Jaques Reifman

Update on mathematical modeling research to support the development of automated insulin delivery systems.

The world leaders in glycemia modeling convened during the Eighth Annual Diabetes Technology Meeting in Bethesda, Maryland, on 14 November 2008, to discuss the current practices in mathematical modeling and make recommendations for its use in developing automated insulin-delivery systems. This report summarizes the collective views of the 25 participating experts in addressing the following four topics: current practices in modeling efforts for closed-loop control; framework for exchange of information and collaboration among research centers; major barriers for the development of accurate models; and key tasks for developing algorithms to build closed-loop control systems. Among the participants, the following main conclusions and recommendations were widely supported: Physiologic variance represents the single largest technical challenge to creating accurate simulation models. A Web site describing different models and the data supporting them should be made publically available, with funding agencies and journals requiring investigators to provide open access to both models and data. Existing simulation models should be compared and contrasted, using the same evaluation and validation criteria, to better assess the state of the art, understand any inherent limitations in the models, and identify gaps in data and/or model capability.

Kinetic modeling sheds light on the mode of action of recombinant factor VIIa on thrombin generation

INTRODUCTIONnThe therapeutic potential of a hemostatic agent can be assessed by investigating its effects on the quantitative parameters of thrombin generation. For recombinant activated factor VII (rFVIIa)--a promising hemostasis-inducing biologic--experimental studies addressing its effects on thrombin generation yielded disparate results. To elucidate the inherent ability of rFVIIa to modulate thrombin production, it is necessary to identify rFVIIa-induced effects that are compatible with the available biochemical knowledge about thrombin generation mechanisms.nnnMATERIALS AND METHODSnThe existing body of knowledge about coagulation biochemistry can be rigorously represented by a computational model that incorporates the known reactions and parameter values constituting the biochemical network. We used a thoroughly validated numerical model to generate activated factor VII (FVIIa) titration curves in the cases of normal blood composition, hemophilia A and B blood, blood lacking factor VII, blood lacking tissue factor pathway inhibitor, and diluted blood. We utilized the generated curves to perform systematic fold-change analyses for five quantitative parameters characterizing thrombin accumulation.nnnRESULTSnThe largest fold changes induced by increasing FVIIa concentration were observed for clotting time, thrombin peak time, and maximum slope of the thrombin curve. By contrast, thrombin peak height was much less affected by FVIIa titrations, and the area under the thrombin curve stayed practically unchanged. Comparisons with experimental data demonstrated that the computationally derived patterns can be observed in vitro.nnnCONCLUSIONSnrFVIIa modulates thrombin generation primarily by accelerating the process, without significantly affecting the total amount of generated thrombin.

A unified mathematical model to quantify performance impairment for both chronic sleep restriction and total sleep deprivation.

Performance prediction models based on the classical two-process model of sleep regulation are reasonably effective at predicting alertness and neurocognitive performance during total sleep deprivation (TSD). However, during sleep restriction (partial sleep loss) performance predictions based on such models have been found to be less accurate. Because most modern operational environments are predominantly characterized by chronic sleep restriction (CSR) rather than by episodic TSD, the practical utility of this class of models has been limited. To better quantify performance during both CSR and TSD, we developed a unified mathematical model that incorporates extant sleep debt as a function of a known sleep/wake history, with recent history exerting greater influence. This incorporation of sleep/wake history into the classical two-process model captures an individuals capacity to recover during sleep as a function of sleep debt and naturally bridges the continuum from CSR to TSD by reducing to the classical two-process model in the case of TSD. We validated the proposed unified model using psychomotor vigilance task data from three prior studies involving TSD, CSR, and sleep extension. We compared and contrasted the fits, within-study predictions, and across-study predictions from the unified model against predictions generated by two previously published models, and found that the unified model more accurately represented multiple experimental studies and consistently predicted sleep restriction scenarios better than the existing models. In addition, we found that the model parameters obtained by fitting TSD data could be used to predict performance in other sleep restriction scenarios for the same study populations, and vice versa. Furthermore, this model better accounted for the relatively slow recovery process that is known to characterize CSR, as well as the enhanced performance that has been shown to result from sleep banking.

A quantitative quasispecies theory-based model of virus escape mutation under immune selection

Viral infections involve a complex interplay of the immune response and escape mutation of the virus quasispecies inside a single host. Although fundamental aspects of such a balance of mutation and selection pressure have been established by the quasispecies theory decades ago, its implications have largely remained qualitative. Here, we present a quantitative approach to model the virus evolution under cytotoxic T-lymphocyte immune response. The virus quasispecies dynamics are explicitly represented by mutations in the combined sequence space of a set of epitopes within the viral genome. We stochastically simulated the growth of a viral population originating from a single wild-type founder virus and its recognition and clearance by the immune response, as well as the expansion of its genetic diversity. Applied to the immune escape of a simian immunodeficiency virus epitope, model predictions were quantitatively comparable to the experimental data. Within the model parameter space, we found two qualitatively different regimes of infectious disease pathogenesis, each representing alternative fates of the immune response: It can clear the infection in finite time or eventually be overwhelmed by viral growth and escape mutation. The latter regime exhibits the characteristic disease progression pattern of human immunodeficiency virus, while the former is bounded by maximum mutation rates that can be suppressed by the immune response. Our results demonstrate that, by explicitly representing epitope mutations and thus providing a genotype–phenotype map, the quasispecies theory can form the basis of a detailed sequence-specific model of real-world viral pathogens evolving under immune selection.

Computational Analysis of the Effects of Reduced Temperature on Thrombin Generation: The Contributions of Hypothermia to Coagulopathy

BACKGROUND:Hypothermia, which can result from tissue hypoperfusion, body exposure, and transfusion of cold resuscitation fluids, is a major factor contributing to coagulopathy of trauma and surgery. Despite considerable efforts, the mechanisms of hypothermia-induced blood coagulation impairment have not been fully understood. We introduce a kinetic modeling approach to investigate the effects of hypothermia on thrombin generation. METHODS:We extended a validated computational model to predict and analyze the impact of low temperatures (with or without concomitant blood dilution) on thrombin generation and its quantitative parameters. The computational model reflects the existing knowledge about the mechanistic details of thrombin generation biochemistry. We performed the analysis for an “average” subject, as well as for 472 subjects in the control group of the Leiden Thrombophilia Study. RESULTS:We computed and analyzed thousands of kinetic curves characterizing the generation of thrombin and the formation of the thrombin–antithrombin complex (TAT). In all simulations, hypothermia in the temperature interval 31°C to 36°C progressively slowed down thrombin generation, as reflected by clotting time, thrombin peak time, and prothrombin time, which increased in all subjects (P < 10−5). Maximum slope of the thrombin curve was progressively decreased, and the area under the thrombin curve was increased in hypothermia (P < 10−5); thrombin peak height remained practically unaffected. TAT formation was noticeably delayed (P < 10−5), but the final TAT levels were not significantly affected. Hypothermia-induced fold changes in the affected thrombin generation parameters were larger for lower temperatures, but were practically independent of the parameter itself and of the subjects’ clotting factor composition, despite substantial variability in the subject group. Hypothermia and blood dilution acted additively on the thrombin generation parameters. CONCLUSIONS:We developed a general computational strategy that can be used to simulate the effects of changing temperature on the kinetics of biochemical systems and applied this strategy to analyze the effects of hypothermia on thrombin generation. We found that thrombin generation can be noticeably impaired in subjects with different blood plasma composition even in moderate hypothermia. Our work provides mechanistic support to the notion that thrombin generation impairment may be a key factor in coagulopathy induced by hypothermia and complicated by blood plasma dilution.

Therapeutic correction of thrombin generation in dilution-induced coagulopathy: Computational analysis based on a data set of healthy subjects

BACKGROUND Prothrombin complex concentrates (PCCs), which contain different coagulation proteins, are attractive alternatives to the standard methods to treat dilution-induced (and, generally, traumatic) coagulopathy. We investigated the ability of a novel PCC composition to restore normal thrombin generation in diluted blood. The performance of the proposed PCC composition (coagulation factors [F] II, IX, and X and the anticoagulant antithrombin), designated PCC-AT, was compared with that of FVIIa and PCC-FVII, which is the PCC composition containing FII, FVII, FIX, and FX (main components of most PCCs). METHODS We used a thoroughly validated computational model to simulate thrombin generation in normal and diluted blood for 472 healthy subjects in the control group of the Leiden Thrombophilia Study. For every simulated thrombin curve, we calculated and analyzed five standard thrombin generation parameters. RESULTS The three therapeutic agents (FVIIa, PCC-FVII, and PCC-AT) caused statistically significant changes in each of the five thrombin generation parameters in diluted blood. Factor VIIa tended to primarily impact clotting time, thrombin peak time, and maximum slope of the thrombin curve, whereas in the case of PCC-FVII, thrombin peak height and the area under the thrombin curve were affected particularly strongly. As a result, these two therapeutics tended to push those respective parameters outside their normal ranges. PCC-AT significantly outperformed both FVIIa and PCC-FVII in its ability to normalize individual thrombin generation parameters in diluted blood. Furthermore, PCC-AT could simultaneously restore all five thrombin generation parameters to their normal levels in every subject in the study group. CONCLUSIONS Our computational results suggest that PCC-AT may demonstrate a superior ability to restore normal thrombin generation compared with FVIIa and PCC-FVII. LEVEL OF EVIDENCE V

A computational study of the respiratory airflow characteristics in normal and obstructed human airways

Obstructive lung diseases in the lower airways are a leading health concern worldwide. To improve our understanding of the pathophysiology of lower airways, we studied airflow characteristics in the lung between the 8th and the 14th generations using a three-dimensional computational fluid dynamics model, where we compared normal and obstructed airways for a range of breathing conditions. We employed a novel technique based on computing the Pearson׳s correlation coefficient to quantitatively characterize the differences in airflow patterns between the normal and obstructed airways. We found that the airflow patterns demonstrated clear differences between normal and diseased conditions for high expiratory flow rates (>2300ml/s), but not for inspiratory flow rates. Moreover, airflow patterns subjected to filtering demonstrated higher sensitivity than airway resistance for differentiating normal and diseased conditions. Further, we showed that wall shear stresses were not only dependent on breathing rates, but also on the distribution of the obstructed sites in the lung: for the same degree of obstruction and breathing rate, we observed as much as two-fold differences in shear stresses. In contrast to previous studies that suggest increased wall shear stress due to obstructions as a possible damage mechanism for small airways, our model demonstrated that for flow rates corresponding to heavy activities, the wall shear stress in both normal and obstructed airways was <0.3Pa, which is within the physiological limit needed to promote respiratory defense mechanisms. In summary, our model enables the study of airflow characteristics that may be impractical to assess experimentally.

Computational analysis of intersubject variability and thrombin generation in dilutional coagulopathy

BACKGROUND: Blood dilution is a frequent complication of massive transfusion during trauma and surgery. This article investigates the quantitative effects of blood plasma dilution on thrombin generation in the context of intersubject variability.

Use of a Food and Drug Administration-Approved Type 1 Diabetes Mellitus Simulator to Evaluate and Optimize a Proportional-Integral-Derivative Controller

Background: Clinical studies have shown that the Medtronic proportional-integral-derivative (PID) control with insulin feedback (IFB) provides stable 24 h glucose control, but with high postprandial glucose. We coupled this algorithm to a Food and Drug Administration-approved type 1 diabetes mellitus simulator to determine whether a proportional-derivative controller with preprogrammed basal rates (PDBASAL) would have better performance. Methods: We performed simulation studies on 10 adult subjects to (1) obtain the basal profiles for the PDBASAL controller; (2) define the pharmacokinetic/pharmacodynamic profile used to effect IFB, (3) optimize the PID and PDBASAL control parameters, (4) evaluate improvements obtained with IFB, and (5) develop a method to simulate changes in insulin sensitivity and assess the ability of each algorithm to respond to such changes. Results: PDBASAL control significantly reduced peak postprandial glucose [252 (standard error = 11) versus 279 (14) mg/dl; p < .001] and increased nadir glucose [102 (3) versus 92 (3) mg/dl; p < .001] compared with PID control (both implemented with IFB). However, with PDBASAL control, fasting glucose remained elevated following a 30% decrease in insulin sensitivity [156 (6) mg/dl; different from the target of 110 mg/dl; p < .001] and remained below target following a 30% increase in insulin sensitivity [84 (2) mg/dl; p < .001]. In both cases, PID control returned glucose levels to target. Conclusions: PDBASAL provides better postprandial glucose control than PID but is not appropriate for subjects whose basal requirements change with insulin sensitivity. Simulations used to compare different control strategies should assess this variability.

Bone mass, microarchitecture and strength are influenced by race/ethnicity in young adult men and women

Lower rates of fracture in both Blacks compared to Whites, and men compared to women are not completely explained by differences in bone mineral density (BMD). Prior evidence suggests that more favorable cortical bone microarchitecture may contribute to reduced fracture rates in older Black compared to White women, however it is not known whether these differences are established in young adulthood or develop during aging. Moreover, prior studies using high-resolution pQCT (HR-pQCT) have reported outcomes from a fixed-scan location, which may confound sex- and race/ethnicity-related differences in bone structure.nnnPURPOSEnWe determined differences in bone mass, microarchitecture and strength between young adult Black and White men and women.nnnMETHODSnWe enrolled 185 young adult (24.2±3.4yrs) women (n=51 Black, n=50 White) and men (n=34 Black, n=50 White) in this cross-sectional study. We used dual-energy X-ray absorptiometry (DXA) to determine areal BMD (aBMD) at the femoral neck (FN), total hip (TH) and lumbar spine (LS), as well as HR-pQCT to assess bone microarchitecture and failure load by micro-finite element analysis (μFEA) at the distal tibia (4% of tibial length). We used two-way ANOVA to compare bone outcomes, adjusted for age, height, weight and physical activity.nnnRESULTSnThe effect of race/ethnicity on bone outcomes did not differ by sex, and the effect of sex on bone outcomes did not differ by race/ethnicty. After adjusting for covariates, Blacks had significantly greater FN, TH and LS aBMD compared to Whites (p<0.05 for all). Blacks also had greater cortical area, vBMD, and thickness, and lower cortical porosity, with greater trabecular thickness and total vBMD compared to Whites. μFEA-estimated FL was significantly higher among Blacks compared to Whites. Men had significantly greater total vBMD, trabecular thickness and cortical area and thickness, but greater cortical porosity than women, the net effects being a higher failure load in men than women.nnnCONCLUSIONnThese findings demonstrate that more favorable bone microarchitecture in Blacks compared to Whites and in men compared to women is established by young adulthood. Advantageous bone strength among Blacks and men likely contributes to their lower risk of fractures throughout life compared to their White and women counterparts.