolve calcium salts or to inhibit their precipitation by addition of naturally occurring organic and inorganic acids. They showed that 1-menthol-Dglucuronic acid solubilizes both calcium carbonate and calcium phosphate salts, that it functions in this way much better than non conjugated glucuronic acid and that incubation of such a mixture with β-glucuronidase leads to precipitation of the salt. The work of Cessi^10 followed in which the solubilizing effect of a glucuronide was observed during the synthesis of the glucuronide by an in vitro biological system. p^32 in the supernatant fluid resulting from dissolution of a solid phase of tricalcium phosphate containing p^32 (placed in the flask with the liver slices) was measured by counting the activity. The increase of p^32 over a control flask was found to vary directly with the glucuronide concentration. Salicylates have been shown to be excreted as the phenolic glucuronide ^40,25,2. Smith^42 has shown that acetylsalicylic acid is probably hydrolyzed in plasma to form salicylic acid. An increase of urinary glucuronides could then be made to occur by the ingestion of various "glucurongenins" (Teague). Prien and Walker^39 have reported an increase of 200 - 400 per cent over the basal level of urinary glucuronides in man during a 2 gm dose of aspirin / day. Glucuronides are manufactured largely by the liver, kidney and mucosa of the alimentary tract^15,23,24. The biosynthesis requires a coenzyme, uridine diphosphate which is thought to react with glucose to produce uridine diphosphoglucose which then may be oxidized to uridine diphosphoglucuronic acid in the presence of DPN^+45. The uridine diphosphoglucuronic acid will then transfer the glucuronic acid to a proper acceptor such as a phenol. The role of ingested glucuronic acid in this metabolic scheme seems to be negligible. Only a small percentage is recovered in the urine^20. Douglas and King using labeled glucurone found the glucuronic acid in the urine to be labeled in such a way as to support the theory that the glucurone breaks to three-carbon fragments. These fragments probably form a six-carbon precursor of glucuronic acid. Urinary tract calculi have been shown by Prien^37 to contain calcium in 90 per cent of 1000 calculi studied. Thirty-three per cent were pure calcium oxalate, 3.4 per cent pure hydroxy apatite and 34 per cent were mixtures of calcium oxalate and hydroxy apatite. Hydroxy apatite is considered to be the main inorganic component of animal bone. The chemical structure of a unit cell is Ca10(PO4)6(OH)2^34,9,4. This crystal is the most common phosphate crystal found in urinary calculi. It is this component of urinary calculi with which this investigation is mainly concerned. EXPERIMENTAL The first series of experiments were designed to find the effect of o-CPG on the dissolution of a urinary tract stone composed chiefly of hydroxy apatite. The degree of dissolution was followed with phosphate determinations, using the colorometric procedure of Fiske and Subbarow.^21 Since uric acid, salicylic acid, salicyluric acid and o-CPG are all found in the urine in increased amounts following ingestion of salicylates, these compounds were examined for their dissolutive effect. The test flask contained 100 mg of a powdered urinary stone composed mainly of hydroxy apatite, and 0.1 mMoles of the test compound. The mixture was placed in a small dialysis bag along with 4-5 glass beads and 10 ml of buffer. This bag was placed in a 50 ml Erlenmeyer flask containing 30 ml of the buffer and a few glass beads. Several drops of toluene were added to prevent bacterial contamination. The buffer used was Michaelis universal veronal buffer, pH 7.8. This pH was chosen because Prien and Walker^39 had found it to be optimal for dissolution of calcium phosphate in their early experiments. The o-CPG was synthesized in this laboratory using the method of Lunsford and Murphey.^28 The flasks were placed in a shaking water bath at 38°C. and aliquots of the external phase in the flasks were analysed at 5 hours and 10 hours. Duplicate flasks were set up for each substance in question and for the control flask which contained hydroxy apatite only. At the end of 5 hours the o-CPG flask showed an increase in the phosphate concentration of 85 per cent over the control. The other substances showed little or no increase. After 10 hours the o-CPG showed an increase of 36 per cent over the control. We conclude that o-CPG increases the dissolution of urinary tract calculi composed mainly of hydroxy apatite. Furthermore, it is suggested from the decreasing per cent of increased dissolution over time that the o-CPG also hastens the equilibrium of dissolution. The experiment was repeated substituting synthetic hydroxy apatite, prepared in this laboratory, for the powdered stone. Estradiol glucuronide was examined as well as o-CPG. After 5.75 hours both glucuronides increased dissolution; the estradiol glucuronide increased the dissolution by 87 per cent and in this case the o-CPG produced a 555 per cent increase. It can be concluded that o-CPG increases dissolution of hydroxy apatite and that it works better on pure hydroxy apatite than on other forms of calcium and phosphate. Other investigators^39,10 have found an increase of about 40 per cent using calcium phosphate. The first possible explanation for these results, which occurred to us was that o-CPG was complexing calcium ion. In order to determine if complex formation with calcium were taking place, conductometric titrations were performed. The titration curves of sodium hydroxide and of calcium hydroxide with o-CPG, glucuronolactone and salicylic acid, were compared. If the sodium hydroxide titration fits well to the calcium hydroxide titration curve, one concludes that no highly conductive ions are produced and complex formation is absent. The results showed that there is a possibility that a slight amount of complex formation may have occurred with glucuronolactone but certainly not with salicylic acid or o-CPG. Further proof that no complexing of calcium was taking place was obtained by measuring conductivity of separate solutions of calcium lactate and o-CPG at different concentrations. They were then combined, each at one half their original concentration and the resultant conductivity compared with the theoretical conductivity which we calculated. Results show that the combined conductivity is about the same as the theoretical and therefore complex formation is absent. This type of experiment was repeated using calcium chloride instead of calcium lactate and the same results were obtained. The only conclusion we can draw is that o-CPG does not complex calcium. It was thought that perhaps o-CPG complexes calcium and phosphate together. To test this hypothesis another dissolution experiment was designed similar to the first ones reported. However, the o-CPG was incubated in one case with phosphate and in another case with barium and phosphate before being added to the synthetic hydroxy apatite. The only test flask which showed a significant difference from the controls was that one in which o-CPG was incubated first with barium and phosphate. Here, the dissolution effect of o-CPG was decreased by 30 per cent. We conclude that calcium and phosphate may be complexed together by o-CPG. In summary we may state that o-CPG increases the dissolution of urinary tract calculi containing hydroxy apatite; it increases the dissolution of synthetic hydroxy apatite; it does not form a complex with calcium but it may form a complex with calcium and phosphate. The results also suggest that it may increase the dissolution of hydroxy apatite by acting at the surface of the crystal. This question requires further investigation