One of the most unexpected outcomes arising from the efforts towards maternal and child mortality reduction is that all too often the objective success has been coupled with increased inequity in the population. The aim of this study is to analyze the determinants of the complex interplay between cost-effectiveness and equity and suggest strategies that will promote an impact on mortality that reduce population child health inequities.We developed a conceptual framework that exposes the nature of the links between the five key determinants that need to be taken into account when planning equitable impact. These determinants are: (i) efficiency of intervention scale-up ; (ii) effectiveness of intervention ; (iii) the impact on mortality ; (iv) cost-effectiveness ; (v) equity structure of the population. The framework is presented visually as a four-quadrant graph.We use the proposed framework to demonstrate why the relationship between cost-effectiveness and equitable impact of an intervention cannot be intuitively predicted or easily planned. The relationships between the five determinants are complex, often nonlinear, context-specific and intervention-specific. We demonstrate that there will be instances when an equity-promoting approach, ie, trying to reach for the poorest and excluded in the population with health interventions, will also be the most cost-effective approach. However, there will be cases in which this will be entirely unfeasible, and where equity-neutral or even inequity-promoting approaches may be substantially more cost-effective. In those cases, investments into health system development among the poorest that would increase the quality and reduce the cost of intervention delivery would be required before intervention scale-up is planned.The relationships between the most important determinants of cost-effectiveness and equitable impact of health interventions used to reduce maternal and child mortality are highly complex, and the effect on equity cannot be predicted intuitively, or by using simple linear models. In recent years, enormous efforts have been made to estimate the global burden of maternal and child mortality and identify the main causes, study the role of risk factors, assess the effectiveness of available interventions, and to track the coverage of those interventions in low and middle-income countries -10. HoweTo understand the roots of this problem, we should appreciate that policy makers at the national and sub-national level have limited resources for scaling up cost-effective health interventions in their populations. When planning the “best buys” for committing their resources in maternal and child health, they are faced with a very complex task. They need to choose between at least several dozen interventions that target neonates, infants, children and mothers, most of which have been proven to be cost-effective in many contexts ,5,8,9. TThe aim of this study is to analyze the determinants of the complex interplay between cost-effectiveness and equity in maternal and child mortality reduction and suggest strategies that promote an impact on mortality that will reduce population child health inequities. To achieve this aim, we develop a transparent framework based on several key epidemiological concepts that can be used to support national-level decision making in health intervention prioritization. Using this framework, we try to expose the complex interplay among factors that influence both cost-effectiveness and equity in child and maternal mortality reduction and identify the key information needs for planning of equitable and cost-effective programs of health intervention scale-up.the cost of intervention scale-up in different equity strata. In our framework, we will divide any population of interest into 5 equity strata (quintiles), each comprising 20% of the population, where Q1 denotes the wealthiest quintile and Q5 the poorest. The cost of achieving complete coverage with any health intervention will clearly differ between the wealthiest (Q1) and the poorest (Q5) quintile, but there is remarkably little information available on the determinants of these costs in each quintile and the actual differences in cost of implementation. It is also clear that these differences between strata will be intervention-specific and also context-specific, rather than following any “standard”, predictable pattern. This means that, for some interventions, the costs may not increase dramatically  with increasing coverage. In fact, wherever the salary of health professionals is the main component of the cost, then it is possible to envisage circumstances in which, for some interventions, it may be even cheaper to cover the poorest quintile  than the wealthiest quintile . However, there will also be many examples where complete intervention coverage will be more readily achieved among the wealthy Q1 than in the poorest Q5, where it may be almost impossible or even unfeasible to achieve.The first important determinant to consider is Those additional costs may be relatively small if the aim was to cover the most accessible 20% or 40% of mothers and children. In these circumstances the relationship between cost and achieved coverage may indeed be approximately linear. However, additional costs of intervention delivery will start increasing in complex and nonlinear patterns when the coverage of the most deprived children and mothers is attempted, because many obstacles need to be overcome to reach them. Because of these additional costs, all too often we observe that the most accessible mothers and children are being covered with ever more interventions, while the marginalized are missing out on all of them. This approach would still be expected to reduce maternal and child mortality, but the progress would be very slow and inequitable. This is because most child and maternal deaths occur among the most inaccessible parts of the population and only a minor part of the mortality burden is being targeted with interventions. The progress that is being achieved benefits only those who are accessible, thus increasing inequity. Reducing the additional costs of intervention delivery when targeting the poor would involve challenges that are related to both supply and demand for the prioritized interventions.. This graph summarizes the efficiency of intervention delivery. In this hypothetical example, it is apparent that for the same intervention it is much cheaper, and therefore more efficient, to achieve full coverage in the most wealthy 20% of the population (Q1) than in the poorest quintile (Q5). In fact, in this example the difference in cost is so large that it poses a question whether the potential for mortality reduction in the poorest quintile (Q5) justifies such an inefficient delivery of a life-saving intervention at such a high cost? Sometimes, even when the equity argument is being respected, it may still be entirely unfeasible to attempt to reach the poorest Q5, because the infrastructure that would allow this in a cost-effective way simply does not exist. In such cases, investing in health system development may need to precede investing in intervention coverage. We will move through the rest of the framework to explore this further, because the answers will rarely be intuitive.One examples of this relationship between cost and achieved intervention scale-up by equity quintiles (Q1-Q5) is shown in the effectiveness of an intervention in different equity strata. The effectiveness of an intervention, or its “potential impact fraction”, indicates which proportion of the current mortality burden that is targeted by an intervention would be averted among those who receive the intervention, in comparison to those that do not receive it. In theory, the effectiveness of an intervention in relation to a specific cause of death – such as a specific antibiotic treatment against childhood pneumonia – should be relatively similar in all settings. This is because it should primarily be determined by the biology of disease and the interplay between the disease and the intervention. However, the experience from the field tells us that the effectiveness of the same intervention may differ substantially between Q1 and Q5. Some of the reasons may be, in the above example, that there is different spectrum of pathogens among the very poor (and less well nourished) (Q5), and /or higher levels of antibiotic resistance, and/ or later presentation with more severe symptoms because of barriers in access to care or differences in care-seeking behaviour, all of which reduces the effectiveness of antibiotic treatment against pneumonia in comparison to Q1 children. In addition, and perhaps even more importantly, the quality of intervention delivery will not be the same in all socio-economic strata. Incomplete or inadequate delivery will be more likely among the poorest (Q5), which will decrease the effectiveness of the intervention against the same cause of death. Taking the example of pneumococcal and Hib vaccine against pneumonia, this may be because of more likely interruption of the cold chain when trying to reach the poorest, lower level of health workers' education and skills which may lead more often to inadequate administration of vaccines, and lower health awareness among the parents of the children leading to lower levels of full attendance for all immunization appointments.The second determinant of cost-effectiveness and equity to consider is Pneumococcus; and if pneumococcal vaccine is nearly 100% effective in preventing pneumococcal pneumonia deaths, then this is the maximum potential effectiveness of pneumococcal vaccine under ideal conditions. However, the adverse factors explained above  may act to reduce its effectiveness to only 20%-30% among the poorest section of the population in Q5, even when the full coverage is achieved  than in the wealthiest quintile (Q1), given that the quintiles are of the same size by definition , and that mortality rates are greater among the poor. However, the graph that captures this relationship  as preventing 15% of deaths in Q5  . For exaIn order to assess cost-effectiveness at the national and local level, policy makers would need to know: (i) what is the differential cost of intervention delivery to achieve full coverage in Q1-Q5?; (ii) what is the difference in effectiveness of this new intervention in Q1-Q5?; (iii) what is the difference in mortality burden between Q1-Q5? The interplay among those key determinants needs to be understood, and relative trade-offs need to be quantified before investment decisions can be made. However, in most contexts and for most available interventions there is simply no information on differential cost of scale-up, differential effectiveness and differential mortality burden by equity strata.We hereby propose a framework that exposes the most important determinants of cost-effectiveness and equitable impact in maternal and child mortality reduction and their interplay. One of the values of this framework is in suggesting how to make interventions delivered to the poorest in the population (Q5) more cost-effective, which is primarily by increasing the efficiency and the quality of intervention delivery, while improving access and promoting care-seeking behaviour and infrastructure to support delivery mechanisms to Q5. The framework also exposes large gaps in information required to understand the interplay between the key determinants - above all, differential cost of intervention delivery by equity strata; differential effectiveness of intervention by equity strata; and differential size and cause composition of mortality burden by equity strata. Finally, the proposed framework should enable modelling of the “thresholds of cost-effectiveness” for the poorest in the population, by starting the analysis from the bottom-left quadrant (“cost-effectiveness graph”) with setting the desired level of cost-effectiveness and, given the burden of mortality, finding the values of effectiveness and cost of scale up that would be required to make the implementation cost-effective while improving equity in the population.


It has been observed experimentally that early distal tubular urea flow exceeds urea delivery by the proximal convoluted tubule to the pars recta and loop of Henle. Moreover, the fractional excretion of urea in the urine may exceed values compatible with the reabsorption known to occur in the proximal convoluted tubule in the cortex. A likely explanation for these observations is that urea may be actively secreted into the pars recta, as proposed in a few studies. However, this hypothesis has yet to be demonstrated experimentally. In this study, we used a mathematical model of the renal medulla of the rat kidney to investigate the impacts of active urea secretion in the intrarenal handling of urea and in the urine concentrating ability. The model represents only the outer and inner medullary zones, with the actions taking place in the cortex incorporated via boundary conditions. Blood flow in the model vasculature is divided into plasma and red blood cell compartments. We compared urea flow rates and other related model variables without and with the hypothetical active urea secretion in the pars recta. The simulation suggests that active urea secretion induces a “urea-selective” improvement in urine concentrating ability by enhancing the efficiency of urea excretion without requiring a higher urine flow rate, and with only modest changes in the excretion of other solutes. These results should encourage experimental studies in order to assess the existence of an active urea secretion in the rodent kidney. Most mammals are able to produce a urine that is more concentrated than blood plasma, a process that is permitted by the anatomical and functional adaptations of the kidney, not found in lower vertebrates. In omnivores and carnivores, urea is the most abundant solute in the urine but its concentration in the blood plasma is relatively low (4–10 mmol/L), compared to other solutes such as sodium (140 mmol/L). Urea, which represents only about 2% of the solutes filtered by the glomeruli, makes up about 40–50% of all solutes in the urine (or even more depending on the protein content of the diet). Accordingly, urea is concentrated up to 100 times in urine with respect to plasma in humans, and up to 1000 times in mice and some desert-adapted rodents  is given byThe transmural flux of solute The first term inside the parentheses on the right is transmural diffusion characterized by permeability The transport parameters are shown in n et al.  and Bankn et al. .x = 0) are given in The boundary concentrations and water flows for descending limbs and DVR at the cortico-medullary border  enter the OM as LAV1, and the remainder of the AVR (labeled “LAV5” and “LAV7”) join LAV2. Thus, at the OM-IM border we impose the following conditionsk  per nephron.where with active urea secretion into pars recta, and the other without (base case). In the base case, active urea secretion was prevented by setting x = 3.0, 4.5, 6.0, and 7.0 mm. The OM segments of the long-loop profiles in To assess the impacts of urea secretion on the urine concentrating mechanism, we computed steady-state model solutions for two cases: one A comparison of urine composition and excretion rates obtained for the two cases is shown in In the base case, tubular fluid flow and concentration profiles are similar to the base-case profiles described in Layton et al. . In mostn et al.  the RBCsn et al. , the lagA substantial radial osmolality gradient was predicted in the inner stripe, with interstitial fluid osmolality in the interbundle regions higher than in the vascular bundles at the same medullary depth. That radial separation is due to the vigorous active NaCl reabsorption of the thick ascending limbs, which lie distant from the vascular bundles. Osmolality differences are much smaller among the three IM regions, even in the upper IM where tubules and vessels still exhibit clearly identifiable organization, because the thin ascending limbs have no significant active NaCl reabsorption. Owing to the high DVR water and solute permeabilities and to the large AVR fenestration fraction, vascular fluid osmolality closely follows the osmolality and concentrations of local interstitial fluid.When active urea secretion is added to the pars recta, urea flow in the long descending limb (LDL) rises from 44 pmol/min per nephron at the cortico-medullary border to 93 pmol/min at the outer–inner stripe border, and urea flow in the short descending limb (SDL) from 73 to 109 pmol/min see C. TakingUT-A2 was found to be expressed along the lower half of the inner stripe segment of the SDL . Urea flow at the SDL loop bend with urea secretion (150 pmol/min per nephron) is 45% higher than without urea secretion. As a result, 43% more urea is delivered into the cortical thick ascending limb of short loops with active urea secretion than without. The difference in urea delivery is even more dramatic in the ascending limbs of long loops: 195% more with active urea secretion than without. The impact of urea secretion is more pronounced along long loops because, like they are in vivo, the simulated juxtamedullary nephrons in the model are assumed to be more tortuous and thus longer, providing a larger surface area for transport.The model assumes that 28% of the urea delivered to the early distal tubule by the cortical ascending limb is reabsorbed in the cortex. As a result, OMCD urea flow rate is substantially higher with active urea secretion than without; and because only a relatively small amount urea is reabsorbed from the OMCD, twice as much urea is delivered to the IM via the CD in the case with urea secretion than in the base case. A comparison of descending limb and CD urea concentration profiles for the two cases can be found in Note that the urea that flows in AVRs has two different origins: (i) urea delivered to the medullary circulation by the efferent arterioles of the juxtamedullary glomeruli (in plasma that has not been filtered) branching into DVRs, and (ii) previously filtered urea delivered to the IM by the terminal IMCD. Thus, active secretion in the pars recta of urea extracted from the AVRs, can take place even in the absence of previous urea accumulation in the IM, or can exceed the urea available through recycling of previously filtered urea.It is noteworthy that active urea secretion enhances the concentrating mechanism, as measured by an increase in CD tubular fluid osmolality in the IM, but not in the OM. Indeed, OMCD fluid osmolality rises slightly more in the base case than in the case with active urea secretion; see To further demonstrate the impact of active urea secretion on urea and fluid excretion rates, we computed model solution for different values of maximum active urea secretion rate, nge of ) B.We have extended a mathematical model of the urine concentrating mechanism in the rat kidney to evaluate the impacts of a hypothesized active urea secretion in the pars recta of the proximal tubule. In this model, transmural transport by tubules and vessels is approximated by single-barrier expressions that summarize experimental results for osmotically driven water fluxes, solute diffusion, and active solute transport. The model, which was solved to steady state, predicts, in all represented structures, concentrations of the solutes represented, the osmolality arising from those solutes, the intratubular (or intravascular) flow rates of water and solutes, the transmural fluxes of water and solutes, and the excretion rates of solutes. The main findings revealed by this simulation is that an active urea secretion in the pars recta allows the kidney to excrete a greater amount of urea without increasing the amount of water required for this excretion and with only a small influence on the excretion of other solutes. This “urea selective” improvement in the kidney's concentrating ability renders the model results very similar to in vivo observations.The conclusion that active urea secretion may introduce “urea selective” improvement in the kidney's concentrating ability was drawn based on the model's prediction of a 55% increase in urinary urea excretion, together with a modest decrease in salt excretion, with proximal tubular active urea secretion. An alternative approach to assess the impact of active era secretion is to match the solute excretions in the two cases, and then compare their urine osmolalities. However, to match the urinary excretion rates would require using different model parameters or boundary conditions in the two cases, which we feel would render it difficult to conclude whether any difference in model urine osmolality is due to active urea secretion or the different parameter values.The existence of an active urea secretion into the proximal straight tubule of some mammalian kidneys is suggested by a number of functional observations in mice, rats, dogs, and humans  in the thin limbs of short loops of Henle that express UT-A2 and that run in close proximity of the vascular bundles in rats, mice and desert-adapted rodents Kriz . This urIt has been proposed that the role of the SDL UT-A2 may lie in the transient buildup of a urea and osmolality gradient in the IM, rather than in the generation of the steady-state gradients . In water diuresis, an almost normal sodium chloride gradient is present in the IM, but the urea gradient is absent Saikia . When vaOwing to urea's mild toxicity (Coombe et al. In summary, this study, using an elaborate model of the rat renal medulla, strongly suggests that an active urea secretion in the pars recta of the proximal tubule takes place in the rat kidney and that it allows a more efficient excretion of urea with negligible impact on the amount of water required for this excretion. In vivo micropuncture studies in rats and mice, as well as microperfusion experiments of isolated medullary pars recta in vitro are required to confirm these modeling results. We hope these “in silico” results will stimulate further experimental research.


Particle swarm optimization (PSO) is employed to investigate the overall performance of a pin fin.The following study will examine the effect of governing parameters on overall thermal/fluid performance associated with different fin geometries, including, rectangular plate fins as well as square, circular, and elliptical pin fins. The idea of entropy generation minimization, EGM is employed to combine the effects of thermal resistance and pressure drop within the heat sink. A general dimensionless expression for the entropy generation rate is obtained by considering a control volume around the pin fin including base plate and applying the conservations equations for mass and energy with the entropy balance. Selected fin geometries are examined for the heat transfer, fluid friction, and the minimum entropy generation rate corresponding to different parameters including axis ratio, aspect ratio, and Reynolds number. The results clearly indicate that the preferred fin profile is very dependent on these parameters. In order to enhance the convective heat transfer from a solid surface, fins of different shapes are used in several applications such as microelectronics, heat exchanger and cooling of engines. The shape of the fin has the main effect on the overall performance and therefore, needs to be optimized for better efficiency. Many researchers including Genetic algorithms (GAs) have been successfully applied in optimizing heat transfer from solid surfaces. Complex optimization involving non-linear constraints can be easily solved using genetic algorithms. Fabbri Recently, Particle Swarm Optimization (PSO) technique has attracted several investigators. This technique is one of the most widely used algorithms to find the optimal values in order to minimize the expectation as a function. PSO algorithm and GA operate within a set of solutions, and interactively update it through the application of a number of heuristics PSO algorithm was developed by Kennedy and Eberhart The above literature survey reveals that PSO has never been used for optimization of pin fin geometry. The main objective of this study is to optimize pin fins of different shapes using the PSO algorithm, which was proposed by Eberhart and Kennedy The algorithm is initialized with a population of random solutions, and then updated through generating new positions In PSO algorithm, each particle keeps the best position that it has achieved so far. The particles update their velocities, from the previous velocity using Eq.1. On the other hand, a particle’s position is adjusted according to the Eq.2. wherepbest) of the particle at time t.gbest) for the population.pbest in interval .gbest in interval .The presented Initialize the particle s with random positions and velocities within the search space.Ns).Calculate the fitness value of each particle. In this study, the fitness value is calculated by dimensionless total entropy generation rate .Therefore, the particles (solutions) should move into better directions. In other words, they should intend to have been decreasing fitness as quickly as possible and exploit the useful information from some other particles besides the best particle In this study, we use the PSO algorithm to minimize the noise of pin fin geometry. We set the range of Uapp and the ambient temperature of the air is assumed to be aT. The surface temperature of the pin wall is wT(>aT). Following Bejan Consider a pin fin of arbitrary cross section rectangular, circular, square, or elliptical as shown in withThe fin parameterwhere Nusselt numbers for the base plate and the selected geometries were developed by khan withThe constant whereThe values of these constants and the values of different parameters for the selected geometries are also presented in Ns) per iteration. This is done by updating the search space of (P) in the interval  and fixing Ns was achieved when p =  28.679, as shown in In the beginning, we have tried to make it clear about the technical way in the algorithm. In our analysis, the PSO algorithm was executed 50 times with 500 iterations each time. Then we reported the best results. In each iteration, there are many solutions, but the algorithm chooses the variables that give the best solution, then compare this with the best solution it has achieved so far . In other words, the global best value is moved towards to a better solution. So, if all the solutions are moved towards better solutions, then, it can be stated that the algorithm can achieved convergence. Accordingly, the global best value will not change. For example, in Ns) for rectangular plate fin (RPF) and elliptical pin fin (EPF), we found the following:In addition, the algorithm was executed 50 times with 500 iterations. By updating Ns) for RPF is received when The minimum value of the dimensionless total entropy generation rate (Ns) for EPF is obtained when Ns for EPF is illustrated in On the other hand, the minimum value of the dimensionless total entropy generation rate (SN) is equal to 1.926e-6 and P = 8.467. The minimum values of SN for rectangular plate fin (RPF), circular pin fin (CPF), square pin fin (SPF), and elliptical pin fin (EPF), withNs, RTOT, and ΔP, with p = 6 andIn Particle swarm optimization (PSO) has been employed successfully to investigate the overall performance of a pin fin with different cross sections. In order to combine the effects of thermal resistance and pressure drop, the idea of entropy generation minimization ( EGM) is employed. We have examined the effects of aspect ratio, Reynolds number, and perimeter of fin on the dimensionless total entropy generation rate. Optimal dimensionless entropy generation rate exists for each geometry. The square geometry is found to be have the worst choice from the point of view of total entropy generation rate. However, rectangular geometry is found to be the best. The results indicate that the preferred fin profile is very dependent on these parameters. It is found that PSO algorithm quickly converges to a good solution, and it is easy to obtain a local optimal value for each selected geometry.


In this paper, we aim to (i) develop integrated computational models that are suitable for investigating the effects of pamidronate and denosumab on MM-induced bone disease and (ii) evaluate the responses to pamidronate and denosumab treatments using these integrated models. To achieve these goals, pharmacokinetic models of pamidronate and denosumab are first developed and then calibrated and validated using different clinical datasets. Next, the integrated computational models are developed by incorporating the simulated transient concentrations of pamidronate and denosumab and simulations of their actions on the MM-bone compartment into the previously proposed MM-bone model. These integrated models are further calibrated and validated by different clinical datasets so that they are suitable to be applied to investigate the responses to the pamidronate and denosumab treatments. Finally, these responses are evaluated by quantifying the bone volume, bone turnover, and MM-cell density. This evaluation identifies four denosumab regimes that potentially produce an overall improved bone-related response compared with the recommended pamidronate regime. This in silico investigation supports the idea that denosumab represents an appropriate alternative to pamidronate in the treatment of MM-induced bone disease.It is unclear whether the new anti-catabolic agent denosumab represents a viable alternative to the widely used anti-catabolic agent pamidronate in the treatment of Multiple Myeloma (MM)-induced bone disease. This lack of clarity primarily stems from the lack of sufficient clinical investigations, which are costly and time consuming. However,  Multiple Myeloma (MM) is a B cell malignancy that is associated with high morbidity and short survival duration after diagnosis. To date, MM remains incurable; therefore, the realistic goal for treating patients with MM is to improve their quality of life and prolong their survival time. Over 70% of patients with MM will develop bone lesions as the MM progress, resulting in osteolytic bone disease that includes severe bone pain, pathological fractures, osteoporosis and hypocalcaemia Two categories of agents are used to treat bone disease according to the terminology from in vitro and in vivo experiments support the direct and indirect anti-MM activities of pamidronate, which may include the inhibition of tumor cell functions, the stimulation of anti-tumor immune reactions, and the enhancement of the cytotoxic activity of chemotherapeutic agents Currently, the most widely used agents to treat MM-induced bone disease are the bisphosphonates, which induce a reduction in both bone resorption and bone turnover through several mechanisms simultaneously  There is an increasing amount of preclinical and clinical evidence showing that a new, promising anti-catabolic agent, denosumab ), is able to improve MM-induced bone disease in silico investigations require less time and money, suggesting that such studies may complement the clinical investigations. We have previously proposed a computational MM-bone model Although clinical investigations represent a direct and reliable way to determine the efficacy of denosumab, this approach is time-consuming and expensive. Alternatively, First, we aim to develop integrated computational models suitable for investigating the effects of pamidronate and denosumab on MM-induced bone disease. To achieve this goal, pharmacokinetic models of pamidronate and denosumab are developed to simulate the transient concentrations of pamidronate and denosumab and are calibrated and validated by different clinical datasets. Integrated computational models are then developed by incorporating the simulated transient concentrations of pamidronate and denosumab and simulations of their actions on the MM-bone compartment into the MM-bone model. Additional clinical datasets are used to calibrate and validate the integrated models. With integrated computational models, it is possible to investigate the effects of pamidronate and denosumab on MM-induced bone disease.in silico responses to pamidronate and denosumab treatments, which help clarify whether denosumab represents a useful alternative to pamidronate in the treatment of MM-induced bone disease. The responses to a variety of regimes (including dosages and administration periods) of pamidronate and denosumab treatments in patients with MM are investigated using the validated integrated models. Furthermore, these responses are evaluated by the defined relative response and the relative index, which are based on quantifying the bone volume, bone turnover and MM-cell density. The outcomes of the evaluation may identify certain denosumab regimes that potentially produce an improved bone-related response compared with the recommended pamidronate regime.The second goal of this paper is to evaluate the This paper is organized as follows. The pharmacokinetic models of pamidronate and denosumab are developed in Section 2.3, the integrated computational models are developed in Section 2.4, and the relative response and the relative index are defined in Section 2.7. In Section 3.1, the pharmacokinetic models of pamidronate and denosumab are calibrated and validated by different clinical datasets, and in Section 3.2, the integrated computational models are calibrated and validated by different clinical datasets. In Section 3.4 and 3.6, the responses to various regimes of pamidronate and denosumab treatments are investigated and evaluated respectively.Absolute median serum type I collagen cross-linked N-telopeptides (NTX), collected at days 1, 2, 3, 4, 8, 15, 22, 29, 43, 57, 71 and 85 in 25 patients with MM after receiving 0.1, 0.3, 1.0, or 3.0 mg/kg denosumab (s.c.) or 90 mg pamidronate (i.v.) All of the above-described datasets were digitalized from graphs of previously published papers using WinDIG version 2.5.We previously proposed a computational MM-bone model After the drugs enter the MM-bone model, the physiological actions of pamidronate and denosumab on the components of the MM-bone model are modeled based on biological evidence, and the modeling of their actions is incorporated into the MM-bone model. As discussed in the Bone-cell densities are a direct way to monitor the imbalance of bone remodeling and to assess the effects of pamidronate and denosumab on MM-induced bone disease; however, only limited and fragmentary clinical data are available in the literature to identify these values MMP = 0.055/day, see Technically, in this manuscript, the drug treatments are applied in a case of quasi-stable MM  in muscle tissue after a subcutaneous injection and in blood (nM) respectively; aK is the absorption of denosumab from the muscle into the blood circulation; eK denotes the linear elimination constant of denosumab; mK is the half-maximal concentration of denosumab in Michaelis–Menten elimination; and maxV is the maximal velocity of Michaelis–Menten elimination. The conceptual model describing the pharmacokinetics of denosumab can be expressed as follows:m2 and 3m represent the pamidronate mass (mg) measured in the blood after an intravenous injection and the retention in the bone (mg) respectively; e2K is the elimination constant of pamidronate by renal function; and 23K and 32K denote the diffusion constants between 2m and 3m respectively. The corresponding governing equations to describe pamidronate pharmacokinetics are as follows:Based on the study of Lipton et al. Den,2m is the denosumab concentration in serum and D,DenK is proportional to the dissociation rate constant of denosumab binding to RANKL  and receptor activator of nuclear factor-κB (RANK) respectively. RANKLR is the maximal number of RANKL molecules that can be expressed on the surface of osteoblast precursors. RANKL,dP is the external production rate of RANKL with the unit of RANKLβ is the endogenous production of RANKL by osteoblast precursors with the unit of RANKLD is the degradation of RANKL. Without drug treatments, the concentrations of RANKL are calculated as follows Pam,3m is the pamidronate concentration retained in the bone. M,Pam,OCaK is the half-maximal concentration of pamidronate to kill active osteoclasts. 1γ is a parameter that can be calibrated to reflect the effects of the co-stimulation with TGF-β and pamidronate.Without drug treatments, the population of active osteoclasts and MM cells are calculated respectively as follows Pam,3m is the pamidronate concentration retained in the bone; M,Pam,MMK is the half-maximal concentration of pamidronate to kill MM cells; 2γ is a parameter that can be calibrated to reflect the effects of pamidronate stimulation. In this analysis, 2γ is set to 1 to simplify the integrated model.In addition, using BV represents normalized bone volume, resk and formk represent relative rate of bone resorption and bone formation respectively with the unit of Finally, the bone volume as a system output of the integrated models is calculated as follows NTXβ denotes the production rate of NTX and NTXD denotes the degradation of NTX. M,NTXK is the half-maximal density of active osteoclasts to control the production of NTX, and n is the Hill coefficient.Because the production of NTX from type I collagen is controlled by the density of the active osteoclasts and serum NTX is cleared by the liver or kidneys, the changes of the serum NTX over time compose one source term  and one sink term . Here, we assume that the concentrations of type I collagen are a constant because they are much greater than the NTX concentrations in the bone. In addition, we assume the following: (i) the production of NTX is controlled by the density of active osteoclasts in the form of the Hill function, and (ii) NTX degrades at the first–order kinetics in the serum. The changes of the serum NTX over time are summarized as follows:predy and expy are simulated values and the corresponding experimental or clinical values respectively. The values of predy are calculated using the routine ‘ode15s’ in Matlab, and the values of expy are collected from the literature  is defined as follows:expy. The closer this value is to 1, the better the agreement is between the simulation results and the experimental data.To evaluate the goodness of fit between simulations and experiments, the coefficient of determination . Higher values of AUCBV, AUCMM and AUCOCa, indicate a greater improvement in MM-induced bone lesions, a greater alleviation of the MM tumor burden and a reduced occurrence of ONJ respectively.Furthermore, after pamidronate and denosumab treatments the accumulated absolute deviation of these variables  over time can be quantified by calculating the area under their curves (AUC), which is the time integral of the change in the variable from the beginning of the treatment to the end of the treatment. http://pi.amgen.com/united_states/xgeva/xgeva_pi.pdf), it is worth mentioning that the administration of 120 mg denosumab every 4 weeks has been recommended to treat the skeletal-related events in patients with bone metastases from solid tumors although there is no experience of over-dosage of denosumab. For this reason, the above mentioned denosumab regime can be probably regarded as a reference regime rather than a recommended regime to treat MM-induced bone disease before more clinical data are available. To evaluate the responses to denosumab treatments in MM-induced bone disease, the pamidronate treatment with the recommended regime is selected as a base treatment. By doing so, the relative response to the denosumab treatment compared with the response to the pamidronate treatment is calculated ; that is, the ratio of the responses to various tested denosumab regimes to the responses to the recommended pamidronate regime is calculated. If the relative response is greater than 1, then the denosumab regime appears to produce a better response than the recommended pamidronate regime; otherwise, the denosumab regime is interpreted to produce a response inferior to that of the recommended pamidronate regime.Pamidronate has been used in clinical settings to treat MM-induced bone disease for many years, and a regime consisting of the intravenous administration of 90 mg pamidronate every 4 weeks for a period of 2 years is recommended. In contrast, denosumab is a novel agent that is still undergoing the phase III clinical trials to treat MM-induced bone disease; accordingly, different denosumab regimes are undergoing testing, and no recommended denosumab regimes are available yet to treat MM-induced bone disease. In the meanwhile, according to the highlights of prescribing information provided by Amgen Inc.  is defined in AUC,relaBV and AUC,relaOCa, represent the responses of the bone volume and the density of osteoclasts to denosumab treatments relative to their responses to pamidronate treatments respectively. The definitions and calculations of AUC,DenoBV, AUC,DenoOCa,, AUC,PamiBV and AUC,PamiOCa, are described in BVW and OCaW represent the weights of the bone volume and the density of osteoclasts to the bone-related response. The density of osteoclasts is assumed to be a less important criterion compared with the bone volume because it is associated with the occurrence of ONJ that is uncommon after pamidronate and denosumab treatments. Specifically, the risk of ONJ associated with pamidronate is 1 to 2% within the first 2 years of the treatment BVW, and OCaW are set to 1and 0.1 respectively according to their relative importance. It should be noted that different evaluation outcomes may be produced when different weights are used. Given that there is no more knowledge to help determine these weights more accurately so far, it is particularly important to experimentally validate the evaluation outcomes that are produced under the current setting of weights.While relaIndex is1.1; that is, if the value of the relaIndex is greater than 1.1, the denosumab regimes would produce a better bone-related response than the recommended pamidronate regime.A greater value of the relative index indicates a better bone-related response to the denosumab regimes compared with the recommended pamidronate regime. Clearly, the thresholds of the 2 values listed in Based on the clinical pharmacokinetic datasets of denosumab in the blood and pamidronate in the bone after a single-dose administration, the optimized pharmacokinetic models of pamidronate and denosumab are obtained, and the optimized parameter values are listed in D,DenoK, M,Pami,OCaK and 1γ) are calibrated by best fitting with the serum NTX concentrations measured in the clinical setting. By assuming that the serum paraprotein changes are proportional to the changes in MM-cell density, the parameter related to the anti-MM action of pamidronate  is calibrated by best fitting with the serum paraprotein concentrations measured in the clinical setting. The original dataset of the paraprotein concentrations (represented as percentage changes from the baseline) are obtained in patients with MM who received pamidronate in combination with chemotherapy or received chemotherapy alone M,Pami,MMK requires the dataset obtained in patients with MM who received pamidronate alone. To account for this difference, we assume that the effects of pamidronate and chemotherapy on the changes in paraprotein concentrations are linear addition. Therefore, the difference between paraprotein changes after the simultaneous pamidronate and chemotherapy treatment (denoted by paraproteinchangeschemo+pami) and those after the chemotherapy treatment alone (denoted by paraproteinchangeschemo) is the paraprotein changes after the pamidronate treatment alone (denoted by paraproteinchangespami); that is, paraproteinchangespami = paraproteinchangeschemo+pami – paraproteinchangeschemo. Given that the two curves (paraproteinchangeschemo+pami and paraproteinchangeschemo) have some scatter, they are firstly smoothed and then used to calculate the difference between them. The details of smoothing the two curves are described in the The parameters related to the anti-catabolic action of pamidronate and denosumab  to pamidronate and denosumab treatments in MM-induced bone disease.t-tests are conducted in SPSS (version 19) to evaluate whether the impact of the anti-MM action of pamidronate on the bone volume is significant, in which the threshold of significance values is set to 0.1.In the integrated computational models, the actions of pamidronate are modeled as both anti-catabolic and anti-MM, and the action of denosumab is modeled as anti-catabolic. As a result of this difference, the issue of whether the anti-MM action of pamidronate has a significant impact on the bone volume arises. To address this issue, the AUCs of the integrated model with pamidronate are compared with those of the integrated model with pamidronate in which the anti-MM action of pamidronate is disabled  are investigated using the validated integrated models. After various multi-dose administrations of pamidronate and denosumab every 30, 60 or 90 days, there are similar responses of the density of osteoclasts and the MM-cell density. For example, the density of osteoclasts decreases under all regimes of pamidronate and denosumab. The greater dosages of pamidronate and denosumab show greater decreases in the density of osteoclasts . It shouIn contrast, the bone volume responds differently to various multi-dose administrations of pamidronate and denosumab every 30, 60 or 90 days. For example, after various multi-dose administrations of pamidronate and denosumab every 30 days, the bone volume increases under all regimes of pamidronate and denosumab. However, the rates of increase in the bone volume drop faster with the increases in the dosage of pamidronate and denosumab . In partThe responses to the recommended pamidronate regime (90 mg administration every 4 weeks) and the reference denosumab regime (120 mg administration every 4 weeks) are highlighted in The above investigations have indicated that pamidronate and denosumab have quite different effects on the MM-cell density and the reason is clear that pamidronate has a direct influence on the MM-cell density while denosumab indirectly influences the MM-cell density. In terms of the bone-related response to pamidronate and denosumab treatments, the two drugs qualitatively produce similar effects because both of them reduce the production rate of active osteoclasts  to investigate the responses to pamidronate and denosumab treatments when their different pharmacokinetics are removed. For example, we simulate the responses to denosumab treatments by increasing the value of One example of almost the strongest responses to denosumab and pamidronate treatments is shown in Since the different pharmacokinetics of pamidronate and denosumab mainly contribute to the different quantitative bone-related response to pamidronate and denosumab treatments, how to administrate pamidronate and denosumab (or the regime of pamidronate and denosumab) plays a key role in improving the bone-related response to pamidronate and denosumab treatments. To clarify whether denosumab represents an alternative to pamidronate in the treatment of MM-induced bone disease, the issue of whether a specific regime of denosumab produces a greater improvement in bone lesions than pamidronate has to be addressed. If a specific regime of denosumab can be found to produce a greater improvement in bone lesions than pamidronate, then denosumab may represent a viable alternative to pamidronate in the treatment of MM-induced bone disease. As a result, the above-described responses to 12 different regimes of denosumab treatments are further evaluated by the defined relative response and the relative index, resulting in the identification of four denosumab regimes that potentially produce an improved bone-related response compared with the recommended pamidronate regime. The responses of the density of osteoclasts, the bone volume and the MM-cell density to the identified denosumab regimes are shown in relaIndex of these identified denosumab regimes is greater than its threshold value of 1.1. Specifically, whereas the relative response AUC,relaBV of the denosumab regimes except for the third are greater than 1, the relative response AUC,relaBV of the third denosumab regime is lower than 1. In contrast, the relative response a,AUC,relaOC of the denosumab regimes except for the third are lower than 1 but the relative response a,AUC,relaOC of the third denosumab regime is greater than 1. These differences in the relative response indicate that the denosumab regimes except for the third improve the responses of the bone volume but worsen the responses of the density of osteoclasts, whereas the third denosumab regime improves the response of the density of osteoclasts but diminishes the response of the bone volume. In other words, compared with the recommended pamidronate regime, all the identified denosumab regimes produce an overall improved bone-related response but cannot improve the responses of the bone volume and the density of osteoclasts simultaneously. In contrast, the relative response AUC,relaMM of the identified denosumab regimes is much lower than 1, as a result, the identified denosumab regimes cannot improve the MM tumor-related response in comparison with the recommended pamidronate regime because denosumab has no anti-MM action in the MM-bone compartment.As summarized in AUC,relaBV, a,AUC,relaOC and relaIndex when the fourth identified denosumab regime is used and those when the reference denosumab regime is used are 1.0417, 1.2972 and 1.0569 respectively, indicating that the fourth identified denosumab regime is superior to the reference denosumab regime in terms of the improvements of both the bone volume and the density of osteoclasts. Therefore, the fourth identified denosumab regime is also clinically feasible. In a word, the four identified denosumab regimes not only produce an overall improved bone-related response compared with the recommended pamidronate regime but also are clinically feasible.Clinically, the first three identified denosumab regimes are feasible because their doses are lower than or equal to the dose of the reference denosumab regime (120 mg) and their administration periods are longer than or equal to the administration period of the reference denosumab regime (every 4 weeks), suggesting that the possible toxicities (at least in terms of the risk of ONJ) caused by these denosumab regimes should be tolerable. On the other hand, the dose of the fourth identified denosumab regime  is larger than that of the reference denosumab regime but the administration period of the fourth identified denosumab regime is longer than that of the reference denosumab regime; as a result, it is difficult to determine whether the fourth identified denosumab regime is feasible in the clinical setting based on the regime on its own right. However, the ratios between AUC,relaBV, a,AUC,relaOC, relaIndex and AUC,relaMM are 1.06, 0.4941, 1.1094 and 0.3876 respectively) compared with the recommended pamidronate regime, this denosumab regime is not regarded as clinical feasibility because its dose is larger than the dose of the reference denosumab regime and it induces a higher risk of ONJ than the reference denosumab regime. In addition, the above-described responses to 11 different regimes of pamidronate treatments (except the recommended pamidronate regime) are further evaluated by the relative response and the relative index. None of the evaluated pamidronate regimes can further improve the bone lesions, alleviate MM-tumor burden and decrease the risk of ONJ simultaneously compared with the recommended pamidronate regime.It should be noted that although the administration of 180 mg denosumab every 30 days produce an overall improved bone-related response  simulation is the current ‘gold standard’ employed by pharmaceutical companies to investigate the responses to a particular pharmacological drug; however, this approach treats the human body as a ‘black box’ or a ‘gray box’ The reliability and accuracy of the evaluation of pamidronate and denosumab treatments in MM-induced bone disease also depend on the calibration and validation of the integrated computational models. After multi-dose pamidronate and denosumab administration, the simulations are consistent with clinical datasets. However, after single-dose denosumab administration, the consistency between the simulations and the clinical datasets seems better qualitative  than quantitative. This effect is mainly caused by the limited clinical data available and the variability of the currently available clinical data. Using more reliable clinical data, this consistency between the simulations and the clinical data may be improved. This consistency may also be improved by refining the integrated models in the future. For example, the proposed models are deterministic whereas biological phenomena are stochastic; therefore, considering stochastic properties, the ability to capture the effects of noise may improve the differences between the best-fit modeling results and the experimental data. In addition, after single-dose pamidronate administration, the simulations only capture the sustainable decrease in NTX levels; therefore, this result may be a shortcoming of the integrated computational model that may undermine the accuracy of the evaluation of pamidronate treatment in MM-induced bone disease.in silico investigations. For example, the validated integrated models can be used to simulate the responses to various regimes of pamidronate and denosumab treatments. Furthermore, the defined relative indices make it possible to effectively identify the improved regime from various regimes because they concurrently contains the items of the bone volume (needs less osteoclasts) and the density of osteoclasts (need more osteoclasts). Indeed, using the integrated models and the defined relative indices, four denosumab regimes have been successfully identified, which increase the bone volume and maintain a high density of osteoclasts compared with the recommended pamidronate regime. Although it is still hard to determine whether these identified regimes are or contain the optimal regime, they are approaching to the optimal regime.Both pamidronate and denosumab increase the bone volume by reducing the density of osteoclasts. On the other hand, the lower density of osteoclasts results in a less bone remodeling, which causes some severe side effects such as ONJ. Therefore, it is important to maintain a reasonable or balanced density of osteoclasts in pamidronate and denosumab treatments in order to increase the bone volume while decreasing the occurrence of side effects. The task to identify such a reasonable density of osteoclasts is difficult in the clinical investigations; however, it becomes easy in the in silico investigations are complementary to clinical investigations. Clinical investigations provide the necessary clinical data for in silico investigations and verify the outcomes of in silico investigations; in silico investigations accelerate the process of evaluating the responses to the drug therapy and the process of screening the drug therapy regimes performed by clinical investigations. This approach of combining clinical investigations with in silico investigations could promote efficiency in the drug evaluation and reduce costs compared with using clinical investigations alone.In this study, we identified four denosumab regimes that potentially produce an overall improved bone-related response compared with the recommended pamidronate regime, supporting the idea that denosumab can represent an alternative to pamidronate in the treatment of MM-induced bone lesions. Although further clinical investigations are required to verify these identified denosumab regimes, this identification greatly narrows the scope of testing regimes for clinical investigations. In this way, in silico comparisons) are necessary to address the issues of whether denosumab can represent an alternative agent to zoledronic acid or which one of pamidronate and zoledronic acid is superior in the treatment of MM-induced bone disease. Since this study has demonstrated that the method of in silico investigations is efficient, it actually paves the way for addressing the above issues by in silico investigations in the future study, although there may be a potential limit of this study due to not currently address the above issues in this study.This study has demonstrated that the computational method is an efficient way to address the issue of that denosumab appears to represent an alternative agent to pamidronate in the treatment of MM-bone disease. In the meanwhile, another issue of whether denosumab can further represent an alternative agent to other bisphosphonates in the treatment of MM-bone disease arises. For example, zoledronic acid is also a widely used bisphosphonates in the treatment of MM-induced bone disease and comparing the efficacy and adverse effects of zoledronic acid with denosumab or other bisphosphonates  is a critical issue in the treatment of MM-bone disease. Several clinical investigations were conducted to compare the responses to zoledronic acid treatments with those to denosumab or pamidronate treatments. A randomized, double-blind study showed that denosumab (120 mg) was non-inferior (tending to superiority) to zoledronic acid (4 mg) in preventing or delaying the skeletal-related events in patients with advanced cancer metastatic to bone or MM In this paper, we illustrated how to investigate the anti-catabolic effects of pamidronate and denosumab treatments in MM-induced bone disease using integrated computational models that link a bone resorption marker with drug pharmacokinetics and drug actions on the MM-bone compartment. This investigation assisted in clarifying whether denosumab represents an alternative to pamidronate in the treatment of MM-induced bone lesions. To develop the integrated computational models, pharmacokinetic models of pamidronate and denosumab were developed to simulate the transient concentrations of pamidronate and denosumab respectively, and were calibrated and validated by different clinical datasets. The integrated computational models were subsequently developed by incorporating the simulated transient concentrations of pamidronate and denosumab and simulations of their actions on the MM-bone compartment into the MM-bone model. These integrated models were also calibrated and validated by different clinical datasets, suggesting that they are suitable to be applied to investigate the responses to pamidronate and denosumab treatments in MM-induced bone disease.Using validated integrated models, a variety of regimes of pamidronate and denosumab treatments were investigated, and the corresponding responses were evaluated by the defined relative responses and the relative index, which are based on the quantification of the responses to pamidronate and denosumab treatments. The outcomes of the evaluation identified four denosumab regimes that potentially produce an overall improved bone-related response compared with the recommended pamidronate regime. This identification supports the idea that denosumab can represent an alternative to pamidronate in the treatment of MM-induced bone disease.in silico investigations are valuable as a complementary approach to clinical investigations. This approach substantially accelerated the process of evaluating the responses to drug therapy and the process of screening drug therapy regimes, leading to the identification of several improved regimes with reduced costs in terms of time and money. In combination with clinical investigations, the proposal of improved regimes may be specifically tested and verified. As a result, clinical investigations combined with in silico investigations have the potential to transform the traditional method of pure screening by clinical investigations, leading to a new approach of mixed screening by in silico investigations and verification by clinical investigations. This combined approach promotes the efficiency of drug evaluation and reduces the costs. In addition, based on the MM-bone model, the method of in silico investigations of the anti-catabolic effects of pamidronate and denosumab on MM-induced bone disease may be utilized to investigate the anti-catabolic effects of other bisphosphonates  or the anabolic effects of novel agents  on MM-induced bone disease.This study indicates that Supporting Information S1D,DenK.The derivation of (DOC)Click here for additional data file.Supporting Information S2The calculations of the area under the curves (AUCs) for the bone volume, the MM-cell density and the density of active osteoclasts.(DOC)Click here for additional data file.Supporting Information S3The smoothed curves of chemotherapy and the combined therapy (chemotherapy + pamidronate).(DOC)Click here for additional data file.


High-density DNA microarrays are useful tools for analyzing sequence changes in DNA samples. Although microarray analysis provides informative signals from a large number of probes, the analysis and interpretation of these signals have certain inherent limitations, namely, complex dependency of signals on the probe sequences and the existence of false signals arising from non-specific binding between probe and target. In this study, we have developed a novel algorithm to detect the single-base substitutions by using microarray data based on a thermodynamic model of hybridization. We modified the thermodynamic model by introducing a penalty for mismatches that represent the effects of substitutions on hybridization affinity. This penalty results in significantly higher detection accuracy than other methods, indicating that the incorporation of hybridization free energy can improve the analysis of sequence variants by using microarray data. To detect differences in the genomic sequences between the different strains, we applied the genomic DNA of a previously sequenced E. coli strain DH1 ME8569 In this study, we have developed a novel algorithm that uses an appropriate thermodynamic model of hybridization to detect single-base substitutions by using microarray data. Into this thermodynamic model, we introduced a penalty for mismatches, which represents the effects of substitutions on hybridization affinity. To evaluate the detection accuracy of sequence substitutions, we used a high-density tiling microarray designed for the A fine-tuned resequencing array covering the whole genome of E. coli W3110 strain was newly developed according to the Affymetrix CustomExpress Arrays. E. coli is approximately 4.65 M bp, 18.6 million probes were required to cover the whole genome, in addition to all possible substitutions described above. All 18.6 million probes were represented on 3 Affymetrix CustomExpress arrays, each containing 5 million probes per array in Because the genome size of For the detection of nucleotide substitution, we developed a model to estimate the number of target molecules hybridized to probes based on a Finite Hybridization (FH) model Next, we considered the penalty in the hybridization free energy due to mismatches between the probe sequence and the target. Here, we assumed that when there is a single base mismatch at the We also estimated the hybridization free energy for the non-specific hybridization, On the basis of the above free energy terms, the reaction coefficients for the probe-target hybridization, non-specific hybridization, and probe folding for the We determined the parameters in the above hybridization mode by fitting the estimated signal intensities of the probes to those observed experimentally. For the fitting, we obtained the intensity signals using the genomic DNA that was used to design the tiling microarray, and computed the residual sum of squares E. coli W3110, we first calculated the above residual sum of squares To identify nucleotide substitutions in a genomic DNA sample that was compared to the reference sequence of After the initial screening to identify genomic regions that might contain nucleotide substitution, we further analyzed the residual errors between the estimated and observed signal intensity ratios to determine the precise position and base type of the substitution. Here, assuming that the relative error between the observed and estimated intensities follows a normal distribution with a constant variance, a log likelihood ratio E. coli W3110 and DH1 ME8569 strain were compared using MUMmer The reference genome sequences of E. coli W3110 and DH1 E. coli strains DH1 and W3110 as the reference. In comparison with the reference genome, the genomic DNA of E. coli DH1 has 227 known single-base substitutions, which are detectable by this array-based approach. We first determined the 343 parameters in the FH model described in the Materials and To evaluate the accuracy of the FH model for detection of single-nucleotide substitutions, we applied a method, in which we compared the intensity data obtained from the genomic DNA samples of Next, by using the parameter values, we screened candidate genomic regions containing alterations by identifying regions showing higher values of the residual error To detect single-nucleotide substitutions, we next evaluated the likelihood of all possible substitutions within each candidate region. et al., which is also based on likelihood estimation To evaluate the detection performance of our method, we compared the detection sensitivity and specificity with the widely used detection algorithm “SNPscanner” proposed by Gresham Given the existence of various types of tiling microarrays with different probe resolutions, evaluation of the effect of probe resolution on the detection performance is important for probe design. Accordingly, using 1-bp-resolution data from our high-density tiling microarray, we investigated how the sensitivity of substitute detection depends on the probe resolution by removing probe data and reducing the tiling resolution to 3 bp, 5 bp, 7 bp, 9 bp, 11 bp, and 13 bp. In this analysis, we discarded non-complementary MM probes, and used the intensity data of PM and complementary MM probes only. E. coli as an example to evaluate our methods for microarray-based SNP detection. The results depend only on the physical properties of genomic DNA and oligo nucleotide probes, while they should be independent of the sources of genomic DNA including prokaryotes and eukaryotes after appropriate extraction of genomic DNA. Thus, we expect that this method will be useful for the other model systems and genomes for future development of microarray-based SNP detection.In conclusion, in this paper, we have presented a new method to identify single-base substitutions based on tiling microarray data by using a thermodynamic model of hybridization between probes and target DNA fragments. By introducing an energy penalty for hybridization free energy due to mismatches between the probe sequence and the target, our model allows the prediction of differences in signal intensities between PM probes and probes with single or double substitutions. Using this model, single-nucleotide substitutions can be identified by the maximum likelihood method. We evaluated this method and showed that it can detect 219 (96.5%) of known substitutions by comparing the microarray data of 2 different E. coli strains. This detection performance was significantly higher than that of an existing method, presumably because of the appropriate modeling of hybridization process. We also showed that the sensitivity of the detection depends on the tiling resolution of the microarray, and found that a resolution of 5 bp or less is necessary for accurate detection of single-base substitutions. It should be note that, since this model can predict absolute signal intensities based on the sequence of probes, we can detect the amplification of a specific region of genome from the change of signal intensities accurately. In this study, we use the genomic DNA of Due to the recent advances in Next-gen sequencer techniques, the use of microarray for SNP detection decreased its impact. However, still it has advantages on the simplicity of experimental procedure and low costs, and thus even though it is not used for advanced researches, it can be used for consumer application as medical device for diagnosis. Therefore, a method to overcome the disadvantages of this method, as low accuracy and high false positive rate, is desirable, and we expect that our study contributes the improvement of the microarray-based SNP detection. We anticipate that our method will improve the detection performance of single-nucleotide substitution in tiling microarray data.