Trauma of lung due to impact load

A quantitative evaluation of lung injury due to impact loading is of general interest. Hemorrhage and edema are the usual sequelae to traumatic pulmonary impact. To gain some quantitative understanding of the phenomena, we perfused excised rabbit lung with Macrodex at isogravimetric condition and monitored lung weight continuously after impact. It is shown that a factor of importance is the rigidity of the surface on which the lung rests. The rate of lung weight increase is smaller if the lung was 'freely' supported on a soft cloth, more if it was supported on a rigid plate. This suggests the influence of stress wave reflection. The critical condition correlates with the initial velocity of impact at the surface of the lung, or with the maximum deflection. For a freely supported lung, the rate of lung weight increase was 22% of the initial total lung weight per h after impact when the impact velocity was 11.5 ms-1, 30% when the velocity was 13.2 ms-1, several 100% at 13.5 ms-1, signaling massive lung injury. Since the velocity of sound in rabbit lung is 33.3 ms-1 when the inflation (transpulmonary) pressure is 10 cm H2O, the critical velocity of 13.5 ms-1 corresponds to a Mach number of 0.4. The maximum surface displacement of the lung is almost linearly proportional to the initial velocity of impact. The exact cause of edema and hemorrhage is unknown; we hypothesize that it is due to tensile stress in the alveolar wall caused by the impact.     

A hypothesis on the mechanism of trauma of lung tissue subjected to impact load

When a compressive impact load is applied on the chest, as in automobile crash or bomb explosion, the lung may be injured and show evidences of edema and hemorrhage. Since soft tissues have good strength in compression, why does a compression wave cause edema? Our hypothesis is that tensile and shear stresses are induced in the alveolar wall on rebound from compression, and that the maximum principal stress (tensile) may exceed critical values for increased permeability of the epithelium to small solutes, or even fracture. Furthermore, small airways may collapse and trap gas in alveoli at a critical strain, causing traumatic atelectasis. The collapsed airways reopen at a higher strain after the wave passes, during which the expansion of the trapped gas will induce additional tension in the alveolar wall. To test this hypothesis, we made three new experiments: (1), measuring the effect of transient overstretch of the alveolar membrane on the rate of lung weight increase; (2) determining the critical pressure for reopening collapsed airways of rabbit lung subjected to cyclic compression and expansion; (3) cyclic compression of lung with trachea closed. We found that in isolated rabbit lung overstretching increases the rate of edema fluid formation, that the critical strain for airway reopening is higher than that for closing, and that these critical strains are strain-rate dependent, but independent of the state of the trachea, whether it is open or closed. Furthermore, a theoretical analysis is presented to show that the maximum principal (tensile) stress is of the same order of magnitude as the maximum initial compressive stress at certain localities of the lung.(ABSTRACT TRUNCATED AT 250 WORDS)     

A high-frequency lung injury mechanism in blunt thoracic impact

When a mechanical load is applied very rapidly to the thoracic wall, part of the internal damage is suspected to be due to a "high-frequency" injury mechanism, that is, a phenomenon in which waves are involved. This paper addresses a specific high-frequency mechanism for lung injury in which a stress wave is generated through rapid acceleration of the body wall. Displacement-related injuries, which are rather "low-frequency" phenomena, are not considered. The present work was done in the context of assessing behind armor blunt trauma (injury to thoracic organs occurring when a bullet is stopped by a body armor) through mathematical modeling. One aspect of the thorax response to high-speed blunt impact and an associated injury mechanism are investigated based on an idealized model of thorax and a set of computations presented in previous papers. The injury mechanism considered elucidates a possible mathematical relationship between the acceleration at the surface of the thoracic wall and the occurrence of lung injury.     

Practical identifiability of biokinetic parameters of a model describing two-step nitrification in biofilms

Parameter estimation and model calibration are key problems in the application of biofilm models in engineering practice, where a large number of model parameters need to be determined usually based on experimental data with only limited information content. In this article, identifiability of biokinetic parameters of a biofilm model describing two-step nitrification was evaluated based solely on bulk phase measurements of ammonium, nitrite, and nitrate. In addition to evaluating the impact of experimental conditions and available measurements, the influence of mass transport limitation within the biofilm and the initial parameter values on identifiability of biokinetic parameters was evaluated. Selection of parameters for identifiability analysis was based on global mean sensitivities while parameter identifiability was analyzed using local sensitivity functions. At most, four of the six most sensitive biokinetic parameters were identifiable from results of batch experiments at bulk phase dissolved oxygen concentrations of 0.8 or 5 mg O(2)/L. High linear dependences between the parameters of the subsets (KO2,AOB,muAOB) and (KO2,NOB,muNOB) resulted in reduced identifiability. Mass transport limitation within the biofilm did not influence the number of identifiable parameters but, in fact, decreased collinearity between parameters, especially for parameters that are otherwise correlated (e.g., muAOB) and KO2,AOB, or muNOB and KO2,NOB). The choice of the initial parameter values had a significant impact on the identifiability of two parameter subsets, both including the parameters muAOB and KO2,AOB. Parameter subsets that did not include the subsets muAOB and KO2,AOB or muNOB and KO2,NOB were clearly identifiable independently of the choice of the initial parameter values.     

Altered Levels of Trace Elements in Acute Lung Injury After Severe Trauma

Trace element (TE) supplementation can reduce the incidence of multiple organ failure after severe trauma. The lung plays a main role in post-injury multiple organ failure. In the present study, the relationship between TEs and acute lung injury (ALI) post-injury was investigated in a rabbit model of severe trauma with an injury severity score of 27. New Zealand white rabbits were randomly assigned to trauma-control, trauma-TE groups, and a control group. During days 1-5 post-trauma, each rabbit in the trauma-TE group received 0.1 ml multi-TE compound intraperitoneally to give a daily dose of 32.50 mg/kg of Zn, 6.35 mg/kg of Cu, 1.38 mg/kg of Mn, and 0.16 mg/kg of Se. Concentrations of blood and lung selenium (Se), copper (Cu), zinc (Zn), and manganese (Mn) were measured at 6 and 24 h, as well as 3, 6, 9, and 14 days after trauma. Levels of glutathione peroxidase (GPx), total superoxide dismutase (SOD), Cu/Zn superoxide dismutase (Cu/Zn-SOD), and malondialdehyde (MDA) in serum and lung tissue and the level of intercellular adhesion molecular-1 (ICAM-1) in serum were detected simultaneously. In addition, the lung coefficient (LC) and the lung permeation index (LPI) were measured. Serum and lung Zn, Se, and Mn levels decreased dramatically by 6 h after trauma in both experimental groups. Cu showed no significant changes after trauma. The serum and lung GPx and SOD levels in the experimental group decreased significantly on days 1 and 3, respectively. Serum and lung MDA began to increase on day 3 in the trauma group but increased less after TE supplementation. Serum ICAM-1 peaked on day 6 in the experimental group. LC and LPI increased gradually post-trauma, peaking on days 6 and 9, respectively. In conclusion, an acute lung injury causes declines of the levels of TEs in serum and lung which can be significantly prevented by TE supplementation and which can also mitigate some of the morphological and biomechanical changes in ALI.     

Small-angle scattering of an extraordinary wave near the upper hybrid resonance

The small-angle scattering of an extraordinary wave by plasma density fluctuations near the upper hybrid resonance is analyzed. It is shown that the efficiency of the small-angle scattering increases markedly as the upper hybrid resonance is approached. The power lost by the probing wave is calculated as a function of distance from the upper hybrid resonance, the parameters of the wavenumber spectrum of density fluctuations, and plasma parameters. The estimates obtained indicate that small-angle scattering, first, may have a strong impact on the experimental results obtained from the enhanced-scattering diagnostic and, second, may be the main cause of the broadening of the frequency spectrum of a signal recorded by this diagnostic technique.     

A 3-D Propagation Model for Emerging Land Mobile Radio Cellular Environments

A tunable stochastic geometry based Three-Dimensional (3-D) scattering model for emerging land mobile radio cellular systems is proposed. Uniformly distributed scattering objects are assumed around the Mobile Station (MS) bounded within an ellipsoidal shaped Scattering Region (SR) hollowed with an elliptically-cylindric scattering free region in immediate vicinity of MS. To ensure the degree of expected accuracy, the proposed model is designed to be tunable (as required) with nine degrees of freedom, unlike its counterparts in the existing literature. The outer and inner boundaries of SR are designed as independently scalable along all the axes and rotatable in horizontal plane around their origin centered at MS. The elevated Base Station (BS) is considered outside the SR at a certain adjustable distance and height w.r.t. position of MS. Closed-form analytical expressions for joint and marginal Probability Density Functions (PDFs) of Angle-of-Arrival (AoA) and Time-of-Arrival (ToA) are derived for both up- and down-links. The obtained analytical results for angular and temporal statistics of the channel are presented along with a thorough analysis. The impact of various physical model parameters on angular and temporal characteristics of the channel is presented, which reveals the comprehensive insight on the proposed results. To evaluate the robustness of the proposed analytical model, a comparison with experimental datasets and simulation results is also presented. The obtained analytical results for PDF of AoA observed at BS are seen to fit a vast range of empirical datasets in the literature taken for various outdoor propagation environments. In order to establish the validity of the obtained analytical results for spatial and temporal characteristics of the channel, a comparison of the proposed analytical results with the simulation results is shown, which illustrates a good fit for 10⁷ scattering points. Moreover, the proposed model is shown to degenerate to various notable geometric models in the literature by an appropriate choice of a few parameters.     

Sensitivity analysis of respiratory parameter uncertainties: impact of criterion function form and constraints

A sensitivity analysis based on weighted least-squares regression is presented to evaluate alternative methods for fitting lumped-parameter models to respiratory impedance data. The goal is to maintain parameter accuracy simultaneously with practical experiment design. The analysis focuses on predicting parameter uncertainties using a linearized approximation for joint confidence regions. Applications are with four-element parallel and viscoelastic models for 0.125- to 4-Hz data and a six-element model with separate tissue and airway properties for input and transfer impedance data from 2-64 Hz. The criterion function form was evaluated by comparing parameter uncertainties when data are fit as magnitude and phase, dynamic resistance and compliance, or real and imaginary parts of input impedance. The proper choice of weighting can make all three criterion variables comparable. For the six-element model, parameter uncertainties were predicted when both input impedance and transfer impedance are acquired and fit simultaneously. A fit to both data sets from 4 to 64 Hz could reduce parameter estimate uncertainties considerably from those achievable by fitting either alone. For the four-element models, use of an independent, but noisy, measure of static compliance was assessed as a constraint on model parameters. This may allow acceptable parameter uncertainties for a minimum frequency of 0.275-0.375 Hz rather than 0.125 Hz. This reduces data acquisition requirements from a 16- to a 5.33- to 8-s breath holding period. These results are approximations, and the impact of using the linearized approximation for the confidence regions is discussed.     

Robust human body model injury prediction in simulated side impact crashes

This study developed a parametric methodology to robustly predict occupant injuries sustained in real-world crashes using a finite element (FE) human body model (HBM). One hundred and twenty near-side impact motor vehicle crashes were simulated over a range of parameters using a Toyota RAV4 (bullet vehicle), Ford Taurus (struck vehicle) FE models and a validated human body model (HBM) Total HUman Model for Safety (THUMS). Three bullet vehicle crash parameters (speed, location and angle) and two occupant parameters (seat position and age) were varied using a Latin hypercube design of Experiments. Four injury metrics (head injury criterion, half deflection, thoracic trauma index and pelvic force) were used to calculate injury risk. Rib fracture prediction and lung strain metrics were also analysed. As hypothesized, bullet speed had the greatest effect on each injury measure. Injury risk was reduced when bullet location was further from the B-pillar or when the bullet angle was more oblique. Age had strong correlation to rib fractures frequency and lung strain severity. The injuries from a real-world crash were predicted using two different methods by (1) subsampling the injury predictors from the 12 best crush profile matching simulations and (2) using regression models. Both injury prediction methods successfully predicted the case occupant's low risk for pelvic injury, high risk for thoracic injury, rib fractures and high lung strains with tight confidence intervals. This parametric methodology was successfully used to explore crash parameter interactions and to robustly predict real-world injuries.     

Washed human platelets prevent ischemia-reperfusion edema in isolated rabbit lungs

Washed human platelets prevent edema formation in isolated rabbit lungs infused with xanthine oxidase, an enzyme that injures endothelial membranes by generating extracellular oxidants. We hypothesized that platelets would similarly preserve membrane permeability in isolated lungs exposed to ischemia-reperfusion injury, a model that perturbs endothelial cells by the generation of intracellular oxidants. Isolated perfused rabbit lungs (IPL) were exposed to warm ischemia-reperfusion to cause lung edema. The infusion of washed human platelets (1.05 +/- 0.02 x 10(10) cells) prevented edema formation as measured by lung weight gain, wet-to-dry lung weight ratios, histological edema, and preservation of paraendothelial cell tight junctions. Inhibition of the platelet glutathione redox cycle with 1,3-bis(2-chloroethyl)-1-nitrosourea, dehydroepiandrosterone, or 1-chloro-2,4-dinitrobenzene interfered with platelet protective effects. In contrast, inhibition of platelet catalase with aminotriazole and H2O2 had no effect on platelet protection. Lung tissue malonyldialdehyde concentrations were similar in isolated lungs exposed to ischemia-reperfusion with or without the infusion of platelets. These results indicate that platelet attenuation of ischemia-reperfusion lung edema depends on platelet glutathione redox cycle antioxidants but not platelet catalase.     

Simultaneous versus sequential optimal experiment design for the identification of multi-parameter microbial growth kinetics as a function of temperature

Optimal experiment design for parameter estimation (OED/PE) has become a popular tool for efficient and accurate estimation of kinetic model parameters. When the kinetic model under study encloses multiple parameters, different optimization strategies can be constructed. The most straightforward approach is to estimate all parameters simultaneously from one optimal experiment (single OED/PE strategy). However, due to the complexity of the optimization problem or the stringent limitations on the system's dynamics, the experimental information can be limited and parameter estimation convergence problems can arise. As an alternative, we propose to reduce the optimization problem to a series of two-parameter estimation problems, i.e., an optimal experiment is designed for a combination of two parameters while presuming the other parameters known. Two different approaches can be followed: (i) all two-parameter optimal experiments are designed based on identical initial parameter estimates and parameters are estimated simultaneously from all resulting experimental data (global OED/PE strategy), and (ii) optimal experiments are calculated and implemented sequentially whereby the parameter values are updated intermediately (sequential OED/PE strategy).This work exploits OED/PE for the identification of the Cardinal Temperature Model with Inflection (CTMI) (Rosso et al., 1993). This kinetic model describes the effect of temperature on the microbial growth rate and encloses four parameters. The three OED/PE strategies are considered and the impact of the OED/PE design strategy on the accuracy of the CTMI parameter estimation is evaluated. Based on a simulation study, it is observed that the parameter values derived from the sequential approach deviate more from the true parameters than the single and global strategy estimates. The single and global OED/PE strategies are further compared based on experimental data obtained from design implementation in a bioreactor. Comparable estimates are obtained, but global OED/PE estimates are, in general, more accurate and reliable.     

Mechanisms of interaction between oxygen and granulocytes in hyperoxic lung injury

Hyperoxia and infused granulocytes act synergistically in producing a nonhydrostatic high-permeability lung edema in the isolated perfused rabbit lung within 4 h, which is substantially greater than that seen with hyperoxia alone. We hypothesized that the interaction between hyperoxia and granulocytes was principally due to a direct effect of hyperoxia on the lung itself. Isolated perfused rabbit lungs that were preexposed to 2 h of hyperoxia (95% O2-5% CO2) prior to the infusion of unstimulated granulocytes (under normoxic conditions) developed significant nonhydrostatic lung edema (P = 0.008) within 2 h when compared with lungs that were preexposed to normoxia (15% O2-5% CO2) prior to granulocyte perfusion. The edema in the hyperoxic-preexposed lungs was accompanied by significant increases in bronchoalveolar lavage (BAL) protein, BAL granulocytes, BAL thromboxane and prostacyclin levels, perfusate chemotactic activity, and lung lipid peroxidation. These findings suggest that the synergistic interaction between hyperoxia and granulocytes in producing acute lung injury involves a primary effect of hyperoxia on the lung itself.     

On the choice of the optimal periodic operation for a continuous fermentation process

In this contribution we investigate the impact of the forcing waveform on the productivity of a continuous bioreactor governed by an unstructured, nonlinear kinetic model. The (periodic) forcing is applied on the substrate concentration in the feed. To this end, some alternative waveforms commonly encountered in practice are evaluated and their performance is compared. An analytical/numerical approach is used. The preliminary analytical step is based on the π‐criterion that gives useful information for small amplitudes. The extension to larger amplitudes, when significant improvements are expected, is then performed through a continuation‐optimization procedure. It is found that the choice of the specific waveform has an impact on the performance of the process and there is no unique best forcing for any process condition, but its choice depends on the operating parameters and the forcing amplitude and frequency values. Further, the influence of the waveform functions on the wash‐out conditions are extensively examined. The analysis shows that all the waveforms examined in this work may lead to significant enlargement of the nontrivial regime with respect to a steady state operation. In particular, square‐wave forcing leads in practice to the extinction of the wash‐out conditions for any feed substrate concentration and for a well defined choice of the forcing parameters. © 2010 American Institute of Chemical Engineers Biotechnol. Prog., 2010     

Application of 1D blood flow models of the human arterial network to differential pressure predictions

A new application of 1D models of the human arterial network is proposed. We take advantage of the sensitivity of the models predictions for the pressure profiles within the main aorta to key model parameter values. We propose to use the patterns in the predicted differences from a base case as a way to infer to the most probable changes in the parameter values. We demonstrate this application using an impedance model that we have recently developed (Johnson, 2010). The input model parameters are all physiologically related, such as the geometric dimensions of large arteries, various blood properties, vessel elasticity, etc. and can therefore be patient specific. As a base case, nominal values from the literature are used. The necessary information to characterize the smaller arteries, arterioles, and capillaries is taken from a physical scaling model (West, 1999). Model predictions for the effective impedance of the human arterial system closely agree with experimental data available in the literature. The predictions for the pressure wave development along the main arteries are also found in qualitative agreement with previous published results. The model has been further validated against our own measured pressure data in the carotid and radial arteries, obtained from healthy individuals. Upon changes in the value of key model parameters, we show that the differences seen in the pressure profiles correspond to qualitatively different patterns for different parameters. This suggests the possibility of using the model in interpreting multiple pressure data of healthy/diseased individuals.     

Selective absorption and scattering of light by solutions of macromolecules and by particulate suspensions

For particulate suspensions and for solutions that scatter light measurably the total absorbance A generally contains contributions due to specific absorption (Aa) and scattering of light (As). The quantity As is closely related to the turbidity tau. In general, spectrophotometry of such systems requires proper modification of the spectrophotometer used in order to permit accurate determination of the absorbance A and of the derived quantities Aa and As. Apparent deviation from Beer's law in such systems is often due to inappropriate experimental technique. After a discussion of the parameters that determine the intensity of light scattered by solutes, an account is given of the experimental precautions to be taken for determination of the absorbance of light scattering suspensions and solutions and of techniques for correcting absorbance spectra for scattering of light. Measurement of the turbidity is briefly confronted with determination of the scattering ratio i90 degrees/Io and the impact of erroneous turbidity measurements on derived molecular parameters is discussed.     

Alterations of filtration coefficients in pulmonary edema of different pathogenesis.

Different pathomechanisms in the development of pulmonary edema are being discussed. We investigated the effect of pathogenetically varying forms of edema on lung vascular barrier function in isolated cell-free perfused rabbit lungs. As an index of permeability, capillary filtration coefficients (Kfc) were determined from the slope of lung weight change over periods of stepwise venous pressure elevation (5, 7.5, and 10 mmHg) before (controls) and 60 min after edema induction. Edema was induced by venous congestion (n = 6), by application of arachidonic acid in the presence of diclofenac sodium (n = 6), and by elastase application (n = 6). Control values ranged from 0.28 to 0.51 ml.min-1 x mmHg-1 x 100 g-1. Kfc was significantly enhanced after edema induction up to 243% of control value in the hydrostatic edema, 357% in the arachidonic acid edema, and 594% in the elastase edema. When the alterations in capillary filtration due to the different types of edema were compared, Kfc was significantly higher in the proteinase edema, indicating an irreversibly damaged barrier function. These data exemplify different pathophysiological characteristics due to the pathogenesis of interstitial edema formation.     

The role of photon scattering in optical signal distortion during arrhythmia and defibrillation

Optical mapping of arrhythmias and defibrillation provides important insights; however, a limitation of the technique is signal distortion due to photon scattering. The goal of this experimental/simulation study is to investigate the role of three-dimensional photon scattering in optical signal distortion during ventricular tachycardia (VT) and defibrillation. A three-dimensional realistic bidomain rabbit ventricular model was combined with a model of photon transport. Shocks were applied via external electrodes to induce sustained VT, and transmembrane potentials (V(m)) were compared with synthesized optical signals (V(opt)). Fluorescent recordings were conducted in isolated rabbit hearts to validate simulation results. Results demonstrate that shock-induced membrane polarization magnitude is smaller in V(opt) and in experimental signals as compared to V(m). This is due to transduction of potentials from weakly polarized midmyocardium to the epicardium. During shock-induced reentry and in sustained VT, photon scattering, combined with complex wavefront dynamics, results in optical action potentials near a filament exhibiting i), elevated resting potential, ii), reduced amplitude relative to pacing, and iii), dual-humped morphologies. A shift of up to 4 mm in the phase singularity location was observed in V(opt) maps when compared to V(m). This combined experimental/simulation study provides an interpretation of optical recordings during VT and defibrillation.     

Platelet-activating factor receptor plays a role in lung injury and death caused by Influenza A in mice

Influenza A virus causes annual epidemics which affect millions of people worldwide. A recent Influenza pandemic brought new awareness over the health impact of the disease. It is thought that a severe inflammatory response against the virus contributes to disease severity and death. Therefore, modulating the effects of inflammatory mediators may represent a new therapy against Influenza infection. Platelet activating factor (PAF) receptor (PAFR) deficient mice were used to evaluate the role of the gene in a model of experimental infection with Influenza A/WSN/33 H1N1 or a reassortant Influenza A H3N1 subtype. The following parameters were evaluated: lethality, cell recruitment to the airways, lung pathology, viral titers and cytokine levels in lungs. The PAFR antagonist PCA4248 was also used after the onset of flu symptoms. Absence or antagonism of PAFR caused significant protection against flu-associated lethality and lung injury. Protection was correlated with decreased neutrophil recruitment, lung edema, vascular permeability and injury. There was no increase of viral load and greater recruitment of NK1.1(+) cells. Antibody responses were similar in WT and PAFR-deficient mice and animals were protected from re-infection. Influenza infection induces the enzyme that synthesizes PAF, lyso-PAF acetyltransferase, an effect linked to activation of TLR7/8. Therefore, it is suggested that PAFR is a disease-associated gene and plays an important role in driving neutrophil influx and lung damage after infection of mice with two subtypes of Influenza A. Further studies should investigate whether targeting PAFR may be useful to reduce lung pathology associated with Influenza A virus infection in humans.     

Slow excitation waves and mechanisms of polymorphic ventricular tachycardia in an experimental model: isolated walls of the right ventricle from rabbit and squirrel

The mechanism of polymorphic disturbances of the heart rhythm is studied on an experimental model, isolated ventricular preparations of ground squirrel and rabbit. Polymorphic arrhythmias are identified from habitus of the isolated preparation pseudoECGs mathematically derived from electrograms registered simultaneously at 32 endocardial and 32 epicardial points. The same electrograms allow one to visualize the excitation wave propagation along each of the preparation surfaces. The comparison of excitation wave pictures and corresponding pseudoECGs enabled us to reveal the conditions necessary and sufficient for polymorphism in heart rhythm disturbances. Polymorphic arrhythmias are due to changes in wave pictures in the regions of retarded excitation propagation.     

HIV model parameter estimates from interruption trial data including drug efficacy and reservoir dynamics

Mathematical models based on ordinary differential equations (ODE) have had significant impact on understanding HIV disease dynamics and optimizing patient treatment. A model that characterizes the essential disease dynamics can be used for prediction only if the model parameters are identifiable from clinical data. Most previous parameter identification studies for HIV have used sparsely sampled data from the decay phase following the introduction of therapy. In this paper, model parameters are identified from frequently sampled viral-load data taken from ten patients enrolled in the previously published AutoVac HAART interruption study, providing between 69 and 114 viral load measurements from 3-5 phases of viral decay and rebound for each patient. This dataset is considerably larger than those used in previously published parameter estimation studies. Furthermore, the measurements come from two separate experimental conditions, which allows for the direct estimation of drug efficacy and reservoir contribution rates, two parameters that cannot be identified from decay-phase data alone. A Markov-Chain Monte-Carlo method is used to estimate the model parameter values, with initial estimates obtained using nonlinear least-squares methods. The posterior distributions of the parameter estimates are reported and compared for all patients.