Effect of Blood Flow on Hemoglobin and Myoglobin Oxygenation in Contracting Muscle Using Near-Infrared Spectroscopy

Insufficient O₂ delivery to, and uptake by skeletal muscle can produce mobility limitations for patients with chronic diseases. Near-infrared spectroscopy (NIRS) can be used to noninvasively quantify the balance between skeletal muscle O₂ delivery and utilization during contraction. However, it is not clear how the oxygenated or deoxygenated NIRS signal should be used to assess muscle O₂ changes. This issue is related to the fact that the contributions of hemoglobin (Hb) and myoglobin (Mb) cannot be distinguished. This conundrum can be resolved by quantitative analysis of experimental data by computer simulations with a mechanistic, mathematical model. Model simulations distinguish dynamic responses of the oxygenated (HbO₂, MbO₂) and deoxygenated (HHb, HMb) contributions to the NIRS signal components (HbMbO₂, HHbMb). Simulations of muscle O₂ uptake and NIRS kinetics correspond closely to published experimental data (Hernández et al., J Appl Physiol 108: 1169-1176, 2010). Simulated muscle O₂ uptake and oxygenation kinetics with different blood flows indicate (1) faster O₂ delivery is responsible for slower muscle oxygenation kinetics; (2) Hb and Mb contributions to the HbMbO₂ are similar (40-60%); and (3) Hb and Mb contributions to the HHbMb are significantly different, 80% and 20%, respectively. The effect of slow blood flow kinetics on oxygenated Hb and Mb contributions is minimal. However, the effect on the imbalance between O₂ delivery and utilization rates causes significant overshoots and undershoots of deoxygenated Hb and Mb contributions. Model analysis in combination with NIRS measurements and information on hemodynamic and microvascular distribution can help to determine the use of NIRS signal in evaluating the factors limiting exercise tolerance in health and disease states.

Soil mobility of synthetic and virus-based model nanopesticides

Large doses of chemical pesticides are required to achieve effective concentrations in the rhizosphere, which results in the accumulation of harmful residues. Precision farming is needed to improve the efficacy of pesticides, but also to avoid environmental pollution, and slow-release formulations based on nanoparticles offer one solution. Here, we tested the mobility of synthetic and virus-based model nanopesticides by combining soil column experiments with computational modelling. We found that the tobacco mild green mosaic virus and cowpea mosaic virus penetrate soil to a depth of at least 30 cm, and could therefore deliver nematicides to the rhizosphere, whereas the Physalis mosaic virus remains in the first 4 cm of soil and would be more useful for the delivery of herbicides. Our experiments confirm that plant viruses are superior to synthetic mesoporous silica nanoparticles and poly(lactic-co-glycolic acid) for the delivery and controlled release of pesticides, and could be developed as the next generation of pesticide delivery systems.

Whole-body iron transport and metabolism: Mechanistic, multi-scale model to improve treatment of anemia in chronic kidney disease

Iron plays vital roles in the human body including enzymatic processes, oxygen-transport via hemoglobin and immune response. Iron metabolism is characterized by ~95% recycling and minor replenishment through diet. Anemia of chronic kidney disease (CKD) is characterized by a lack of synthesis of erythropoietin leading to reduced red blood cell (RBC) formation and aberrant iron recycling. Treatment of CKD anemia aims to normalize RBC count and serum hemoglobin. Clinically, the various fluxes of iron transport and accumulation are not measured so that changes during disease (e.g., CKD) and treatment are unknown. Unwanted iron accumulation in patients is known to lead to adverse effects. Current whole-body models lack the mechanistic details of iron transport related to RBC maturation, transferrin (Tf and TfR) dynamics and assume passive iron efflux from macrophages. Hence, they are not predictive of whole-body iron dynamics and cannot be used to design individualized patient treatment. For prediction, we developed a mechanistic, multi-scale computational model of whole-body iron metabolism incorporating four compartments containing major pools of iron and RBC generation process. The model accounts for multiple forms of iron in vivo, mechanisms involved in iron uptake and release and their regulation. Furthermore, the model is interfaced with drug pharmacokinetics to allow simulation of treatment dynamics. We calibrated our model with experimental and clinical data from peer-reviewed literature to reliably simulate CKD anemia and the effects of current treatment involving combination of epoietin-alpha and iron dextran. This in silico whole-body model of iron metabolism predicts that a year of treatment can potentially lead to 90% downregulation of ferroportin (FPN) levels, 15-fold increase in iron stores with only a 20% increase in iron flux from the reticulo-endothelial system (RES). Model simulations quantified unmeasured iron fluxes, previously unknown effects of treatment on FPN-level and iron stores in the RES. This mechanistic whole-body model can be the basis for future studies that incorporate iron metabolism together with related clinical experiments. Such an approach could pave the way for development of effective personalized treatment of CKD anemia.

Diffusion and Uptake of Tobacco Mosaic Virus as Therapeutic Carrier in Tumor Tissue: Effect of Nanoparticle Aspect Ratio

Nanoparticle-based technologies, including platforms derived from plant viruses, hold great promise for targeting and delivering cancer therapeutics to solid tumors by overcoming dose-limiting toxicities associated with chemotherapies. A growing body of data indicates advantageous margination and penetration properties of high aspect-ratio nanoparticles, which enhance payload delivery, resulting in increased efficacy. Our lab has demonstrated that elongated rod-shaped and filamentous macromolecular nucleoprotein assemblies from plant viruses have higher tissue diffusion rates than spherical particles. In this study, we developed a mathematical model to quantify diffusion and uptake of tobacco mosaic virus (TMV) in a spheroid system approximating a capillary-free segment of a solid tumor. Model simulations predict TMV concentration distribution with time in a tumor spheroid for different sizes and cell densities. From simulations of TMV concentration distribution, we can quantify the effect of TMV aspect ratio (e.g., nanorod length-to-width) with and without cellular uptake by modulated surface chemistry. This theoretical analysis can be applied to other viral or nonviral delivery systems to complement the experimental development of the next generation of nanotherapeutics.

Relating tissue/organ energy expenditure to metabolic fluxes in mouse and human: experimental data integrated with mathematical modeling

Mouse models of human diseases are used to study the metabolic and physiological processes leading to altered whole-body energy expenditure (EE), which is the sum of EE of all body organs and tissues. Isotopic techniques, arterio-venous difference of substrates, oxygen, and blood flow measurements can provide essential information to quantify tissue/organ EE and substrate oxidation. To complement and integrate experimental data, quantitative mathematical model analyses have been applied in the design of experiments and evaluation of metabolic fluxes. In this study, a method is presented to quantify the energy expenditure of the main mouse organs using metabolic flux measurements. The metabolic fluxes and substrate utilization of the main metabolic pathways of energy metabolism in the mouse tissue/organ systems and the whole body are quantified using a mathematical model based on mass and energy balances. The model is composed of six organ/tissue compartments: brain, heart, liver, gastrointestinal tract, muscle, and adipose tissue. Each tissue/organ is described with a distinct system of metabolic reactions. This model quantifies metabolic and energetic characteristics of mice under overnight fasting conditions. The steady-state mass balances of metabolites and energy balances of carbohydrate and fat are integrated with available experimental data to calculate metabolic fluxes, substrate utilization, and oxygen consumption in each tissue/organ. The model serves as a paradigm for designing experiments with the minimal reliable measurements necessary to quantify tissue/organs fluxes and to quantify the contributions of tissue/organ EE to whole-body EE that cannot be easily determined currently.

Mathematical modelling of glycosaminoglycan production by stem cell aggregates incorporated with growth factor-releasing polymer microspheres

Systems composed of high density cells incorporated with growth factor-releasing polymer microspheres have recently been shown to promote chondrogenic differentiation and cartilage formation. Within these systems, the effects of spatial and temporal patterning of growth factor release on hyaline cartilage-specific extracellular matrix production have been examined. However, at present, it is unclear which microsphere densities and growth factor delivery profiles are optimal for inducing human mesenchymal stem cell differentiation and glycosaminoglycan production. A mathematical model to describe glycosaminoglycan production as a function of initial microsphere loading and microsphere degradation rate over a period of 3 weeks is presented. Based on predictions generated by this model, it may be feasible to design a bioactive microsphere system with specific spatiotemporal growth factor presentation characteristics to promote glycosaminoglycan production at controllable rates. Copyright © 2014 John Wiley & Sons, Ltd.

Computational modeling and analysis of iron release from macrophages

A major process of iron homeostasis in whole-body iron metabolism is the release of iron from the macrophages of the reticuloendothelial system. Macrophages recognize and phagocytose senescent or damaged erythrocytes. Then, they process the heme iron, which is returned to the circulation for reutilization by red blood cell precursors during erythropoiesis. The amount of iron released, compared to the amount shunted for storage as ferritin, is greater during iron deficiency. A currently accepted model of iron release assumes a passive-gradient with free diffusion of intracellular labile iron (Fe2+) through ferroportin (FPN), the transporter on the plasma membrane. Outside the cell, a multi-copper ferroxidase, ceruloplasmin (Cp), oxidizes ferrous to ferric ion. Apo-transferrin (Tf), the primary carrier of soluble iron in the plasma, binds ferric ion to form mono-ferric and di-ferric transferrin. According to the passive-gradient model, the removal of ferrous ion from the site of release sustains the gradient that maintains the iron release. Subcellular localization of FPN, however, indicates that the role of FPN may be more complex. By experiments and mathematical modeling, we have investigated the detailed mechanism of iron release from macrophages focusing on the roles of the Cp, FPN and apo-Tf. The passive-gradient model is quantitatively analyzed using a mathematical model for the first time. A comparison of experimental data with model simulations shows that the passive-gradient model cannot explain macrophage iron release. However, a facilitated-transport model associated with FPN can explain the iron release mechanism. According to the facilitated-transport model, intracellular FPN carries labile iron to the macrophage membrane. Extracellular Cp accelerates the oxidation of ferrous ion bound to FPN. Apo-Tf in the extracellular environment binds to the oxidized ferrous ion, completing the release process. Facilitated-transport model can correctly predict cellular iron efflux and is essential for physiologically relevant whole-body model of iron metabolism.

Mechanistic, mathematical model to predict the dynamics of tissue genesis in bone defects via mechanical feedback and mediation of biochemical factors

The link between mechanics and biology in the generation and the adaptation of bone has been well studied in context of skeletal development and fracture healing. Yet, the prediction of tissue genesis within - and the spatiotemporal healing of - postnatal defects, necessitates a quantitative evaluation of mechano-biological interactions using experimental and clinical parameters. To address this current gap in knowledge, this study aims to develop a mechanistic mathematical model of tissue genesis using bone morphogenetic protein (BMP) to represent of a class of factors that may coordinate bone healing. Specifically, we developed a mechanistic, mathematical model to predict the dynamics of tissue genesis by periosteal progenitor cells within a long bone defect surrounded by periosteum and stabilized via an intramedullary nail. The emergent material properties and mechanical environment associated with nascent tissue genesis influence the strain stimulus sensed by progenitor cells within the periosteum. Using a mechanical finite element model, periosteal surface strains are predicted as a function of emergent, nascent tissue properties. Strains are then input to a mechanistic mathematical model, where mechanical regulation of BMP-2 production mediates rates of cellular proliferation, differentiation and tissue production, to predict healing outcomes. A parametric approach enables the spatial and temporal prediction of endochondral tissue regeneration, assessed as areas of cartilage and mineralized bone, as functions of radial distance from the periosteum and time. Comparing model results to histological outcomes from two previous studies of periosteum-mediated bone regeneration in a common ovine model, it was shown that mechanistic models incorporating mechanical feedback successfully predict patterns (spatial) and trends (temporal) of bone tissue regeneration. The novel model framework presented here integrates a mechanistic feedback system based on the mechanosensitivity of periosteal progenitor cells, which allows for modeling and prediction of tissue regeneration on multiple length and time scales. Through combination of computational, physical and engineering science approaches, the model platform provides a means to test new hypotheses in silico and to elucidate conditions conducive to endogenous tissue genesis. Next generation models will serve to unravel intrinsic differences in bone genesis by endochondral and intramembranous mechanisms.

Arising as a consequence of trauma, tumor resection, removal of necrotic or infected tissue, and congenital abnormalities, critical-sized defects are too large to heal spontaneously and therefore require surgical intervention. New surgical approaches harness the regenerative power of the periosteum, a tissue membrane covering most bones, which provides a niche for stem cells and plays a key role in healing after injury. The interplay of mechanical, cellular and biochemical mechanisms involved in periosteum-mediated tissue genesis and healing remains elusive, providing the impetus for the current study. Here, we develop a mechanistic, mathematical model to predict the dynamics of tissue genesis by periosteum-derived stem cells within a bone defect surrounded by periosteum or a periosteum substitute. A mechanical finite element model is coupled with a model of cellular dynamics to simulate a tested clinical scenario in which the patient's own periosteum is left around the defect after injury. Model predictions incorporating mechanical feedback match spatiotemporal patterns of bone tissue regeneration observed in a series of in vivo ovine experiments. Through combination of computational, physical and engineering science approaches, the model platform provides a means to test new hypotheses in silico. This will provide criteria conducive to endogenous tissue genesis that can be tested in follow on experiments.

Distinguishing the effects of convective and diffusive O₂ delivery on VO₂ on-kinetics in skeletal muscle contracting at moderate intensity

With current techniques, experimental measurements alone cannot characterize the effects of oxygen blood-tissue diffusion on muscle oxygen uptake (Vo₂) kinetics in contracting skeletal muscle. To complement experimental studies, a computational model is used to quantitatively distinguish the contributions of convective oxygen delivery, diffusion into cells, and oxygen utilization to Vo₂ kinetics. The model is validated using previously published experimental Vo₂ kinetics in response to slowed blood flow (Q) on-kinetics in canine muscle (τQ = 20 s, 46 s, and 64 s) [Goodwin ML, Hernández A, Lai N, Cabrera ME, Gladden LB. J Appl Physiol. 112:9-19, 2012]. Distinctive effects of permeability-surface area or diffusive conductance (PS) and Q on Vo₂ kinetics are investigated. Model simulations quantify the relationship between PS and Q, as well as the effects of diffusion associated with PS and Q dynamics on the mean response time of Vo₂. The model indicates that PS and Q are linearly related and that PS increases more with Q when convective delivery is limited by slower Q dynamics. Simulations predict that neither oxygen convective nor diffusive delivery are limiting Vo₂ kinetics in the isolated canine gastrocnemius preparation under normal spontaneous conditions during transitions from rest to moderate (submaximal) energy demand, although both operate close to the tipping point.

Model analysis of the relationship between intracellular PO2 and energy demand in skeletal muscle

On the basis of experimental studies, the intracellular O(2) (iPo(2))-work rate (WR) relationship in skeletal muscle is not unique. One study found that iPo(2) reached a plateau at 60% of maximal WR, while another found that iPo(2) decreased linearly at higher WR, inferring capillary permeability-surface area (PS) and blood-tissue O(2) gradient, respectively, as alternative dominant factors for determining O(2) diffusion changes during exercise. This relationship is affected by several factors, including O(2) delivery and oxidative and glycolytic capacities of the muscle. In this study, these factors are examined using a mechanistic, mathematical model to analyze experimental data from contracting skeletal muscle and predict the effects of muscle contraction on O(2) transport, glycogenolysis, and iPo(2). The model describes convection, O(2) diffusion, and cellular metabolism, including anaerobic glycogenolysis. Consequently, the model simulates iPo(2) in response to muscle contraction under a variety of experimental conditions. The model was validated by comparison of simulations of O(2) uptake with corresponding experimental responses of electrically stimulated canine muscle under different O(2) content, blood flow, and contraction intensities. The model allows hypothetical variation of PS, glycogenolytic capacity, and blood flow and predictions of the distinctive effects of these factors on the iPo(2)-contraction intensity relationship in canine muscle. Although PS is the main factor regulating O(2) diffusion rate, model simulations indicate that PS and O(2) gradient have essential roles, depending on the specific conditions. Furthermore, the model predicts that different convection and diffusion patterns and metabolic factors may be responsible for different iPo(2)-WR relationships in humans.

Coding region polyadenylation generates a truncated tRNA synthetase that counters translation repression

Posttranscriptional regulatory mechanisms superimpose "fine-tuning" control upon "on-off" switches characteristic of gene transcription. We have exploited computational modeling with experimental validation to resolve an anomalous relationship between mRNA expression and protein synthesis. The GAIT (gamma-interferon-activated inhibitor of translation) complex repressed VEGF-A synthesis to a low, constant rate independent of VEGF-A mRNA expression levels. Dynamic model simulations predicted an inhibitory GAIT-element-interacting factor to account for this relationship and led to the identification of a truncated form of glutamyl-prolyl tRNA synthetase (EPRS), a GAIT constituent that mediates binding to target transcripts. The truncated protein, EPRS(N1), shields GAIT-element-bearing transcripts from the inhibitory GAIT complex, thereby dictating a "translational trickle" of GAIT target proteins. EPRS(N1) mRNA is generated by polyadenylation-directed conversion of a Tyr codon in the EPRS-coding sequence to a stop codon (PAY(∗)). Genome-wide analysis revealed multiple candidate PAY(∗) targets, including the authenticated target RRM1, suggesting a general mechanism for production of C terminus-truncated regulatory proteins.

Computational Model of Cellular Metabolic Dynamics in Skeletal Muscle Fibers during Moderate Intensity Exercise

Human skeletal muscles have different fiber types with distinct metabolic functions and physiological properties. The quantitative metabolic responses of muscle fibers to exercise provide essential information for understanding and modifying the regulatory mechanisms of skeletal muscle. Since in vivo data from skeletal muscle during exercise is limited, a computational, physiologically based model has been developed to quantify the dynamic metabolic responses of many key chemical species. This model distinguishes type I and II muscle fibers, which share the same blood supply. An underlying hypothesis is that the recruitment and metabolic activation of the two main types of muscle fibers differ depending on the pre-exercise state and exercise protocols. Here, activation measured by metabolic response (or enzymatic activation) in single fibers is considered linked but distinct from fiber recruitment characterized by the number (or mass) of each fiber type involved during a specific exercise. The model incorporates species transport processes between blood and muscle fibers and most of the important reactions/pathways in cytosol and mitochondria within each fiber type. Model simulations describe the dynamics of intracellular species concentrations and fluxes in muscle fibers during moderate intensity exercise according to various experimental protocols and conditions. This model is validated by comparing model simulations with experimental data in single muscle fibers and in whole muscle. Model simulations demonstrate that muscle-fiber recruitment and metabolic activation patterns in response to exercise produce significantly distinctive effects depending on the exercise conditions.

Regulation of Adipose Tissue Metabolism in Humans: Analysis of Responses to the Hyperinsulinemic-Euglycemic Clamp Experiment

The suppression of lipolysis is one of the key metabolic responses of the adipose tissue during hyperinsulinemia. The failure to respond and resulting increase in plasma fatty acids could contribute to the development of insulin resistance and perturbations in the fuel homeostasis in the whole body. In this study, a mechanistic, computational model of adipose tissue metabolism in vivo has been enhanced to simulate the physiological responses during hyperinsulinemic-euglycemic clamp experiment in humans. The model incorporates metabolic intermediates and pathways that are important in the fed state. In addition, it takes into account the heterogeneity of triose phosphate pools (glycolytic vs. glyceroneogenic), within the adipose tissue. The model can simulate not only steady-state responses at different insulin levels, but also concentration dynamics of major metabolites in the adipose tissue venous blood in accord with the in vivo data. Simulations indicate that (1) regulation of lipoprotein lipase (LPL) reaction is important when the intracellular lipolysis is suppressed by insulin; (2) intracellular diglyceride levels can affect the regulatory mechanisms; and (3) glyceroneogenesis is the dominant pathway for glycerol-3-phosphate synthesis even in the presence of increased glucose uptake by the adipose tissue. Reduced redox and increased phosphorylation states provide a favorable milieu for glyceroneogenesis in response to insulin. A parameter sensitivity analysis predicts that insulin-stimulated glucose uptake would be more severely affected by impairment of GLUT4 translocation and glycolysis than by impairment of glycogen synthesis and pyruvate oxidation. Finally, simulations predict metabolic responses to altered expression of phosphoenolpyruvate carboxykinase (PEP-CK). Specifically, the increase in the rate of re-esterification of fatty acids observed experimentally with the overexpression of PEPCK in the adipose tissue would be accompanied by the up-regulation of acyl Co-A synthase.

Modeling of laser coagulation of tissue with MRI temperature monitoring

Light energy from a laser source that is delivered into body tissue via a fiber-optic probe with minimal invasiveness has been used to ablate solid tumors. This thermal coagulation process can be guided and monitored accurately by continuous magnetic resonance imaging (MRI) since the laser energy delivery system does not interfere with MRI. This report deals with mathematical modeling and analysis of laser coagulation of tissue. This model is intended for "real-time" analysis of magnetic resonance images obtained during the coagulation process to guide clinical treatment. A mathematical model is developed to simulate the thermal response of tissue to a laser light heating source. For fast simulation, an approximate solution of the thermal model is used to predict the dynamics of temperature distribution and tissue damage induced by a laser energy line source. The validity of these simulations is tested by comparison with MRI-based temperature data acquired from in vivo experiments in rabbits. The model-simulated temperature distribution and predicted lesion dynamics correspond closely with MRI-based data. These results demonstrate the potential for using this combination of fast modeling and MRI technologies during laser heating of tissue for online prediction of tumor lesion size during laser heating.

Hemoglobin and myoglobin contributions to skeletal muscle oxygenation in response to exercise

The quantitative contributions of hemoglobin and myoglobin oxygenation in skeletal muscle depend on physiological factors, especially muscle blood flow (Q( m )) and capillary permeability-surface area (PS). Near-infrared spectroscopy (NIRS) can be used to quantify total heme oxidation, but it is unable to distinguish between hemoglobin and myoglobin. Therefore, a mechanistic computational model has been developed to distinguish the contributions of oxygenated hemoglobin and myoglobin to the total NIRS signal. Model simulations predict how Q( m ) and PS can affect oxygenated hemoglobin and myoglobin.Although both hemoglobin and myoglobin oxygenation decrease with impaired Q( m ), simulations show that myoglobin provides a greater contribution to the overall NIRS signal. A decrease of PS primarily affects myoglobin oxygenation. Based on model simulations, the contribution of myoglobin oxygenation to the total NIRS signal can be significantly different under pathophysiological conditions, such as diabetes and peripheral arterial disorder.

Computational model of cellular metabolic dynamics: effect of insulin on glucose disposal in human skeletal muscle

Identifying the mechanisms by which insulin regulates glucose metabolism in skeletal muscle is critical to understanding the etiology of insulin resistance and type 2 diabetes. Our knowledge of these mechanisms is limited by the difficulty of obtaining in vivo intracellular data. To quantitatively distinguish significant transport and metabolic mechanisms from limited experimental data, we developed a physiologically based, multiscale mathematical model of cellular metabolic dynamics in skeletal muscle. The model describes mass transport and metabolic processes including distinctive processes of the cytosol and mitochondria. The model simulated skeletal muscle metabolic responses to insulin corresponding to human hyperinsulinemic-euglycemic clamp studies. Insulin-mediated rate of glucose disposal was the primary model input. For model validation, simulations were compared with experimental data: intracellular metabolite concentrations and patterns of glucose disposal. Model variations were simulated to investigate three alternative mechanisms to explain insulin enhancements: Model 1 (M.1), simple mass action; M.2, insulin-mediated activation of key metabolic enzymes (i.e., hexokinase, glycogen synthase, pyruvate dehydrogenase); or M.3, parallel activation by a phenomenological insulin-mediated intracellular signal that modifies reaction rate coefficients. These simulations indicated that models M.1 and M.2 were not sufficient to explain the experimentally measured metabolic responses. However, by application of mechanism M.3, the model predicts metabolite concentration changes and glucose partitioning patterns consistent with experimental data. The reaction rate fluxes quantified by this detailed model of insulin/glucose metabolism provide information that can be used to evaluate the development of type 2 diabetes.

Modeling oxygenation in venous blood and skeletal muscle in response to exercise using near-infrared spectroscopy

Noninvasive, continuous measurements in vivo are commonly used to make inferences about mechanisms controlling internal and external respiration during exercise. In particular, the dynamic response of muscle oxygenation (Sm(O(2))) measured by near-infrared spectroscopy (NIRS) is assumed to be correlated to that of venous oxygen saturation (Sv(O(2))) measured invasively. However, there are situations where the dynamics of Sm(O(2)) and Sv(O(2)) do not follow the same pattern. A quantitative analysis of venous and muscle oxygenation dynamics during exercise is necessary to explain the links between different patterns observed experimentally. For this purpose, a mathematical model of oxygen transport and utilization that accounts for the relative contribution of hemoglobin (Hb) and myoglobin (Mb) to the NIRS signal was developed. This model includes changes in microvascular composition within skeletal muscle during exercise and integrates experimental data in a consistent and mechanistic manner. Three subjects (age 25.6 +/- 0.6 yr) performed square-wave moderate exercise on a cycle ergometer under normoxic and hypoxic conditions while muscle oxygenation (C(oxy)) and deoxygenation (C(deoxy)) were measured by NIRS. Under normoxia, the oxygenated Hb/Mb concentration (C(oxy)) drops rapidly at the onset of exercise and then increases monotonically. Under hypoxia, C(oxy) decreases exponentially to a steady state within approximately 2 min. In contrast, model simulations of venous oxygen concentration show an exponential decrease under both conditions due to the imbalance between oxygen delivery and consumption at the onset of exercise. Also, model simulations that distinguish the dynamic responses of oxy-and deoxygenated Hb (HbO(2), HHb) and Mb (MbO(2), HMb) concentrations (C(oxy) = HbO(2) + MbO(2); C(deoxy) = HHb + HMb) show that Hb and Mb contributions to the NIRS signal are comparable. Analysis of NIRS signal components during exercise with a mechanistic model of oxygen transport and metabolism indicates that changes in oxygenated Hb and Mb are responsible for different patterns of Sm(O(2)) and Sv(O(2)) dynamics observed under normoxia and hypoxia.

Permeability change of arterial endothelium is an age-dependent function of lesion size in apolipoprotein E-null mice

The remodeling process of the arterial wall in atherosclerosis involves intimal thickening, which can be related to the barrier functions of the endothelial cell layer (ECL) and internal elastic lamina (IEL) using horseradish peroxidase (HRP) as a tracer. To evaluate the ECL and IEL permeabilities ( PECL and PIEL, respectively) and intimal transport parameters, e.g., apparent HRP velocity ( VI) and diffusivity, we compared simulations with a mathematical model to experimental data. In this study, we injected HRP into the vein of apolipoprotein E-null mice and measured HRP concentration profiles in lesioned areas of aortas. Lesion size was characterized by lower, middle, and upper ranges of the intimal/medial thickness (δI/δM): 0 < δI/δM ≤ 0.5, 0.5 < δI/δM ≤ 1.0, and δI/δM > 1.0. The PECL (in micrometers per minute) of 5-mo-old mice in the middle range (0.98 ± 0.14) was significantly greater than that in the lower range (0.21 ± 0.03) but not significantly different from mice in the upper range (0.99 ± 0.55). The PECL of 12-mo-old mice increased significantly with the relative intimal thickness: 0.27 ± 0.04 in the lower range, 1.12 ± 0.15 in the middle range, and 1.74 ± 0.24 in the upper range. In both age groups, VI (in micrometers per minute) increased significantly from lower to upper ranges of intimal thickness. However, PIEL did not change significantly with relative intimal thickness and age. In the upper range of intimal thickness, PECL and VI were significantly greater in 12-mo-old mice than in 5-mo-old mice. These data indicate an interaction between lesion growth and aging that leads to progressive loss in the integrity of the endothelial barrier function. Furthermore, the IEL is not a significant barrier between the intima and tunica media in the atherosclerotic process.

Mathematical Modeling of Thermal Ablation in Tissue Surrounding a Large Vessel

Thermal ablation of a solid tumor in a tissue with radio-frequency (rf) energy can be accomplished by using a probe inserted into the tissue under the guidance of magnetic resonance imaging. The extent of the ablation can be significantly reduced by heat loss from capillary perfusion and by blood flow in a large vessel in the tissue. A mathematical model is presented of the thermal processes that occur during rf ablation of a tissue near a large blood vessel, which should not be damaged. Temperature distribution dynamics are described by the combination of a 3D bioheat transport in tissue together with a 1D model of convective-dispersive heat transport in the blood vessel. The objective was to determine how much of the tissue can be ablated without damaging the blood vessel. This was achieved by simulating the tissue temperature distribution dynamics and by determining the optimal power inputs so that a maximum temperature increase in the tissue was achieved without inducing tissue damage at the edge of the large vessel. The main contribution of this study is to provide a model analysis for pretreatment and, eventually, for intra-operative application to thermal ablation of a tumor located near a large blood vessel.

Drug-eluting polymer implants in cancer therapy

BACKGROUND

Drug-eluting polymer implants present a compelling parenteral route of administration for cancer chemotherapy. With potential for minimally invasive, image-guided placement and highly localized drug release, these delivery systems are playing an increasingly important role in cancer management. This is particularly true as the use of labile proteins and other bioactive molecules is likely to increase in the upcoming years.

OBJECTIVE

In this review, we present the current trends in the application of Pre-formed and in situ-forming systems as drug-eluting implants for cancer chemotherapy.

METHODS

We outline the clinically available options as well as up-and-coming technologies and their advantages and challenges. We also describe ongoing related innovations with image-guided drug delivery, mathematical modeling of implanted delivery systems and implanted drug delivery in combination with other therapies.

RESULTS/CONCLUSION

Whether used alone or combined with other minimally invasive procedures, drug-eluting polymeric implants will play a significant role in the future of cancer management.

Role of NADH/NAD+ transport activity and glycogen store on skeletal muscle energy metabolism during exercise: in silico studies

Skeletal muscle can maintain ATP concentration constant during the transition from rest to exercise, whereas metabolic reaction rates may increase substantially. Among the key regulatory factors of skeletal muscle energy metabolism during exercise, the dynamics of cytosolic and mitochondrial NADH and NAD+ have not been characterized. To quantify these regulatory factors, we have developed a physiologically based computational model of skeletal muscle energy metabolism. This model integrates transport and reaction fluxes in distinct capillary, cytosolic, and mitochondrial domains and investigates the roles of mitochondrial NADH/NAD+ transport (shuttling) activity and muscle glycogen concentration (stores) during moderate intensity exercise (60% maximal O2 consumption). The underlying hypothesis is that the cytosolic redox state (NADH/NAD+) is much more sensitive to a metabolic disturbance in contracting skeletal muscle than the mitochondrial redox state. This hypothesis was tested by simulating the dynamic metabolic responses of skeletal muscle to exercise while altering the transport rate of reducing equivalents (NADH and NAD+) between cytosol and mitochondria and muscle glycogen stores. Simulations with optimal parameter estimates showed good agreement with the available experimental data from muscle biopsies in human subjects. Compared with these simulations, a 20% increase (or approximately 20% decrease) in mitochondrial NADH/NAD+ shuttling activity led to an approximately 70% decrease (or approximately 3-fold increase) in cytosolic redox state and an approximately 35% decrease (or approximately 25% increase) in muscle lactate level. Doubling (or halving) muscle glycogen concentration resulted in an approximately 50% increase (or approximately 35% decrease) in cytosolic redox state and an approximately 30% increase (or approximately 25% decrease) in muscle lactate concentration. In both cases, changes in mitochondrial redox state were minimal. In conclusion, the model simulations of exercise response are consistent with the hypothesis that mitochondrial NADH/NAD+ shuttling activity and muscle glycogen stores affect primarily the cytosolic redox state. Furthermore, muscle lactate production is regulated primarily by the cytosolic redox state.

Metabolic dynamics in skeletal muscle during acute reduction in blood flow and oxygen supply to mitochondria: in-silico studies using a multi-scale, top-down integrated model

Control mechanisms of cellular metabolism and energetics in skeletal muscle that may become evident in response to physiological stresses such as reduction in blood flow and oxygen supply to mitochondria can be quantitatively understood using a multi-scale computational model. The analysis of dynamic responses from such a model can provide insights into mechanisms of metabolic regulation that may not be evident from experimental studies. For the purpose, a physiologically-based, multi-scale computational model of skeletal muscle cellular metabolism and energetics was developed to describe dynamic responses of key chemical species and reaction fluxes to muscle ischemia. The model, which incorporates key transport and metabolic processes and subcellular compartmentalization, is based on dynamic mass balances of 30 chemical species in both capillary blood and tissue cells (cytosol and mitochondria) domains. The reaction fluxes in cytosol and mitochondria are expressed in terms of a general phenomenological Michaelis-Menten equation involving the compartmentalized energy controller ratios ATP/ADP and NADH/NAD(+). The unknown transport and reaction parameters in the model are estimated simultaneously by minimizing the differences between available in vivo experimental data on muscle ischemia and corresponding model outputs in coupled with the resting linear flux balance constraints using a robust, nonlinear, constrained-based, reduced gradient optimization algorithm. With the optimal parameter values, the model is able to simulate dynamic responses to reduced blood flow and oxygen supply to mitochondria associated with muscle ischemia of several key metabolite concentrations and metabolic fluxes in the subcellular cytosolic and mitochondrial compartments, some that can be measured and others that can not be measured with the current experimental techniques. The model can be applied to test complex hypotheses involving dynamic regulation of cellular metabolism and energetics in skeletal muscle during physiological stresses such as ischemia, hypoxia, and exercise.

The role of Ca2+ in coupling cardiac metabolism with regulation of contraction: in silico modeling

The heart adapts the rate of mitochondrial ATP production to energy demand without noticeable changes in the concentration of ATP, ADP and Pi, even for large transitions between different workloads. We suggest that the changes in demand modulate the cytosolic Ca2+ concentration that changes mitochondrial Ca2+ to regulate ATP production. Thus, the rate of ATP production by the mitochondria is coupled to the rate of ATP consumption by the sarcomere cross-bridges (XBs). An integrated model was developed to couple cardiac metabolism and mitochondrial ATP production with the regulation of Ca2+ transient and ATP consumption by the sarcomere. The model includes two interrelated systems that run simultaneously utilizing two different integration steps: (1) The faster system describes the control of excitation contraction coupling with fast cytosolic Ca2+ transients, twitch mechanical contractions, and associated fluctuations in the mitochondrial Ca2+. (2) A slower system simulates the metabolic system, which consists of three different compartments: blood, cytosol, and mitochondria. The basic elements of the model are dynamic mass balances in the different compartments. Cytosolic Ca2+ handling is determined by four organelles: sarcolemmal Ca2+ influx and efflux; sarcoplasmic reticulum (SR) Ca2+ release and sequestration (SR); binding and dissociation from sarcomeric regulatory troponin complexes; and mitochondrial Ca2+ flows. Mitochondrial Ca2+ flows are determined by the Ca2+ uniporter and the mitochondrial Na+Ca2+ exchanger. The cytosolic Ca2+ determines the rate of ATP consumption by the sarcomere. Ca2+ binding to troponin regulates the rate of XBs recruitment and force development. The mitochondrial Ca2+ concentration determines the pyruvate dehydrogenase activity and the rate of ATP production by the F(1)-F(0) ATPase. The workload modulates the cytosolic Ca2+ concentration through feedback loops. The preload and afterload affect the number of strong XBs. The number of strong XBs determines the affinity of troponin for Ca2+, which alters the cytosolic Ca2+ transient. Model simulations quantify the role of Ca2+ in simultaneously controlling the power of contraction and the rate of ATP production. It explains the established empirical observation that significant changes in the metabolic fluxes can occur without significant changes in the key nucleotide (ATP and ADP) concentrations. Quantitative investigations of the mechanisms underlying the cardiac control of biochemical to mechanical energy conversion may lead to novel therapeutic modalities for the ischemic and failing myocardium.

Role of the malate-aspartate shuttle on the metabolic response to myocardial ischemia

The malate-aspartate (M-A) shuttle provides an important mechanism to regulate glycolysis and lactate metabolism in the heart by transferring reducing equivalents from cytosol into mitochondria. However, experimental characterization of the M-A shuttle has been incomplete because of limitations in quantifying cytosolic and mitochondrial metabolites. In this study, we developed a multi-compartment model of cardiac metabolism with detailed presentation of the M-A shuttle to quantitatively predict non-observable fluxes and metabolite concentrations under normal and ischemic conditions in vivo. Model simulations predicted that the M-A shuttle is functionally localized to a subdomain that spans the mitochondrial and cytosolic spaces. With the onset of ischemia, the M-A shuttle flux rapidly decreased to a new steady state in proportion to the reduction in blood flow. Simulation results suggest that the reduced M-A shuttle flux during ischemia was not due to changes in shuttle-associated enzymes and transporters. However, there was a redistribution of shuttle-associated metabolites in both cytosol and mitochondria. Therefore, the dramatic acceleration in glycolysis and the switch to lactate production that occur immediately after the onset of ischemia is mediated by reduced M-A shuttle flux through metabolite redistribution of shuttle associated species across the mitochondrial membrane.

Modeling cellular metabolism and energetics in skeletal muscle: large-scale parameter estimation and sensitivity analysis

Skeletal muscle plays a major role in the regulation of whole-body energy metabolism during physiological stresses such as ischemia, hypoxia, and exercise. Current experimental techniques provide relatively little in vivo data on dynamic responses of metabolite concentrations and metabolic fluxes in skeletal muscle to such physiological stimuli. As a complementary approach to experimental measurements and as a framework for quantitatively analyzing available in vivo data, a physiologically based model of skeletal muscle cellular metabolism and energetics is developed. This model, which incorporates key transport and reaction processes, is based on dynamic mass balances of 30 chemical species in capillary (blood) and tissue (cell) domains. The reaction fluxes in the cellular domain are expressed in terms of a generalized Michaelis?Menten equation involving energy controller ratios ATP/ADP and ATP/ADP and NADH/NAD+ . This formalism introduces a large number of unknown parameters ( approximately 90). Estimating these parameters from in vivo sparse data and evaluating dynamic sensitivities of the model outputs with respect to these parameters is a challenging problem. Parameter estimation is accomplished using an efficient, nonlinear, constraint-based, optimization algorithm that minimizes differences between available experimental data and corresponding model outputs by explicitly utilizing equality constraints on resting fluxes and concentrations. With the estimated parameter values, the model is able to simulate dynamic responses to reduced blood flow (ischemia) of key metabolite concentrations and metabolic fluxes, both measured and nonmeasured. A general parameter sensitivity analysis is carried out to determine and characterize the parameters having the most and least effects on the measured outputs.

Dynamics of MRI-Guided thermal ablation of VX2 tumor in paraspinal muscle of rabbits

This study combines fast magnetic resonance imaging (MRI) and model simulation of tissue thermal ablation for monitoring and predicting the dynamics of lesion size for tumor destruction. In vivo experiments were conducted using radiofrequency (RF) thermal ablation in paraspinal muscle of rabbit with a VX2 tumor. Before ablation, turbo-spin echo (TSE) images visualized the 3-D tumor (necrotic core and tumor periphery) and surrounding normal tissue. MR gradient-recalled echo (GRE) phase and magnitude images were acquired repeatedly in 3.3 s at 30-s intervals during and after thermal ablation to follow tissue temperature distribution dynamics and lesion development in tumor and surrounding normal tissue. Final lesion sizes estimated from GRE magnitude, post-ablation TSE, and stained histologic images were compared. Model simulations of temperature distribution and lesion development dynamics closely corresponded to the experimental data from MR images in tumor and normal tissue. The combined use of MR image monitoring and model simulation has the potential for improving pretreatment planning and real-time prediction of lesion-size dynamics for guidance of thermal ablation of tumors.

Model of oxygen transport and metabolism predicts effect of hyperoxia on canine muscle oxygen uptake dynamics

Previous studies have shown that increased oxygen delivery, via increased convection or arterial oxygen content, does not speed the dynamics of oxygen uptake, V̇o2m, in dog muscle electrically stimulated at a submaximal metabolic rate. However, the dynamics of transport and metabolic processes that occur within working muscle in situ is typically unavailable in this experimental setting. To investigate factors affecting V̇o2m dynamics at contraction onset, we combined dynamic experimental data across working muscle with a mechanistic model of oxygen transport and metabolism in muscle. The model is based on dynamic mass balances for O2, ATP, and PCr. Model equations account for changes in cellular ATPase, oxidative phosphorylation, and creatine kinase fluxes in skeletal muscle during exercise, and cellular respiration depends on [ADP] and [O2]. Model simulations were conducted at different levels of arterial oxygen content and blood flow to quantify the effects of convection and diffusion of oxygen on the regulation of cellular respiration during step transitions from rest to isometric contraction in dog gastrocnemius muscle. Simulations of arteriovenous O2 differences and V̇o2m dynamics were successfully compared with experimental data (Grassi B, Gladden LB, Samaja M, Stary CM, Hogan MC. J Appl Physiol 85: 1394–1403, 1998; and Grassi B, Gladden LB, Stary CM, Wagner PD, Hogan MC. J Appl Physiol 85: 1404–1412, 1998), thus demonstrating the validity of the model, as well as its predictive capability. The main findings of this study are: 1) the estimated dynamic response of oxygen utilization at contraction onset in muscle is faster than that of oxygen uptake; and 2) hyperoxia does not accelerate the dynamics of diffusion and consequently muscle oxygen uptake at contraction onset due to the hyperoxia-induced increase in oxygen stores. These in silico derived results cannot be obtained from experimental observations alone.

Modeling doxorubicin transport to improve intratumoral drug delivery to RF ablated tumors

A mathematical model of drug transport provides an ideal strategy to optimize intratumoral drug delivery implants to supplement radiofrequency (RF) ablation for tumor treatment. To simulate doxorubicin transport in non-ablated and ablated liver tumors, a one-dimensional, cylindrically symmetric transport model was generated using a finite element method (FEM). Parameters of this model, the diffusion (D) and elimination (gamma) coefficients for doxorubicin, were estimated using drug distributions measured 4 and 8 days after placing biodegradable implants in non-ablated and ablated rabbit VX2 liver carcinomas. In non-ablated tumor, values of diffusion and elimination parameters were 25% and 94% lower than normal liver tissue, respectively. In ablated tumor, diffusion near the ablation center was 75% higher than non-ablated tumor but decreased to the non-ablated tumor value at the ablation periphery. Drug elimination in ablated tumor was zero for the first four days, but by day 8 returned to 98% of the value for non-ablated tumor. Three-dimensional (3-D) simulations of drug delivery from implants with and without RF thermal ablation underscore the benefit of using RF ablation to facilitate local drug distribution. This study demonstrates the use of computational modeling and optimal parameter estimation to predict local drug pharmacokinetics from intratumoral implants after ablation.

A mechanistic model of controlled drug release from polymer millirods: Effects of excipients and complex binding

The incorporation of different cyclodextrin (CD) excipients such as HPbeta-CD, beta-CD, gamma-CD or alpha-CD into polymer millirods for complexing beta-lapachone (beta-lap), a potent anti-cancer drug, significantly improved the drug release kinetics with various drug release patterns. However, such a complex system requires a mechanistically based model in order to provide a quantitative understanding of the many molecular events and processes that are essential for the rational development of millirod implants. This study focuses on mathematical modeling of drug release from PLGA cylindrical millirods. This millirod system incorporates multiple components: a PLGA matrix; excipient in free and complex forms; drug in free, bound, and crystalline forms. The model characterizes many dynamic transport and complexation processes that include radial diffusion, excipient complexation and crystalline drug dissolution. Optimal estimates of the model parameters were obtained by minimizing the difference between model simulation and experimentally measured drug release kinetics. The effects of different drug loadings on the drug release rate were simulated and compared with other data to validate this model. Whereas our model can simulate all the experimental data, the Higuchi model can simulate only some of them. Furthermore, our model incorporates mechanisms by which the processes underlying drug release from a polymer matrix can be quantitatively analyzed. These processes include drug entrapment/dissolution in the matrix, drug recrysallization, and supersaturation. This modeling study shows that complex binding capacity, which affects drug initial conditions, drug-polymer interactions, and bound drug behavior in aqueous solution, is crucial in controlling drug release kinetics.

Validity of model approximations for receptor-ligand kinetics in nuclear medicine

An appropriate mathematical model is required for quantitative analysis of high affinity radioligands as direct or surrogate probes to measure receptor distribution, affinity, concentration, binding potential, and endogenous or exogenous ligand occupancy levels. For studies with positron emission tomography (PET) or single photon emission computed tomography (SPECT), the receptor-ligand compartment model has been well established and widely used. This pharmacokinetic model is represented mathematically by a set of nonlinear ordinary differential equations. Variations of models for PET and SPECT account for radioactive decay differently. These are not equivalent and entail assumptions or approximations that may be not appreciated. In this study, a general form of the model is presented and compared with others with various approximations, which are valid only under specific conditions. The various approximate formulations were analytically compared to the exact model to identify the terms that were neglected in the approximate formulations. The extent to which the approximations impact the model solutions was assessed by computer simulations based on numerical solutions to each set of equations. Specifically, each model formulation was tested using three simulated injection protocols representing a typical PET experiment, a typical SPECT experiment, and an extreme experiment where both the injected activity and the specific activity were very high. No significant differences were found among the output of the three model formulations when the PET and SPECT injection protocols were tested. The only conditions that produced significant differences occurred when the specific activity and the administered activity were simultaneously very high. These conditions, however, have little practical relevance to experimentally achievable conditions due to radiation dose and specific activity of radiopharmaceuticals

MRI-guided Thermal Ablation Therapy: Model and Parameter Estimates to Predict Cell Death from MR Thermometry Images

Solid tumors and other pathologies can be treated using laser thermal ablation under interventional magnetic resonance imaging (iMRI) guidance. A model was developed to predict cell death from magnetic resonance (MR) thermometry measurements based on the temperature-time history, and validated using in vivo rabbit brain data. To align post-ablation T2-weighted spin-echo MR lesion images to gradient-echo MR images, from which temperature is derived, a registration method was used that aligned fiducials placed near the thermal lesion. The outer boundary of the hyperintense rim in the post-ablation MR lesion image was used as the boundary for cell death, as verified from histology. Model parameters were simultaneously estimated using an iterative optimization algorithm applied to every interesting voxel in 328 images from multiple experiments having various temperature histories. For a necrotic region of 766 voxels across all lesions, the model provided a voxel specificity and sensitivity of 98.1 and 78.5%, respectively. Mislabeled voxels were typically within one voxel from the segmented necrotic boundary with median distances of 0.77 and 0.22 mm for false positives (FP) and false negatives (FN), respectively. As compared to the critical temperature cell death model and the generalized Arrhenius model, our model typically predicted fewer FP and FN. This is good evidence that iMRI temperature maps can be used with our model to predict therapeutic regions in real-time during treatment.

Linking pulmonary oxygen uptake, muscle oxygen utilization and cellular metabolism during exercise

The energy demand imposed by physical exercise on the components of the oxygen transport and utilization system requires a close link between cellular and external respiration in order to maintain ATP homeostasis. Invasive and non-invasive experimental approaches have been used to elucidate mechanisms regulating the balance between oxygen supply and consumption during exercise. Such approaches suggest that the mechanism controlling the various subsystems coupling internal to external respiration are part of a highly redundant and hierarchical multi-scale system. In this work, we present a "systems biology" framework that integrates experimental and theoretical approaches able to provide simultaneously reliable information on the oxygen transport and utilization processes occurring at the various steps in the pathway of oxygen from air to mitochondria, particularly at the onset of exercise. This multi-disciplinary framework provides insights into the relationship between cellular oxygen consumption derived from measurements of muscle oxygenation during exercise and pulmonary oxygen uptake by indirect calorimetry. With a validated model, muscle oxygen dynamic responses is simulated and quantitatively related to cellular metabolism under a variety of conditions.

Robust experiment design for estimating myocardial beta adrenergic receptor concentration using PET

Myocardial beta adrenergic receptor (beta-AR) concentration can substantially decrease in congestive heart failure and significantly increase in chronic volume overload, such as in severe aortic valve regurgitation. Positron emission tomography (PET) with an appropriate ligand-receptor model can be used for noninvasive estimation of myocardial beta-AR concentration in vivo. An optimal design of the experiment protocol, however, is needed for sufficiently precise estimates of beta-AR concentration in a heterogeneous population. Standard methods of optimal design do not account for a heterogeneous population with a wide range of beta-AR concentrations and other physiological parameters and consequently are inadequate. To address this, we have developed a methodology to design a robust two-injection protocol that provides reliable estimates of myocardial beta-AR concentration in normal and pathologic states. A two-injection protocol of the high affinity beta-AR antagonist [18F]-(S)-fluorocarazolol was designed based on a computer-generated (or synthetic) population incorporating a wide range of beta-AR concentrations. Timing and dosage of the ligand injections were optimally designed with minimax criterion to provide the least bad beta-AR estimates for the worst case in the synthetic population. This robust experiment design for PET was applied to experiments with pigs before and after beta-AR upregulation by chemical sympathectomy. Estimates of beta-AR concentration were found by minimizing the difference between the model-predicted and experimental PET data. With this robust protocol, estimates of beta-AR concentration showed high precision in both normal and pathologic states. The increase in beta-AR concentration after sympathectomy predicted noninvasively with PET is consistent with the increase shown by in vitro assays in pig myocardium. A robust experiment protocol was designed for PET that yields reliable estimates of beta-AR concentration in a population with normal and pathologic states. This methodology is applicable in general to optimal estimation of parameters in heterogeneous populations.

MRI-guided laser thermal ablation: model to predict cell death from MR thermometry images for real-time therapy monitoring

Solid tumors and other pathologies can be treated using laser thermal ablation under interventional magnetic resonance imaging (iMRI) guidance. We developed a model to predict cell death from MR thermometry measurements and applied it to in vivo rabbit brain data. To align post-ablation T2-weighted spin-echo MR lesion images to gradient echo MR images, from which temperature is derived, we used a registration method that aligned fiducials placed near the thermal lesion. We used the outer boundary of the hyperintense rim in the post-ablation MR lesion image as the boundary for cell death, as verified from histology. Model parameters were simultaneously estimated using an iterative optimization algorithm applied to every interesting pixel in 328 images from multiple experiments having various temperature histories. For a necrotic region of 766 voxels across all lesions, the model gave a voxel specificity and sensitivity of 98.1% and 78.4%, respectively. Median distance between the segmented necrotic boundary and the mislabeled voxels was within one MR voxel. Furthermore, our model predicted fewer errors as compared to the critical temperature cell death model. This is good evidence that iMRI temperature maps can be used with our model to predict therapeutic regions in real-time.

Magnetic resonance imaging and model prediction for thermal ablation of tissue

PURPOSE

To monitor and predict tissue temperature distributions and lesion boundaries during thermal ablation by combining MRI and thermal modeling methods.

MATERIALS AND METHODS

Radiofrequency (RF) ablation was conducted in the paraspinal muscles of rabbits with MRI monitoring. A gradient-recalled echo (GRE) sequence via a 1.5T MRI system provided tissue temperature distribution from the phase images and lesion progression from changes in magnitude images. Post-ablation GRE estimates of lesion size were compared with post-ablation T2-weighted turbo-spin-echo (TSE) images and hematoxylin and eosin (H&E)-stained histological slices. A three-dimensional (3D) thermal model was used to simulate and predict tissue temperature and lesion size dynamics.

RESULTS

The lesion area estimated from repeated GRE images remained constant during the post-heating period when the temperature of the lesion boundary was less than a critical temperature. The final lesion areas estimated from multi-slice (M/S) GRE, TSE, and histological slices were not statistically different. The model-simulated tissue temperature distribution and lesion area closely corresponded to the GRE-based MR measurements throughout the imaging experiment.

CONCLUSION

For normal tissue in vivo, the dynamics of tissue temperature distribution and lesion size during RF thermal ablation can be 1) monitored with GRE phase and magnitude images, and 2) simulated for prediction with a thermal model.

Multi-organ system model of O2 and CO2 transport during isocapnic and poikilocapnic hypoxia

A multi-organ systems model of O(2) and CO(2) transport is developed to analyze the control of ventilation and blood flow during hypoxia. Among the aspects of the control processes that this model addressed are possible mechanisms responsible for the second phase of the ventilatory hypoxic response to mild hypoxia, i.e., hypoxic ventilatory decline (HVD). Species mass transport processes are described by compartmental mass balances in brain, heart, skeletal muscle, and "other tissues" connected in parallel via the circulation. In pulmonary and systemic capillaries and in the vasculature connecting the systemic tissues, species transport processes are represented by a one-dimensional, convection-dispersion model. The effects of bicarbonate acid-base buffering, hemoglobin, and myoglobin on the transport processes are included. The model incorporates feedback control mechanisms through a cardiorespiratory control system in which peripheral and central chemoreceptors sense O(2) and CO(2) partial pressures. Model simulations of the ventilatory responses to isocapnic and poikilocapnic hypoxia show two phases with distinct dynamics. A fast phase is discernable immediately after switching from normoxic to hypoxic conditions, while a delayed slow phase (HVD) typically becomes manifested after several minutes. Model simulations allow quantitative evaluation of several proposed mechanisms to account for HVD. Under isocapnic hypoxia, simulations indicate that an increase in brain blood flow has no effect on HVD, but that HVD can be entirely described by central ventilatory depression (CVD). Under poikilocapnic hypoxia, the hypocapnia caused by hypoxic hyperventilation has no effect on HVD.

Multi-scale computational model of fuel homeostasis during exercise: effect of hormonal control

A mathematical model of the whole-body metabolism is developed to predict fuel homeostasis during exercise by using hormonal control over cellular metabolic processes. The whole body model is composed of seven tissue compartments: brain, heart, liver, GI (gastrointestinal) tract, skeletal muscle, adipose tissue, and "other tissues". Each tissue compartment is described by dynamic mass balances and major cellular metabolic reactions. The glucagon-insulin controller is incorporated into the whole body model to predict hormonal changes during exercise. Moderate [150 W power output at 60% of peak oxygen consumption (VO(2max))] exercise for 60 min was implemented by increasing ATP utilization rates in heart and skeletal muscle. Arterial epinephrine level was given as an input function, which directly affects heart and skeletal muscle metabolism and indirectly other tissues via glucagon-insulin controller. Model simulations were validated with experimental data from human exercise studies. The exercise induced changes in hormonal signals modulated metabolic flux rates of different tissues in a coordinated way to achieve glucose homeostasis, demonstrating the efficacy of hormonal control over cellular metabolic processes. From experimental measurements of whole body glucose balance and arterial substrate concentrations, this model could predict the dynamic changes of hepatic glycogenolysis and gluconeogenesis, which are not easy to measure experimentally, suggesting the higher contribution of glycogenolysis ( approximately 75%). In addition, it could provide dynamic information on the relative contribution of carbohydrates and lipids for fuel oxidation in skeletal muscle. Model simulations indicate that external fuel supplies from other tissue/organ systems to skeletal muscle become important for prolonged exercise emphasizing the significance of interaction among tissues. In conclusion, this model can be used as a valuable complement to experimental studies due to its ability to predict what is difficult to measure directly, and usefulness to provide information about dynamic behaviors.

Effects of Synchronized Cardiac Assist Device on Cardiac Energetics

A novel physiological cardiac assist device (PCAD), the LEV RAM assist device, which is synchronized with the failing heart ejection, was developed to improve the failing heart systolic and diastolic functions and cardiac energetics. The PCAD uses a single short cannula, which is inserted into the beating left ventricle (LV) by means of a specially designed device. Blood is ejected from the PCAD into the LV after the opening of the aortic valve and augments the cardiac stroke work. The same amount of blood is withdrawn from the LV into the PCAD, through the same cannula, during the diastole. The study aims to test the effects of the PCAD on cardiac energetics and coronary blood flow. Adult normal sheep were anesthetized and the heart was exposed by left thoracotomy. Pressures transducers (Millar Instruments, Inc., Houston, TX) were inserted into the LV and aorta. LV volume was measured by sonocrystals (Sonometrics Corp., London, Ontario, Canada) and impedance catheter (CD Lycom, Argonstrat 116 Zoetermeer, 2718 SP The Netherlands). Flowmeters (transonic) measured the cardiac output (CO) and the coronary arteries (left anterior descending (LAD) and circumflex) flows. A thin cannula was inserted into the coronary sinus and the oxygen content of the LV and the coronary sinus were determined (AVOXimeter-1000). Pressure-volume loops, myocardial energetics, and coronary flow were measured. The displaced PCAD volume was 11 mL. Four different levels of assist were studied by changing the frequency of the assist: (1) assist beat after three successive regular beats [1:4], (2) assist every third beat [1:3], (3) alternate assist and normal beat [1:2], and (4) continuous assist [1:1]. Cardiac output (CO) and stroke volume (SV) increased proportionally with increasing frequency of assist. Systolic mechanical efficiency of the PCAD was above 90%. Simultaneously, the PCAD decreased the end-diastolic volume (EDV; diastolic unloading). The PCAD increased coronary flow and decreased cardiac arterial-venous O(2) difference. We conclude that the PCAD efficiently augments CO and stroke work, decreases preload, and decreases the coronary arterial-venous O(2) difference; all these may expedite cardiac reverse remodeling, and promote recovery of function and eventual easy explanation of the device.

Computational model of glucose homeostasis during exercise

A mathematical model of whole-body metabolism is developed to predict glucose homeostasis during exercise by using a hormonal controller over cellular metabolic processes. Model simulations were validated with experimental data from exercise studies in humans. The exercise-induced changes in hormonal signals modulated metabolic flux rates of various tissues in a coordinated way to maintain blood glucose constant. This study demonstrates the efficacy of a multi-tissue controller to accomplish blood glucose homeostasis by integrating the outputs of tissues under hormonal control. In conclusion, this model can be used as a valuable complement to experimental studies due to its ability to predict what is difficult to measure directly and to provide dynamic information about the system.

Macromolecular Transport in the Arterial Wall: Alternative Models for Estimating Barriers

Early atherosclerosis, or atherogenesis, is characterized by the abnormal accumulation of plasma-borne macromolecules (e.g., LDL) in the arterial intima. The change of barrier characteristics of tissue in the arterial wall requires evaluation of macromolecular transport across the endothelial cell layer (ECL) and internal elastic lamina (IEL), the luminal and abluminal boundaries of the arterial intima, respectively. In this study, alternative mathematical models are derived from dynamic mass balances to describe macromolecular transport across the arterial wall. One model considers each medial layer as a spatially lumped compartment, whereas another model consists of a spatially lumped intima and spatially distributed media. Model simulations of a tracer concentration distribution in the arterial wall are compared with concentration distributions of horseradish peroxidase (HRP) after i.v. injection in mice. For each model, optimal parameter values are obtained that yield model outputs matching the data well for two different HRP circulation times. The model parameter estimates show that the ECL is the major barrier for macromolecular transport across the normal arterial wall. Sensitivity analysis indicates that the parameter estimates of the transport coefficients of the ECL and IEL are well determined. Optimal circulation times are determined and expected to yield improved precision of parameter estimates in future experiments to reflect disease progression.

Regulation of cardiac energetics: role of redox state and cellular compartmentation during ischemia

The heart is capable of altering its metabolic rate during exercise or ischemia. Under most state transitions, the heart maintains the concentration of adenosine triphosphate (ATP) at relatively constant values, in spite of large fluctuations in metabolic rate or in the delivery of fuels and oxygen. However, the mechanisms responsible for the regulation of cardiac energetics under conditions of increased demand or reduced supply are still under debate. To improve quantitative understanding of the regulation of glycolysis and oxidative phosphorylation under physiological and pathological conditions, it is essential to assess the dynamics of cytosolic and mitochondrial nicotinamide adenine dinucleotide (NAD(+)) and its reduced form (NADH) during stress (e.g., ischemia, exercise). However, at present there are no reliable methods to measure the dynamics of redox state in vivo in these subcellular compartments. In the present study, computer simulations with a mathematical model of myocardial energy metabolism are used to investigate the role of cytosolic and mitochondrial redox states in regulating cardiac energetics during reduced myocardial blood flow.

Regulation of lactate production at the onset of ischaemia is independent of mitochondrial NADH/NAD+: insights from in silico studies

Ischaemia decreases mitochondrial NADH oxidation, activates glycolysis, increases the NADH/NAD+ ratio, and causes lactate production. The mechanisms that regulate anaerobic glycolysis and the NADH/NAD+ ratio during ischaemia are unclear. Although continuous measurements of metabolic fluxes and NADH/NAD+ in cytosol and mitochondria are not possible in vivo with current experimental techniques, computational models can be used to predict these variables by simulations with in silico experiments. Such predictions were obtained using a mathematical model of cellular metabolism in perfused myocardium. This model, which distinguishes cytosolic and mitochondrial domains, incorporates key metabolic species and processes associated with energy transfer. Simulation of metabolic responses to mild, moderate and severe ischaemia in large animals showed that mitochondrial NADH/NAD+ was rapidly reset to higher values in proportion to the reduced O2 delivery and myocardial oxygen consumption . Cytosolic NADH/NAD+, however, showed a biphasic response, with a sharp initial increase that was due to activation of glycogen breakdown and glycolysis, and corresponded with lactate production. Whereas the rate of glycolysis and the malate-aspartate shuttle had a significant effect on the cytosolic NADH/NAD+, their effects on the mitochondrial NADH/NAD+ were minimal. In summary, model simulations of the metabolic response to ischaemia showed that mitochondrial NADH/NAD+ is primarily determined by O2 consumption, while cytosolic NADH/NAD+ is largely a function of glycolytic flux during the initial phase, and is determined by mitochondrial NADH/NAD+ and the malate-aspartate shuttle during the steady state.

Alterations in Internal Elastic Lamina Permeability As a Function of Age and Anatomical Site Precede Lesion Development in Apolipoprotein E–Null Mice

Early atherosclerosis is characterized by the accumulation of plasma-borne macromolecules (eg, low-density lipoproteins) in the arterial intima, which is bordered by endothelial cells (EC) and the internal elastic lamina (IEL). This accumulation is believed to be secondary to increased EC permeability. We hypothesized that a decrease in IEL permeability may precede lesion development and contribute to macromolecular accumulation. To test this hypothesis, we quantified EC and IEL permeability in lesion-free areas of the thoracic and abdominal aortas of chow-fed C57BL/6 control and atherosclerotic-prone apolipoprotein E (apoE)-null mice at 3 and 5 months of age. Between 3 and 5 months of age, apoE-null mice begin to develop atherosclerotic lesions in the thoracic aorta. No significant differences in EC and IEL permeability were observed at either time in C57BL/6 control mice. In contrast, 78% and 19% decreases in IEL permeability of the thoracic aorta and abdominal aorta, respectively, were observed between 3 to 5 months of age in apoE-null mice (thoracic: 2.05±1.33 and 0.44±0.15 μm/min, P <0.001; abdominal: 1.13±0.58 and 0.93±0.44 μm/min, P <0.05). To further determine whether decreased IEL permeability is linked with atherosclerotic lesion development, we quantified IEL permeability in the greater and lesser curvature of the aortic arch. In apoE-null mice, the lesser curvature of the aortic arch develops lesions before the greater curvature. We found a significant and sustained decrease (59%) in IEL permeability in the lesser curvature of the aortic arch compared with the greater curvature. These data suggest that atherogenesis involves the pathological remodeling of the IEL, not the endothelium before lesion development. This remodeling may be attributable to local responses of the endothelium and smooth muscle cells to hyperlipidemia.

Mechanistic model of cardiac energy metabolism predicts localization of glycolysis to cytosolic subdomain during ischemia

A new multidomain mathematical model of cardiac cellular metabolism was developed to simulate metabolic responses to reduced myocardial blood flow. The model is based on mass balances and reaction kinetics that describe transport and metabolic processes of 31 key chemical species in cardiac tissue. The model has three distinct domains (blood, cytosol, and mitochondria) with interdomain transport of chemical species. In addition to distinguishing between cytosol and mitochondria, the model includes a subdomain in the cytosol to account for glycolytic metabolic channeling. Myocardial ischemia was induced by a 60% reduction in coronary blood flow, and model simulations were compared with experimental data from anesthetized pigs. Simulations with a previous model without compartmentation showed a slow activation of glycogen breakdown and delayed lactate production compared with experimental results. The addition of a subdomain for glycolysis resulted in simulations showing faster rates of glycogen breakdown and lactate production that closely matched in vivo experimental data. The dynamics of redox (NADH/NAD+) and phosphorylation (ADP/ATP) states were also simulated. These controllers are coupled to energy transfer reactions and play key regulatory roles in the cytosol and mitochondria. Simulations showed a similar dynamic response of the mitochondrial redox state and the rate of pyruvate oxidation during ischemia. In contrast, the cytosolic redox state displayed a time response similar to that of lactate production. In conclusion, this novel mechanistic model effectively predicted the rapid activation of glycogen breakdown and lactate production at the onset of ischemia and supports the concept of localization of glycolysis to a subdomain of the cytosol.