Transit time dispersion in the pulmonary arterial tree

Knowledge of the contributions of arterialand venous transit time dispersion to the pulmonary vascular transittime distribution is important for understanding lung function and forinterpreting various kinds of data containing information aboutpulmonary function. Thus, to determine the dispersion of blood transittimes occurring within the pulmonary arterial and venous trees, imagesof a bolus of contrast medium passing through the vasculature ofpump-perfused dog lung lobes were acquired by using an X-ray microfocalangiography system. Time-absorbance curves from the lobar artery andvein and from selected locations within the intrapulmonary arterial tree were measured from the images. Overall dispersion within the lunglobe was determined from the difference in the first and second moments(mean transit time and variance, respectively) of the inlet arterialand outlet venous time-absorbance curves. Moments at selected locationswithin the arterial tree were also calculated and compared with thoseof the lobar artery curve. Transit times for the arterial pathwaysupstream from the smallest measured arteries (200-µm diameter) wereless than ~20% of the total lung lobe mean transit time. Transittime variance among these arterial pathways (interpathway dispersion)was less than ~5% of the total variance imparted on the bolus as itpassed through the lung lobe. On average, the dispersion that occurredalong a given pathway (intrapathway dispersion) was negligible. Similar results were obtained for the venous tree. Taken together, the resultssuggest that most of the variation in transit time in theintrapulmonary vasculature occurs within the pulmonary capillary bedrather than in conducting arteries or veins.

     

The variance of transit times of indicators through a vascular bed

A new method is developed of determining the variance of the times of transit of an indicator through a vascular bed (or through any perfused organ) from the time-course of the arterial-venous concentration difference, observed between two steady states. The method is illustrated using previously published data on arterial and hepatic venous radioactivities following a single injection of ¹³¹I-labelled serum albumin in man.     

How well mixed is inert gas in tissues?

The washout of inert gas from tissues typically follows multiexponential curves rather than monoexponential curves as would be expected from homogeneous, well-mixed compartment. This implies that the ratio for the square root of the variance of the distribution of transit times to the mean (relative dispersion) must be greater than 1. Among the possible explanations offered for multiexponential curves are heterogeneous capillary flow, uneven capillary spacing, and countercurrent exchange in small veins and arteries. By means of computer simulations of the random walk of gas molecules across capillary beds with parameters of skeletal muscle, we find that heterogeneity involving adjacent capillaries does not suffice to give a relative dispersion greater than one. Neither heterogeneous flow, nor variations in spacing, nor countercurrent exchange between capillaries can account for the multiexponential character of experimental tissue washout curves or the large relative dispersions that have been measured. Simple diffusion calculations are used to show that many gas molecules can wander up to several millimeters away from their entry point during an average transit through a tissue bed. Analytical calculations indicate that an inert gas molecule in an arterial vessel will usually make its first vascular exit from a vessel larger than 20 micron and will wander in and out of tissue and microvessels many times before finally returning to the central circulation. The final exit from tissue will nearly always be into a vessel larger than 20 micron. We propose the hypothesis that the multiexponential character of skeletal muscle tissue inert gas washout curves must be almost entirely due to heterogeneity between tissue regions separated by 3 mm or more, or to countercurrent exchanges in vessels larger than 20 micron diam.     

A stochastic catch-effort method for estimating animal abundance

A method for estimating the size of a heavily exploited animal population from catch data and relative-harvest-effort data is presented. The method assumes a competing-risk model of adult deaths and captures that is similar to the hazard-regression model of Cox (1972, Journal of the Royal Statistical Society, Series B 34, 187-220). This model avoids making any assumptions about birth rates or juvenile mortality rates, and allows the user to incorporate an arbitrary number of time-dependent covariates into the natural and catch hazard functions. Estimates of the population's size, together with asymptotic error bounds and predictions of subsequent catches, are derived from maximum likelihood estimates of the parameters of the model. A simulation study is presented which indicates that this method is far more accurate than previously available catch-effort techniques. The method is illustrated with some fisheries data. A series of models is fitted to the data with the objective of improving the goodness of fit while maintaining biologic plausibility of the model. In this example a 68% reduction in the mean sum of squares for error is obtained and the accuracy of future catch predictions is greatly improved. This method is particularly appropriate for estimating the sizes of commercially exploited aquatic populations whose sizes are too large to make mark-recapture techniques feasible, and which are not amenable to line-transect techniques.     

State-vector models of the cell cycle 1. Parametrization and fits to labeled mitoses data

In this paper we study the Hahn model of the cell cycle from the point of view that a cell population's age distribution is more relevant to labeled mitoses data than is the distribution of its transit times.Closed-form relationships are derived between the transition probabilities of the Hahn model and the transit time of the mean of a cohort of labeled cells (with the variance of their transit time through mitosis). Constraints result which define the acceptable values for the number of ages in the state vector and the length of the time step (rarely does the dimension of the state vector equal the number of time steps in the generation time).A generalization to distinct probabilities for G₁, S and G₂M is presented, and the automatic fitting of fraction-labeled mitoses (FLM) data is described. The doubling time of the population is used to define the daughter factor, via the largest eigenvalue of the state transition matrix. The performance of the generalized Hahn model is compared to that of other commonly used fitting methods using two sets of FLM data from the literature. The synthesis of continuous labeling curves is discussed as an independent check of the parametrization. Based on the stable age distribution resulting from fits to experimental FLM data, it is shown that a nonlinear relationship exists between biological age and time.     

A mathematical model of indicator extraction by the pulmonary endothelium via saturation kinetics

When a bolus containing a nonpermeating indicator and an indicator which permeates the endothelial cell membrane by a saturable process is injected into the blood flowing into the lung, the instantaneous extraction ratio curves measured in the pulmonary venous outflow are asymmetric with respect to the nonpermeating indicator curve. If the bolus contains a sufficient quantity of the permeating indicator that the capillary concentration begins to saturate the transfort mechanism, the extraction ratio curves are concave upward as well. The purpose of this study was to determine whether a mathematical model which represents endothelial extraction by Michaelis-Menten kinetics could explain the time variation in the instantaneous extraction ratio curves. The venous concentration curves were assumed to be the result of the endothelial transfort and distributed capillary input and transit times. In addition, we evaluated a method for estimating the kinetic parameters (K_m and V_max) of the saturable transfort process in such an organ. The results of simulations indicate that the important features of the data can be reproduced by the model, and that useful estimates of the kinetic parameters will be obtained from linear multiple regression analysis of the venous concentration curves if the standard deviation of the capillary input time distribution is not less than that of the capillary transit time distribution.     

Pulmonary arterial transit times

To begin to characterize the pulmonary arterial transport function we rapidly injected a bolus containing a radiopaque dye and a fluorescence dye into the right atrium of anesthetized dogs. The concentrations of the dye indicators were measured in the main pulmonary artery (fluoroscopically) and in a subpleural pulmonary arteriole (by fluorescence microscopy). The resulting concentration vs. time curves were subjected to numerical deconvolution and moment analysis to determine how the bolus was dispersed as it traveled through the arteriole stream tube from the main pulmonary artery to the arteriole. The mean transit time and standard deviation of the transport function from the main pulmonary artery to the arterioles studied averaged 1.94 and 1.23 s, respectively, and the relative dispersion (ratio of standard deviation to mean transit time) was approximately 64%. This relative dispersion is at least as large as those reported for the whole dog lung, indicating that relative to their respective mean transit times the dispersion upstream from the arterioles is comparable to that taking place in capillaries and/or veins. The standard deviations of the transport functions were proportional to their mean transit times. Thus the relative dispersion from the main pulmonary artery to the various arterioles studied was fairly consistent. However, there were variations in mean transit time even between closely adjacent arterioles, suggesting that variations in mean transit times between arteriole stream tubes also contribute to the dispersion in the pulmonary arterial tree.     

Transit times through the cycle phases of jejunal crypt cells of the mouse. Analysis in terms of the mean values and the variances.

Mean transit times as well as variances of the transit times through the individual phases of the cell cycle have been determined for the crypt epithelial cells of the jejunum of the mouse. To achieve this the fraction of labelled mitoses (FLM) technique has been modified by double labelling with [3H] and [14C]thymidine. Mice were given a first injection of [3H]thymidine, and 2 hr later a second injection of [14C]thymidine. This produces a narrow subpopulation of purely 3H-labelled cells at the beginning of G2-phase and a corresponding subpopulation of purely 14C-labelled cells at the beginning of the S-phase. When these two subpopulations progress through the cell cycle, one obtains FLM waves of purely 3H- and purely 14C-labelled mitoses. These waves have considerably better resolution than the conventional FLM-curves. From the temporal positions of the observed maxima the mean transit times of the cells through the individual phases of the cycle can be determined. Moreover one obtains from the width of the individual waves the variances of the transit times through the individual phases. It has been found, that the variances of the transit times through successive phases are additive. This indicates that the transit times of cells through successive phases are independently distributed. This statistical independence is an implicit assumption in most of the models applied to the analysis of FLM curves, however there had previously been no experimental support of this assumption. A further result is, that the variance of the transit time through any phase of the cycle is proportional to the mean transit time. This implies that the progress of the crypt epithelial cells is subject to an equal degree of randomness in the various phases of the cycle.     

Response to Comment on “Retinal pulse wave velocity measurement using spectral‐domain optical coherence tomography”

Spahr et al. recently commented on our latest paper “Retinal pulse wave velocity measurement using spectral‐domain optical coherence tomography” with a conclusion that the measured retinal pulse wave velocity (rPWV) in our paper was contradictory to theoretical predictions and previously published results. However, the theoretical predictions by Spahr et al. based on Moens‐Korteweg equation are questionable, since the Moens‐Korteweg equation should not be used for small arteries like retinal arteries. Previously, various measurements of rPWV using different technologies have been reported. The results on human and rats are not consistent. As the rPWV is an unknown value, we argue that the time delay derived between 2 arterial sites should be verified to see if the delay truly represents the pulse wave transit time. In the future, special emphasis should be placed on demonstration of the reproducibility of technologies and data analysis of large samples.     

O2 exchange between blood and brain tissues studied with 18O2 indicator-dilution technique

A technique has been developed to record 18O2 dilution curves of an organ in vivo by use of 51Cr-labeled erythrocytes as a reference tracer. The technique employs anaerobic sampling of venous outflow following an intraarterial injection of tracer-laden blood and off-line determination of [18O2] and [51Cr] profiles in the venous outflow. O2 and reference indicator-dilution curves of cerebral circulation were recorded in eight experiments with six halothane-anesthetized dogs. Autologous blood labeled with the tracers was injected into a carotid artery, and brain venous outflow was sampled from the sagittal sinus. The total net extraction of O2 tracer was equal to the extraction of elemental O2. Instantaneous extraction of 18O2 along the outflow curve fell linearly with time, from an initial value of 0.6-0.7 to very small or even negative values toward the end of a pulse. This indicates that O2 undergoes a flow-limited distribution. In all experiments, the mean transit time of unmetabolized 18O2 was longer than the mean transit time of the Cr tracer. An index of the tissue O2 dilution space, hence the mean tissue PO2, is calculated from this data with the use of a modified central volume principle. This estimate of mean tissue PO2 increases as a linear function of sagittal sinus PO2 with a slope of 0.97. The method may provide an index of the critical PO2 of venous blood, the PO2 below which O2 diffusion from blood to tissue may limit its rate of metabolic uptake.     

Arterial and venous circulation of the leg after intermittent venous occlusion

We study the arterial and venous circulation of the normal leg by strain gauge plethysmography and venous occlusion (thigh tourniquet). We propose the application of a simplified linear physical model of the venous circulation. It helps to analyse the plethysmographic data recorded during and after the congestion. It ignores the arterial inflow and consider the post-occlusive venous volume decay in function of time as being monoexponential. The venous compliance (C) is measured when the volume has reached a steady-state level during the congestion (known pressure). The time-constant (T) characterizes the volume decay in function of time when the occlusion is released. The tourniquet is successively inflated with two levels of pressure (30 and 60 mm Hg) in order to check if the system is actually linear as predicted by the model. The venous outflow is not strictly monoexponential and the model is only suitable to describe the beginning of the curve. The compliance does not behave linearly, the values measured at 30 mm Hg, being higher than at 60 mm Hg ($ 26%). The time-constant T is slightly influenced by the level of pressures. The calculated resistance is therefore lower at low pressure. We also study the arterial inflow before and after the venous congestion (3 min, 60 mm Hg). We observe a post-venous occlusion hyperaemia (mean rest flow: 5.2%/min, mean hyperemic flow: 12.1%/min) followed by a drop of the inflow (mean minimal flow: 3.4%/min). We evaluate the quantitative influence of neglecting the arterial inflow on the computing of the venous properties. The simplification appears acceptable.     

Coincidence detectors and two-pulse visual temporal integration: new theoretical results and comparison with data

Exact predictions for two-pulse visual temporal integration data are derived from the Bouman-van der Velden quantum coincidence model for threshold vision. The predictions of the model start with complete summation for superposed pulses, then pass to a transition zone of partial integration, and finally reach the level of probability summation for pulses presented with large interstimulus intervals. From our results we can clearly reject the assumption of constant integration times with the basic model. We thus generalize the coincidence model to allow for variable integration times, derive the corresponding predictions for two-pulse integration data, and compare these predictions to published data currently available. It is shown that detectors of low order of coincidence generally underestimate the actual reduction of threshold intensity (or equivalently the corresponding increase of the detection probability) for two pulses as compared to the singlepulse performance.     

Pulmonary clearance of radiotracers after positive end-expiratory pressure or acute lung injury

In anesthetized rabbits we measured clearance from lung to blood of eight aerosolized technetium-99m-labeled compounds: diethylenetriaminepentaacetate (99mTc-DTPA); cytochrome c; myoglobin; a myoglobin polymer; albumin; and anionic, cationic, and neutral dextrans of equivalent molecular size. We investigated the effect of applying positive end-expiratory pressure (PEEP) and, on a subsequent occasion, of injecting oleic acid intravenously to produce acute lung injury on the pulmonary clearance rate. Base-line clearance rates were monoexponential and varied with the molecular weights of the radiotracers. For each tracer the rate of clearance was increased a similar degree by either PEEP or oleic acid. However, with PEEP, clearance remained monoexponential, whereas after oleic acid, smaller molecular-weight radiotracers had multiexponential clearance curves. This suggests that after oleic acid the alveolar epithelium breaks down in a nonuniform fashion. We conclude that differentiation of the effect of PEEP from that of severe lung injury caused by oleic acid is not readily accomplished by either increasing the size of the tracer molecule or by varying the molecular charge.     

Transit time dispersion in pulmonary and systemic circulation: effects of cardiac output and solute diffusivity

We present an in vivo method for analyzing the distribution kinetics of physiological markers into their respective distribution volumes utilizing information provided by the relative dispersion of transit times. Arterial concentration-time curves of markers of the vascular space [indocyanine green (ICG)], extracellular fluid (inulin), and total body water (antipyrine) measured in awake dogs under control conditions and during phenylephrine or isoproterenol infusion were analyzed by a recirculatory model to estimate the relative dispersions of transit times across the systemic and pulmonary circulation. The transit time dispersion in the systemic circulation was used to calculate the whole body distribution clearance, and an interpretation is given in terms of a lumped organ model of blood-tissue exchange. As predicted by theory, this relative dispersion increased linearly with cardiac output, with a slope that was inversely related to solute diffusivity. The relative dispersion of the flow-limited indicator antipyrine exceeded that of ICG (as a measure of intravascular mixing) only slightly and was consistent with a diffusional equilibration time in the extravascular space of approximately 10 min, except during phenylephrine infusion, which led to an anomalously high relative dispersion. A change in cardiac output did not alter the heterogeneity of capillary transit times of ICG. The results support the view that the relative dispersions of transit times in the systemic and pulmonary circulation estimated from solute disposition data in vivo are useful measures of whole body distribution kinetics of indicators and endogenous substances. This is the first model that explains the effect of flow and capillary permeability on whole body distribution of solutes without assuming well-mixed compartments.     

Future perspectives: What lies ahead for Neuronal Ceroid Lipofuscinosis research?

Progress is being made in all aspects of Neuronal Ceroid Lipofuscinosis (NCL) research, resulting in many recent advances. These advances encompass several areas that were previously thought intractable, ranging from basic science, through to a better understanding of the clinical presentation of different forms of NCL, therapeutic development, and new clinical trials that are underway. Increasing numbers of original NCL research papers continue to be published, and this new sense of momentum is greatly encouraging for the field. Here, we make some predictions as to what we can anticipate in the next few years.     

TRANSIT TIMES THROUGH THE CYCLE PHASES OF JEJUNAL CRYPT CELLS OF THE MOUSE ANALYSIS IN TERMS OF THE MEAN VALUES AND THE VARIANCES

Mean transit times as well as variances of the transit times through the individual phases of the cell cycle have been determined for the crypt epithelial cells of the jejunum of the mouse. To achieve this the fraction of labelled mitoses (FLM) technique has been modified by double labelling with [³H] and [¹⁴C]thymidine. Mice were given a first injection of [³H]thymidine, and 2 hr later a second injection of [¹⁴C]thymidine. This produces a narrow subpopulation of purely ³H-labelled cells at the beginning of G₂-phase and a corresponding subpopulation of purely ¹⁴C-labelled cells at the beginning of the S-phase. When these two subpopulations progress through the cell cycle, one obtains FLM waves of purely ³H- and purely ¹⁴C-labelled mitoses. These waves have considerably better resolution than the conventional FLM-curves. From the temporal positions of the observed maxima the mean transit times of the cells through the individual phases of the cycle can be determined. Moreover one obtains from the width of the individual waves the variances of the transit times through the individual phases. It has been found, that the variances of the transit times through successive phases are additive. This indicates that the transit times of cells through successive phases are independently distributed. This statistical independence is an implicit assumption in most of the models applied to the analysis of FLM curves, however there had previously been no experimental support of this assumption. A further result is, that the variance of the transit time through any phase of the cycle is proportional to the mean transit time. This implies that the progress of the crypt epithelial cells is subject to an equal degree of randomness in the various phases of the cycle.     

Coulomb Interactions between Cytoplasmic Electric Fields and Phosphorylated Messenger Proteins Optimize Information Flow in Cells

Background

Normal cell function requires timely and accurate transmission of information from receptors on the cell membrane (CM) to the nucleus. Movement of messenger proteins in the cytoplasm is thought to be dependent on random walk. However, Brownian motion will disperse messenger proteins throughout the cytosol resulting in slow and highly variable transit times. We propose that a critical component of information transfer is an intracellular electric field generated by distribution of charge on the nuclear membrane (NM). While the latter has been demonstrated experimentally for decades, the role of the consequent electric field has been assumed to be minimal due to a Debye length of about 1 nanometer that results from screening by intracellular Cl⁻ and K⁺. We propose inclusion of these inorganic ions in the Debye-Huckel equation is incorrect because nuclear pores allow transit through the membrane at a rate far faster than the time to thermodynamic equilibrium. In our model, only the charged, mobile messenger proteins contribute to the Debye length.

Findings

Using this revised model and published data, we estimate the NM possesses a Debye-Huckel length of a few microns and find this is consistent with recent measurement using intracellular nano-voltmeters. We demonstrate the field will accelerate isolated messenger proteins toward the nucleus through Coulomb interactions with negative charges added by phosphorylation. We calculate transit times as short as 0.01 sec. When large numbers of phosphorylated messenger proteins are generated by increasing concentrations of extracellular ligands, we demonstrate they generate a self-screening environment that regionally attenuates the cytoplasmic field, slowing movement but permitting greater cross talk among pathways. Preliminary experimental results with phosphorylated RAF are consistent with model predictions.

Conclusion

This work demonstrates that previously unrecognized Coulomb interactions between phosphorylated messenger proteins and intracellular electric fields will optimize information transfer from the CM to the NM in cells.     

Regional pulmonary transit times in humans

We measured the frequency distribution of erythrocyte (RBC) transit times in resected lobes of lungs in eight human subjects undergoing thoracotomy for peripheral lung tumors. RBC transit times were measured by the injection of radiolabeled blood flow and volume markers, which were counted in samples from the resected lung. In five of these subjects, the measurements from the resected lung were compared with preoperative measurements of the transit times of radiolabeled RBCs with a gamma camera-computer system. Time-activity curves from the cardiac chambers and the lung or its regions were obtained from which transit times were calculated by the centroid and deconvolution techniques. The reproducibility of transit times measured by this technique was assessed in another eight normal subjects, after sequential bolus injections of radiolabeled cells. The mean transit time of the upper lung region was longer (5.1 +/- 0.5 s) than that of the lower (4.1 +/- 0.6 s, P less than 0.05) in the preoperative study. Similarly, the mean transit time of the upper lung slice was longer (5.5 +/- 0.3 s) than that of the lower slice (3.8 +/- 0.3 s, P less than 0.05) in the resected lung specimens. We conclude that there was good agreement between these techniques and that there are long transit times in the upper regions of human lungs.     

Repair between dose fractions: a simpler method of analyzing and reporting apparently biexponential repair

Increasing numbers of animal experiments in situ are reporting that repair of sublethal radiation damage in vivo slows down with time, usually described as two components of (monoexponential) repair. For repair of DNA strand breaks, plotting the reciprocal of proportion unrepaired as a function of time yielded straight lines. Two processes have been suggested as causing this: (1) a second-order process (bimolecular) instead of first-order (exponential) and (2) a skewed distribution of monoexponential rates. The present paper investigates whether such plots of hyperbolic or reciprocal repair are relevant for laboratory animal tissue results. Published repair data were reanalyzed from laboratory animal experiments that employed split doses or two fractions per day. Graphs are presented of the reciprocal proportion of damage remaining as a function of the interval between the two doses. If the reciprocal model applies, the graphs would be straight lines. Different animal data showed no inconsistency with straight reciprocal plots. These reciprocal plots describe well with one parameter tau, the first half-time, repair curves previously thought to be "biexponential", and to require three parameters. Straight reciprocal plots mean that in a constant time interval tau the unrepaired damage falls from 1 to (1/2), then from (1/2) to (1/3), then (1/3) to (1/4), etc. A much larger proportion of damage would therefore remain unrepaired at several half-times than is estimated by current mono- or biexponential models. The practical implications for clinical radiotherapy are important.     

Vertical gradient of pulmonary capillary transit times

The key determinants of alveolar capillary perfusion are transit times and the extent of recruitment. Capillaries are known to be heavily recruited in the dependent lung, but there are no direct data that bear on how capillary transit times might be affected by gravity. We directly determined mean capillary transit times on the surface of the upper, middle, and lower lung by measuring the passage of fluorescent dye through the capillaries using in vivo television microscopy. In anesthetized dogs, mean capillary transit times averaged 12.3 s in the upper lung, 3.1 s in the midlung, and 1.6 s in the lower lung. This near order of magnitude variation in speed of blood transit establishes that there is a vertical gradient of capillary transit times in the lung. As expected, dependent capillary networks were nearly fully recruited, whereas relatively few capillaries were perfused in the upper lung. The lengthy transit times and sparsely perfused capillary beds in the upper lung combine to provide a substantial part of pulmonary gas exchange reserve.