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PubMed2003

Application of a mathematical model to prevent in vivo amplification of antibiotic-resistant bacterial populations during therapy.

The worldwide increase in the prevalence of multi-antibiotic-resistant bacteria has threatened the physician's ability to provide appropriate therapy for infections. The relationship between antimicrobial drug concentration and infecting pathogen population reduction is of primary interest. Using data derived from mice infected with the bacterium Pseudomonas aeruginosa and treated with a fluoroquinolone antibiotic, a mathematical model was developed that described relationships between antimicrobial drug exposures and changes in drug-susceptible and -resistant bacterial subpopulations at an infection site. Dosing regimens and consequent drug exposures that amplify or suppress the emergence of resistant bacterial subpopulations were identified and prospectively validated. Resistant clones selected in vivo by suboptimal regimens were characterized. No mutations were identified in the quinolone resistance-determining regions of gyrA/B or parC/E. However, all resistant clones demonstrated efflux pump overexpression. At base line, MexAB-OprM, MexCD-OprJ, and MexEF-OprN were represented in the drug-resistant population. After 28 hours of therapy, MexCD-OprJ became the predominant pump expressed in the resistant clones. The likelihood of achieving resistance-suppression exposure in humans with a clinically prescribed antibiotic dose was determined. The methods developed in this study provide insight regarding how mathematical models can be used to identify rational dosing regimens that suppress the amplification of the resistant mutant population.

Animals↗
PubMed2003

Mathematical model predicts a critical role for osteoclast autocrine regulation in the control of bone remodeling.

Bone remodeling occurs asynchronously at multiple sites in the adult skeleton and involves resorption by osteoclasts, followed by formation of new bone by osteoblasts. Disruptions in bone remodeling contribute to the pathogenesis of disorders such as osteoporosis, osteoarthritis, and Paget's disease. Interactions among cells of osteoblast and osteoclast lineages are critical in the regulation of bone remodeling. We constructed a mathematical model of autocrine and paracrine interactions among osteoblasts and osteoclasts that allowed us to calculate cell population dynamics and changes in bone mass at a discrete site of bone remodeling. The model predicted different modes of dynamic behavior: a single remodeling cycle in response to an external stimulus, a series of internally regulated cycles of bone remodeling, or unstable behavior similar to pathological bone remodeling in Paget's disease. Parametric analysis demonstrated that the mode of dynamic behavior in the system depends strongly on the regulation of osteoclasts by autocrine factors, such as transforming growth factor beta. Moreover, simulations demonstrated that nonlinear dynamics of the system may explain the differing effects of immunosuppressants on bone remodeling in vitro and in vivo. In conclusion, the mathematical model revealed that interactions among osteoblasts and osteoclasts result in complex, nonlinear system behavior, which cannot be deduced from studies of each cell type alone. The model will be useful in future studies assessing the impact of cytokines, growth factors, and potential therapies on the overall process of remodeling in normal bone and in pathological conditions such as osteoporosis and Paget's disease.

Autocrine Communication↗
PubMed1983

Experimental and mathematical models of Escherichia coli plasmid transfer in vitro and in vivo.

Little is known about the factors that govern plasmid transfers in natural ecosystems such as the gut. The consistent finding by earlier workers that plasmid transfer in the normal gut can be detected only at very low rates, if at all, has given rise to numerous speculations concerning the presence in vivo of various inhibitors of plasmid transfer. Plasmids R1, R1drd-19, and pBR322 were studied in Escherichia coli K-12 and wild-type E. coli hosts in two experimental systems: (i) gnotobiotic mice carrying a synthetic indigenous microflora (F-strains) which resemble in their function the normal indigenous microflora of the mouse large intestine, and (ii) anaerobic continuous-flow cultures of indigenous large intestinal microflora of the mouse, which can simulate bacterial interactions observed in the mouse gut. Mathematical models were developed to estimate plasmid transfer rates as a measure of the "fertility," i.e., of the intrinsic ability to transfer the plasmid under the environmental conditions of the gut. The models also evaluate the effects of plasmid segregation, reduction of the growth rates of plasmid-bearing bacterial hosts, repression of transfer functions, competition for nutrients, and bacterial attachment to the wall of the gut or culture vessel. Some confidence in the validity of these mathematical models was gained because they were able to reproduce a number of known phenomena such as the repression of fertility of the R1 plasmid, as well as known differences in the transmission and mobilization of the plasmids studied. Interpretation of the data obtained permitted a number of conclusions, some of which were rather unexpected. (i) Fertility of plasmid-bearing E. coli in the normal intestine was not impaired. The observed low rates of plasmid transfer in the normal gut can be explained on quantitative grounds alone and do not require hypothetical inhibitory mechanisms. (ii) Conditions for long-term spread and maintenance throughout human or animal populations of a diversity of conjugative and nonconjugative plasmids may be optimal among E. coli strains of low fertility, as are found among wild-type strains. (iii) E. coli strains carrying plasmid pBR322 plus R1drd-19 were impaired in their ability to transfer R1drd-19, but strains carrying pBR322 were significantly better recipients of R1drd-19 than a plasmid-free recipient E. coli. (iv) Long-term coexistence of plasmid-bearing and plasmid-free E. coli, in spite of undiminished fertility, appeared to be due to a detrimental effect of the plasmid on the growth rate of its host bacterium, rather than due to high rates of plasmid segregation. (v) Mathematical analysis of experimental data published by earlier investigators is consistent with the conclusion that plasmid transfer occurs consistently in the human gut, but that the resulting transconjugant E. coli populations are too small to be detected regularly with the culture methods used by earlier investigators. It is concluded that the long-term interactions observed were often the consequences of minor differences in parameters such as growth rates, fertility, rates of segregation, etc., which were too small to be detected except by precise mathematical analysis of long-term experiments, but which were nevertheless decisive determinants of the ultimate fates of the plasmids and their hosts.

Animals↗
PubMed2002

Testing a mathematical model of the yeast cell cycle.

We derived novel, testable predictions from a mathematical model of the budding yeast cell cycle. A key qualitative prediction of bistability was confirmed in a strain simultaneously lacking cdc14 and G1 cyclins. The model correctly predicted quantitative dependence of cell size on gene dosage of the G1 cyclin CLN3, but it incorrectly predicted strong genetic interactions between G1 cyclins and the anaphase-promoting complex specificity factor Cdh1. To provide constraints on model generation, we determined accurate concentrations for the abundance of all nine cyclins as well as the inhibitor Sic1 and the catalytic subunit Cdc28. For many of these we determined abundance throughout the cell cycle by centrifugal elutriation, in the presence or absence of Cdh1. In addition, perturbations to the Clb-kinase oscillator were introduced, and the effects on cyclin and Sic1 levels were compared between model and experiment. Reasonable agreement was obtained in many of these experiments, but significant experimental discrepancies from the model predictions were also observed. Thus, the model is a strong but incomplete attempt at a realistic representation of cell cycle control. Constraints of the sort developed here will be important in development of a truly predictive model.

CDC28 Protein Kinase, S cerevisiae↗
PubMed2002

Mathematic modeling of the risk of HBV, HCV, and HIV transmission by window-phase donations not detected by NAT.

BACKGROUND: Blood transfusion centers around the world have introduced minipool NAT to reduce the risk of HBV, HCV, and HIV transmission by blood donations drawn in the infectious window phase. What would be the reduction in the residual risk when minipool NAT would be replaced by single-donation NAT? STUDY DESIGN AND METHODS: A mathematic model was developed to estimate the probability of virus transmission by blood transfusion when NAT screening methods are used for virologic safety testing. The major assumptions used are threefold: 1) The viral nucleic acid concentrations in the early window phase of infection double in 2.8 (HBV), 0.74 (HCV), and 0.90 (HIV) days. 2) The detectability of low copy numbers of viral DNA or RNA by the screening assay can be described with a probit model. 3) The probability of infection depends linearly on the logarithm of the administered dose, with 50-percent infectivity rates at 10 (HBV and HCV) or 1000 (HIV) viral nucleic acid copies per transfusion unit (estimates based on NAT studies with samples of known infectivity in chimpanzees). RESULTS: A reasonably simple equation was obtained that allows studying the effect of the sensitivity of the NAT assay and of the pool size used for screening on the residual risk of transfusion-transmitted infection. The computations are illustrated by using observed sensitivity estimates of various NAT methods. By using epidemiologic data among European donors over 1997 as baseline, the calculations predict that the incidence of virus transmission per 10-million RBC transfusions reduces with the following numbers when lowering the test pool size from 96 to 1 (single-donation testing): HBV from 11 to 13 to 3.3 to 5.1, HCV from 1.7 to 2.0 to 0.5 to 0.8, and HIV from 0.47 to 0.62 to 0.010 to 0.045 (ranges for the different NAT screening methods). CONCLUSION: A proper mathematic model for the calculation of residual infection risk by blood transfusion helps understand the impact of introducing new NAT methods for blood safety testing.

Blood Donors↗
PubMed1985

[Mathematical modeling of the dynamics of the intensity of the mutation process. II. Dynamic evaluation of the frequencies of hereditary pathology].

Mathematical models were devised to evaluate the dynamics of hereditary pathology frequencies, based on registration of spontaneous abortions, congenital malformations and Down disease in the city of Angarsk during 12 years. The models provide an opportunity to detect the fact of the presence or absence of temporary tendencies. The average frequency of spontaneous abortions and units of hereditary pathology have not been changed for 12 years, the frequency of Down disease being decreased, while congenital malformations seem to change with certain periodicity. In cases of insufficient sample sizes, the prolongation of observation for a period of several years does not facilitate the task of construction of models which could adequately describe multifactor-conditioned processes.

Abortion, Spontaneous↗
PubMedDate not supplied

A mathematical model for the estimation of human embryonic and fetal age.

Precise determination of donor age in human embryonic and fetal tissue is crucial for cell transplantation due to the existence of distinct time windows within which successful grafting is possible. This study demonstrates that between 4-12 wk postconception embryonic and fetal age can be estimated based on various morphometric parameters measured on a routine basis in suction abortion material. The greatest length, the neck-rump length, the foot length, and the proximal and distal arm and leg length were correlated with the anamnestic and ultrasonographically estimated age. Multivariate regression analyses showed a linear correlation between age and the logarithmic value of the various morphometric parameters. The best correlation was found for a mathematical model combining the limb parameters (r = 0.904; p < 0.001; n = 37). A prospective follow-up study (n = 40) was carried out to test the validity of the mathematical model. A high correlation was found between the calculated age and the estimated age based on anamnestic data (r = 0.749, p < 0.001). Outliers due to errors in the anamnestic data were readily identified by comparing anamnestic with calculated age. This method allows determination of embryonic and fetal age within and beyond the age group of the Carnegie classification and may, therefore, be useful for the needs of experimental and clinical cell transplantation.

Animals↗
PubMed1981

A mathematical model for the liver uptake and excretion of 99mTc-diethyl IDA.

A mathematical model for the liver uptake and excretion of 99mTc-diethyl IDA has been formulated and data from four patient studies have been fitted to the model, resulting in values for the model parameters. The model includes compartments for blood, extravascular space, hepatocytes, bile ducts, and kidneys. The parameter values obtained reflect a rapid exchange between blood and extravascular space and a significant reverse flow of the radiopharmaceutical from the liver to the blood.

Adult↗
PubMed1999

[Physiological analysis of a mathematical model for predicting somatic eigenstates under combined stresses].

Objective. To put a mathematical model for predicting human somatic eigenstates (HS) into practical engineering design of countermeasures against combined stresses (hypoxia, heat, noise and vibration) in an aircraft cabin, and confirm the model from the human physiological viewpoint. Method. Published works on these 4 stresses were employed to verify the main and interactive effects which had been previously proved mathematically. Result. The main effects of 4 stresses and the significant interactive effects of 2 from 4 stresses agreed with the published experiments in single or in the same combination of these stresses. Conclusion. The model is reasonable in human physiological consideration and has been adopted in engineering design.

Adaptation, Physiological↗
PubMed1975

A mathematical model for the determination of cardiac regurgitant and ejection fractions from radioisotope angiocardiograms.

A mathematical model taking into account the pulsatile pumping action of the heart has been developed which describes, in terms of a set of four recursive equations, the activity in the atrium and in the ventricle of the left or right heart at successive end-systoles and end-diastoles after bolus injection. The resulting closed form solutions permit calculations of chamber forward ejection fractions and valvular regurgitant fractions from computerized radioisotope angiocardiogram data. The method has been applied to a series of over thirty clinical studies with encouraging results.

Angiocardiography↗
PubMed2004

Mathematical modeling confirms the length-dependency of telomere shortening.

Telomeres, the ends of chromosomes, shorten with each cell division in human somatic cells, because of the end-replication problem, C-strand processing and oxidative damage. On the other hand, the reverse transcriptase telomerase can add back telomeric repeats at the telomere ends. It has been suggested that once telomeres have reached a critical length, cells cease proliferation, also known as senescence. Evidence is accumulating that telomere shortening and subsequent senescence might play a crucial role in life-threatening diseases. So far, mathematical models described telomere shortening as an autonomous process, where the loss per cell division does not depend on the telomere length itself. In this study, published measurements of telomere distributions in human fibroblasts and human endothelial cells were used to show that telomeres shorten in a length-dependent fashion. Thereafter, a mathematical model of telomere attrition was composed, in which a shortening factor and an autonomous loss were incorporated. It was assumed that the percentage of senescence was related to the percentage of telomeres below a critical length. The model was compared with published data of telomere length and senescence of human endothelial cells using the maximum likelihood method. This enabled the estimation of physiologically important parameters and confirmed the length-dependency of telomere shortening.

Aging↗
PubMed2004

Combining mathematical models and statistical methods to understand and predict the dynamics of antibiotic-sensitive mutants in a population of resistant bacteria during experimental evolution.

Temporarily discontinuing the use of antibiotics has been proposed as a means to eliminate resistant bacteria by allowing sensitive clones to sweep through the population. In this study, we monitored a tetracycline-sensitive subpopulation that emerged during experimental evolution of E. coli K12 MG1655 carrying the multiresistance plasmid pB10 in the absence of antibiotics. The fraction of tetracycline-sensitive mutants increased slowly over 500 generations from 0.1 to 7%, and loss of resistance could be attributed to a recombination event that caused deletion of the tet operon. To help understand the population dynamics of these mutants, three mathematical models were developed that took into consideration recurrent mutations, increased host fitness (selection), or a combination of both mechanisms (full model). The data were best explained by the full model, which estimated a high mutation frequency (lambda = 3.11 x 10(-5)) and a significant but small selection coefficient (sigma = 0.007). This study emphasized the combined use of experimental data, mathematical models, and statistical methods to better understand and predict the dynamics of evolving bacterial populations, more specifically the possible consequences of discontinuing the use of antibiotics.

Anti-Bacterial Agents↗
PubMed2004

A mathematical model for the laser treatment of heart disease.

Transmyocardial laser revascularisation (TMLR) is used to treat patients with severe coronary artery disease. A laser is used to create narrow tunnels within ischemic heart muscle in an attempt to reperfuse the area with oxygenated blood directly from the left-ventricular chamber. It has been hypothesised that initially blood flow through the patent tunnels plays an important role in the efficacy of the treatment (J. Am. College Cordiol. 25(1) (1995) 258) and Waters (J. Fluid Mech. 433 (2001) 193) developed a simple mathematical model to show that this blood flow enhances the quantity of oxygenated blood drawn into the tunnel and the subsequent delivery of oxygen to the tissue. To date, however, the optimum parameter values for this clinical technique have not been determined, e.g. the radius of the laser-drilled tunnels and their relative spacing. We present a mathematical model to determine the distribution of oxygen for a wide range of the governing parameters. Our results indicate that the tunnel radius has a significant effect on the degree of tissue reperfusion and predictions for the optimum tunnel spacing are made.

Animals↗
PubMed2003

Validation of a mathematical model predicting the response to growth hormone treatment in prepubertal children with idiopathic growth hormone deficiency.

OBJECTIVE: To validate a mathematical model developed by Ranke et al. (J Clin Endocrinol Metab 1999;84:1174-7783) to predict the GH response during the first years of GH replacement therapy. PATIENTS AND METHODS: 38 children with idiopathic GH deficiency (GHD) met all inclusion criteria for the prediction model, but the group differed in some characteristics from the cohort from which the model was derived. RESULTS: Using the model for the 1st year including maximum GH after stimulation and the equation for the 6th year, the predicted value corresponded well with actual height gain. Differences were found when the growth response of the 1st year excluding maximum GH and that of the 2nd-5th year were calculated, resulting in a significant underestimation of actual height gain (-0.63 to -1.07 cm/year). CONCLUSION: The mathematical prediction model tended to underpredict the growth response to GH treatment in our patients with pronounced GHD. The severity of GHD seems to be an important parameter for the 1st year prediction.

Body Height↗
PubMed1999

Ionic targets for drug therapy and atrial fibrillation-induced electrical remodeling: insights from a mathematical model.

UNLABELLED: Recent advances in molecular electrophysiology have made possible the development of more selective ion channel blockers for therapeutic use. However, more information is needed about the effects of blocking specific channels on repolarization in normal human atrium and in atrial cells of patients with atrial fibrillation (AF). AF-induced electrical remodeling is associated with reductions in transient outward current (Ito), ultrarapid delayed rectifier current (IKur), and L-type calcium current (ICa,L). Direct evaluation of the results of ion channel depression is limited by the nonspecificity of the available pharmacological probes. OBJECTIVES: Using a mathematical model of the human atrial action potential (AP), we aimed to: (1) evaluate the role of ionic abnormalities in producing AP changes characteristic of AF in humans and (2) explore the effects of specific channel blockade on the normal and AF-modified AP (AFAP). METHODS: We used our previously developed mathematical model of the normal human atrial AP (NAP) based on directly measured currents. We constructed a model of the AFAP by incorporating experimentally-measured reductions in Ito (50%), IKur (50%), and ICa,L (70%) current densities observed in AF. RESULTS: The AFAP exhibits the reductions in AP duration (APD) and rate-adaption typical of AF. The reduction in ICa,L alone can account for most of the morphological features of the AFAP. Inhibition of Ito by 90% leads to a reduction in APD measured at -60 mV in both the NAP and AFAP. Inhibition of the rapid component of the delayed rectifier (IKr) by 90% slows terminal repolarization of the NAP and AFAP and increases APD by 38% and 34%, respectively. Inhibition of IKur by 90% slows early repolarization and increases plateau height, activating additional IK and causing no net change in APD at 1 Hz in the NAP. In the presence of AF-induced ionic modifications, IKur inhibition increases APD by 12%. Combining IKur and IKr inhibition under both normal and AF conditions synergistically increases APD. In the NAP, altering the model parameters to reproduce other typical measured AP morphologies can significantly alter the response to K(+)-channel inhibition. CONCLUSIONS: (1) The described abnormalities in Ito, IKur and ICa,L in AF patients can account for the effects of AF on human AP properties; (2) AP prolongation by IKur block is limited by increases in plateau height that activate more IK; (3) Blockers of IKur may be more effective in prolonging APD in patients with AF; 4) Inhibition of both IKur and IKr produces supra-additive effects on APD. These observations illustrate the importance of secondary current alterations in the response of the AP to single channel blockade, and have potentially important implications for the development of improved antiarrhythmic drug therapy for AF.

Action Potentials↗
PubMed1988

Mathematical model of simultaneous diffusion and binding of antitumor antibodies in multicellular human tumor spheroids.

Multicellular tumor spheroids are widely used as in vitro models of poorly vascularized tumor nodules in vivo. The uptake kinetics of tumor-associated antibodies in multicellular tumor spheroids is assumed to be governed by passive diffusion and irreversible binding of the antibodies with binding sites on the cell surface. By further assuming that the spheroids are homogeneous with respect to diffusion and binding, a mathematical model has been developed which permits the extraction of the macroscopic diffusion constant D and the macroscopic binding rate k from empirical studies. The model was applied to uptake kinetics data obtained (a) with a melanoma-associated monoclonal antibody 96.5 (isotype IgG2a)-human multicellular melanoma spheroid system exhibiting strong antibody to cell binding and (b) with the same monoclonal antibody-human multicellular colon adenocarcinoma HT29 spheroid system exhibiting nonspecific binding. The spheroids had approximately 300 microns diameter. The constants D and k were estimated to be 0.45 micron2 s-1 and 2.0 x 10(-3) s-1, respectively, for the system with specific binding. Saturation of binding sites occurred. In the nonspecific binding system, D and k were found to be 0.10 micron2 s-1 and 1.0 x 10(-5) s-1. No saturation of binding sites occurred. D and k were also estimated to be, respectively, 0.52 micron2 s-1 and 6.4 x 10(-5) s-1 for another melanoma-associated monoclonal antibody 140.240 (same isotype as 96.5) in the melanoma spheroid system exhibiting moderate cell binding with the antibody. The mathematical model describes well the system exhibiting nonspecific binding, but requires modifications and further development for the systems exhibiting moderate to strong binding.

Adenocarcinoma↗
PubMed1990

Mathematical modeling of antimicrobial susceptibility data of Staphylococcus haemolyticus for 11 antimicrobial agents, including three experimental glycopeptides and an experimental lipoglycopeptide.

Antimicrobial MIC data were obtained for 96 strains of Staphylococcus haemolyticus and the following 11 antimicrobial agents: methicillin, gentamicin, rifampin, fusidic acid, ciprofloxacin, vancomycin, teicoplanin; three experimental glycopeptides, MDL 62,873, MDL 62,208, and MDL 62,224; and an experimental lipoglycopeptide, ramoplanin. Resistance to methicillin and gentamicin was present in over 50% of the strains, although resistance to the other agents was present in less than 10%. It is shown how application of mathematical modeling techniques can add to the understanding of such MIC data. MICs of methicillin and gentamicin were highly correlated, suggesting that evolutionary pressures for development of resistance to these agents were similar. The structural relationships among the glycopeptides were accurately reflected in their spatial relationships within the model. MICs of ramoplanin were negatively correlated with MICs of some other antimicrobial agents, particularly gentamicin, suggesting that this agent is more active against gentamicin-resistant strains. Methicillin-resistant strains were more tightly clustered than were methicillin-susceptible strains, suggesting that methicillin-resistant strains were more closely related to each other than were methicillin-susceptible strains. Mathematical modeling techniques enable more detailed analysis of MIC data.

Anti-Bacterial Agents↗
PubMed1998

A mathematical model for ligand/receptor/G-protein dynamics and actin polymerization in human neutrophils.

A mathematical model is proposed for describing the dynamics of the chemotactic peptide-stimulated actin polymerization response in human neutrophils. The response pathway utilizes the guanine nucleotide binding protein (G-protein) signal transduction cascade common to many receptor systems and allows adaptation in the continued presence of ligand. The development of such a model is an important first step toward understanding, predicting, and ultimately manipulating neutrophil responses. The model is divided into two parts, ligand/receptor/G-protein dynamics and the actin polymerization mechanism. Fast (receptor precoupled to G-protein) and slow (free receptor) signaling pathways involving ligand/receptor/G-protein interactions produce an activated signaling molecule. The actin polymerization mechanisms utilizes an actin binding protein which complexes with actin monomer and inhibits polymerization in an unstimulated cell. During stimulation, the activated signaling molecule enhances the dissociation of monomer/binding protein complexes, allowing the actin polymerization response to occur. The fast and slow signaling pathways are predicted to have different roles in controlling the time course of this actin polymerization. Additionally, precoupled receptors are predicted to have a larger ligand association rate constant than non-precoupled (free) receptors. Model simulations agree with many of the experimentally observed characteristics of both the stimulated F-actin response and ligand/receptor binding kinetics for both the fluorescent peptide ligand CHO-norleucyl-leucyl-phenylalanyl-norleucyl-tyrosyl-lysine-fluorescein (CHO-NLFNTK-fl) and the non-fluorescent peptide ligand CHO-methionyl-leucyl-phenylalanine (CHO-MLF).

Actins↗