Predicting Patient Status in Chronic Thromboembolic Pulmonary Hypertension Using a Biophysical Model.

Chronic thromboembolic pulmonary hypertension (CTEPH) involves abnormally high blood pressure in the pulmonary vessels and is associated with small vessel vasculopathy and pre-capillary proximal occlusions. Management of CTEPH disease is challenging, therefore accurate diagnosis is crucial in ensuring effective treatment and improved patient outcomes. The treatment of choice for CTEPH is pulmonary endarterectomy, which is an invasive surgical intervention to remove thrombi. Following PEA, a number of patients experience poor outcomes or worse-than-expected improvements, which may indicate that they have significant small vessel disease. A method that can predict the extent of distal remodelling may provide useful clinical information to plan appropriate CTEPH patient treatment. Here, a novel biophysical modelling approach has been developed to estimate and quantify the extent of distal remodelling. This method includes a combination of mathematical modelling and computed tomography pulmonary angiography to first model the geometry of the pulmonary arteries and to identify the under-perfused regions in CTEPH. The geometric model is then used alongside haemodynamic measurements from right heart catheterisation to predict distal remodelling. In this study, the method is tested and validated using synthetically generated remodelling data. Then, a preliminary application of this technique to patient data is shown to demonstrate the potential of the approach for use in the clinical setting.Clinical relevance- Patient-specific modelling can help provide useful information regarding the extent of distal vasculopathy on a per-patient basis, which remains challenging. Physicians can be unsure of outcomes following pulmonary endarterectomy. Therefore, the predictive aspect of the patient's response to surgery can help with clinical decision-making.

An in silico approach to understanding the interaction between cardiovascular and pulmonary lymphatic dysfunction.

The lung is extremely sensitive to interstitial fluid balance, yet the role of pulmonary lymphatics in lung fluid homeostasis and its interaction with cardiovascular pressures is poorly understood. In health, there is a fine balance between fluid extravasated from the pulmonary capillaries into the interstitium and the return of fluid to the circulation via the lymphatic vessels. This balance is maintained by an extremely interdependent system governed by pressures in the fluids (air and blood) and tissue (interstitium), lung motion during breathing, and the permeability of the tissues. Chronic elevation in left atrial pressure (LAP) due to left heart disease increases the capillary blood pressure. The consequent fluid accumulation in the delicate lung tissue increases its weight, decreases its compliance, and impairs gas exchange. This interdependent system is difficult, if not impossible, to study experimentally. Computational modeling provides a unique perspective to analyze fluid movement in the cardiopulmonary vasculature in health and disease. We have developed an initial in silico model of pulmonary lymphatic function using an anatomically structured model to represent ventilation and perfusion and underlying biophysical laws governing fluid transfer at the interstitium. This novel model was tested against increased LAP and noncardiogenic effects (increased permeability). The model returned physiologically reasonable values for all applications, predicting pulmonary edema when LAP reached 25 mmHg and with increased permeability.NEW & NOTEWORTHY This model presents a novel approach to understanding the interaction between cardiac dysfunction and pulmonary lymphatic function, using anatomically structured models and biophysical equations to estimate regional variation in fluid transport from blood to interstitial and lymphatic flux. This fluid transport model brings together advanced models of ventilation, perfusion, and lung mechanics to produce a detailed model of fluid transport in health and various altered pathological conditions.

In Silico Ventilation Within the Dose-Volume is Predictive of Lung Function Post-radiation Therapy in Patients with Lung Cancer.

Lung cancer is a leading cause of death worldwide. Radiation therapy (RT) is one method to treat this disease. A common side effect of RT for lung cancer is radiation-induced lung damage (RILD) which leads to loss of lung function. RILD often compounds pre-existing smoking-related regional lung function impairment. It is difficult to predict patient outcomes due to large variability in individual response to RT. In this study, the capability of image-based modelling of regional ventilation in lung cancer patients to predict lung function post-RT was investigated. Twenty-five patient-based models were created using CT images to define the airway geometry, size and location of tumour, and distribution of emphysema. Simulated ventilation within the 20 Gy isodose volume showed a statistically significant negative correlation with the change in forced expiratory volume in 1 s 12-months post-RT (p = 0.001, R = - 0.61). Patients with higher simulated ventilation within the 20 Gy isodose volume had a greater loss in lung function post-RT and vice versa. This relationship was only evident with the combined impact of tumour and emphysema, with the location of the emphysema relative to the dose-volume being important. Our results suggest that model-based ventilation measures can be used in the prediction of patient lung function post-RT.

Inspiratory respiratory mechanics estimation by using expiratory data for reverse-triggered breathing cycles.

BACKGROUND AND OBJECTIVE: Model-based lung mechanics monitoring can provide clinically useful information for guiding mechanical ventilator treatment in intensive care. However, many methods of measuring lung mechanics are not appropriate for both fully and partially sedated patients, and are unable provide lung mechanics metrics in real-time. This study proposes a novel method of using lung mechanics identified during passive expiration to estimate inspiratory lung mechanics for spontaneously breathing patients. METHODS: Relationships between inspiratory and expiratory modeled lung mechanics were identified from clinical data from 4 fully sedated patients. The validity of these relationships were assessed using data from a further 4 spontaneously breathing patients. RESULTS: For the fully sedated patients, a linear relationship was identified between inspiratory and expiratory elastance, with slope 1.04 and intercept 1.66. The r value of this correlation was 0.94. No cohort-wide relationship was determined for airway resistance. Expiratory elastance measurements in spontaneously breathing patients were able to produce reasonable estimates of inspiratory elastance after adjusting for the identified difference between them. CONCLUSIONS: This study shows that when conventional methods fail, typically ignored expiratory data may be able to provide clinicians with the information needed about patient condition to guide MV therapy.

The Lung Physiome and virtual patient models: From morphometry to clinical translation.

The understanding or prediction of specific functions of the lung can be made using compact models that have identifiable parameters and that are custom designed to the problem of interest. However, when structure contributes to function - as is the case with most lung pathologies - structure-based, biophysical models become essential. Here we describe the application of structure-based models within the lung Physiome framework to identifying and explaining patient risk in 12patients diagnosed with acute pulmonary embolism. The model integrates perfusion, ventilation, and gas exchange to predict arterial blood gases and pulmonary artery pressure in individual patient models in response to patient-specific blood clot distribution, with full or partial arterial occlusion. The necessity for a patient-specific approach with biophysical models that account for scale-specific structure and function is demonstrated.

Do Pulmonary Cavity Shapes Influence Lung Function?

Distribution of lung tissue within the chest cavity is a key contributor to delivery of both blood and air to the gas exchange regions of the lung. This distribution is multifactorial with influences from parenchyma, gravity, and level of inflation. We hypothesize that the manner in which lung inflates, for example, the primarily diaphragmatic nature of normal breathing, is an important contributor to regional lung tissue distribution. To investigate this hypothesis, we present an organ-level model of lung tissue mechanics, which incorporates pleural cavity change due to change in lung volume or posture. We quantify the changes using shape and density metrics in ten healthy subjects scanned supine at end-inspiratory and end-expiratory volumes and ten subjects scanned at both supine and prone end-inspiratory volumes. Comparing end-expiratory to end-inspiratory volume, we see primarily a change in the cranial-caudal dimension of the lung, reflective of movement of diaphragm. In the diaphragmatic region, there is greater regional lung expansion than in the cranial aspect, which is restricted by the chest wall. When moving from supine to prone, a restriction of lung was observed anteriorly, resulting in a generally reduced lung volume and a redistribution of air volume posteriorly. In general, we see the highest in lung tissue density heterogeneity in regions of the lung that are most inflated. Using our computational model, we quantify the impact of pleural cavity shape change on regional lung distribution and predict the impact on regional elastic recoil pressure.

A virtual patient model for mechanical ventilation.

BACKGROUND AND OBJECTIVES: Mechanical ventilation (MV) is a primary therapy for patients with acute respiratory failure. However, poorly selected ventilator settings can cause further lung damage due to heterogeneity of healthy and damaged alveoli. Varying positive-end-expiratory-pressure (PEEP) to a point of minimum elastance is a lung protective ventilator strategy. However, even low levels of PEEP can lead to ventilator induced lung injury for individuals with highly inflamed pulmonary tissue. Hence, models that could accurately predict peak inspiratory pressures after changes to PEEP could improve clinician confidence in attempting potentially beneficial treatment strategies. METHODS: This study develops and validates a physiologically relevant respiratory model that captures elastance and resistance via basis functions within a well-validated single compartment lung model. The model can be personalised using information available at a low PEEP to predict lung mechanics at a higher PEEP. Proof of concept validation is undertaken with data from four patients and eight recruitment manoeuvre arms. RESULTS: Results show low error when predicting upwards over the clinically relevant pressure range, with the model able to predict peak inspiratory pressure with less than 10% error over 90% of the range of PEEP changes up to 12 cmH2O. CONCLUSIONS: The results provide an in-silico model-based means of predicting clinically relevant responses to changes in MV therapy, which is the foundation of a first virtual patient for MV.

Metrics of lung tissue heterogeneity depend on BMI but not age.

Altered parenchymal microstructure and complexity have been observed in older age. How to distinguish between healthy, expected changes and early signs of pathology remains poorly understood. An objective quantitative analysis of computed tomography imaging was conducted to compare mean lung density, tissue density distributions, and tissue heterogeneity in 16 subjects, 8 aged >60 yr who were gender and body mass index matched with 8 subjects aged <30 yr. Subjects had never been smokers, with no prior respiratory disease, and no radiologically identified abnormalities on computed tomography. Volume-controlled breath hold imaging acquired at 80% vital capacity (end inspiration) and 55% vital capacity (end expiration) were used for analysis. Mean lung density was not different between the age groups at end inspiration ( P = 0.806) but was larger in the younger group at end expiration (0.26 ± 0.033 vs. 0.22 ± 0.026, P = 0.008), as is expected due to increased air trapping in the older population. However, gravitational gradients of tissue density did not differ with age; the only difference in distribution of tissue density between the two age groups was a lower density in the apices of the older group at end expiration. The heterogeneity of the lung tissue assessed using two metrics showed significant differences between end inspiration and end expiration, no dependence on age, and a significant relationship with body mass index at both lung volumes when heterogeneity was calculated using quadtree decomposition but only at end expiration when using a fractal dimension. NEW & NOTEWORTHY Changes to lung tissue heterogeneity can be a normal part of aging but can also be an early indicator of disease. We use novel techniques, which have previously not been used on thoracic computed tomography imaging, to quantify lung tissue heterogeneity in young and old healthy subjects. Our results show no dependence on age but a significant correlation with body mass index.

Gravity outweighs the contribution of structure to passive ventilation-perfusion matching in the supine adult human lung.

Gravity and matched airway/vascular tree geometries are both hypothesized to be key contributors to ventilation-perfusion (V̇/Q̇) matching in the lung, but their relative contributions are challenging to quantify experimentally. We used a structure-based model to conduct an analysis of the relative contributions of tissue deformation (the "Slinky" effect), other gravitational mechanisms (weight of blood and gravitational gradient in tissue elastic recoil), and matched airway and arterial tree geometry to V̇/Q̇ matching and therefore to total lung oxygen exchange. Our results showed that the heterogeneity in V̇ and Q̇ were lowest and the correlation between V̇ and Q̇ was highest when the only mechanism for V̇/Q̇ matching was either tissue deformation or matched geometry. Heterogeneity in V̇ and Q̇ was highest and their correlation was poorest when all mechanisms were active (that is, at baseline). Eliminating the contribution of matched geometry did not change the correlation between V̇ and Q̇ at baseline. Despite the much larger heterogeneities in V̇ and Q̇ at baseline, the contribution of in-common (to V̇ and Q̇) gravitational mechanisms provided sufficient compensatory V̇/Q̇ matching to minimize the impact on oxygen transfer. In summary, this model predicts that during supine normal breathing under gravitational loading, passive V̇/Q̇ matching is predominantly determined by shared gravitationally induced tissue deformation, compliance distribution, and the effect of the hydrostatic pressure gradient on vessel and capillary size and blood pressures. Contribution from the matching airway and arterial tree geometries in this model is minor under normal gravity in the supine adult human lung. NEW & NOTEWORTHY We use a computational model to systematically analyze contributors to ventilation-perfusion matching in the lung. The model predicts that the multiple effects of gravity are the predominant mechanism in providing passive ventilation-perfusion matching in the supine adult human lung under normal gravitational loads, while geometric matching of airway and arterial trees plays a minor role.

Evidence for age-dependent air-space enlargement contributing to loss of lung tissue elastic recoil pressure and increased shear modulus in older age.

As a normal part of mature aging, lung tissue undergoes microstructural changes such as alveolar air-space enlargement and redistribution of collagen and elastin away from the alveolar duct. The older lung also experiences an associated decrease in elastic recoil pressure and an increase in specific tissue elastic moduli, but how this relates mechanistically to microstructural remodeling is not well-understood. In this study, we use a structure-based mechanics analysis to elucidate the contributions of age-related air-space enlargement and redistribution of elastin and collagen to loss of lung elastic recoil pressure and increase in tissue elastic moduli. Our results show that age-related geometric changes can result in reduction of elastic recoil pressure and increase in shear and bulk moduli, which is consistent with published experimental data. All elastic moduli were sensitive to the distribution of stiffness (representing elastic fiber density) in the alveolar wall, with homogenous stiffness near the duct and through the septae resulting in a more compliant tissue. The preferential distribution of elastic proteins around the alveolar duct in the healthy young adult lung therefore provides for a more elastic tissue.NEW & NOTEWORTHY We use a structure-based mechanics analysis to correlate air-space enlargement and redistribution of elastin and collagen to age-related changes in the mechanical behavior of lung parenchyma. Our study highlights that both the cause (redistribution of elastin and collagen) and the structural effect (alveolar air-space enlargement) contribute to decline in lung tissue elastic recoil with age; these results are consistent with published data and provide a new avenue for understanding the mechanics of the older lung.

Multiscale modelling of the feto-placental vasculature.

The placenta provides all the nutrients required for the fetus through pregnancy. It develops dynamically, and, to avoid rejection of the fetus, there is no mixing of fetal and maternal blood; rather, the branched placental villi 'bathe' in blood supplied from the uterine arteries. Within the villi, the feto-placental vasculature also develops a complex branching structure in order to maximize exchange between the placental and maternal circulations. To understand the development of the placenta, we must translate functional information across spatial scales including the interaction between macro- and micro-scale haemodynamics and account for the effects of a dynamically and rapidly changing structure through the time course of pregnancy. Here, we present steps towards an anatomically based and multiscale approach to modelling the feto-placental circulation. We assess the effect of the location of cord insertion on feto-placental blood flow resistance and flow heterogeneity and show that, although cord insertion does not appear to directly influence feto-placental resistance, the heterogeneity of flow in the placenta is predicted to increase from a 19.4% coefficient of variation with central cord insertion to 23.3% when the cord is inserted 2 cm from the edge of the placenta. Model geometries with spheroidal and ellipsoidal shapes, but the same volume, showed no significant differences in flow resistance or heterogeneity, implying that normal asymmetry in shape does not affect placental efficiency. However, the size and number of small capillary vessels is predicted to have a large effect on feto-placental resistance and flow heterogeneity. Using this new model as an example, we highlight the importance of taking an integrated multi-disciplinary and multiscale approach to understand development of the placenta.

Hypoxic pulmonary vasoconstriction as a contributor to response in acute pulmonary embolism.

Hypoxic pulmonary vasoconstriction (HPV) is an adaptive response unique to the lung whereby blood flow is diverted away from areas of low alveolar oxygen to improve ventilation-perfusion matching and resultant gas exchange. Some previous experimental studies have suggested that the HPV response to hypoxia is blunted in acute pulmonary embolism (APE), while others have concluded that HPV contributes to elevated pulmonary blood pressures in APE. To understand these contradictory observations, we have used a structure-based computational model of integrated lung function in 10 subjects to study the impact of HPV on pulmonary hemodynamics and gas exchange in the presence of regional arterial occlusion. The integrated model includes an experimentally-derived model for HPV. Its function is validated against measurements of pulmonary vascular resistance in normal subjects at four levels of inspired oxygen. Our results show that the apparently disparate observations of previous studies can be explained within a single model: the model predicts that HPV increases mean pulmonary artery pressure in APE (by 8.2 ± 7.0% in these subjects), and concurrently shows a reduction in response to hypoxia in the subjects who have high levels of occlusion and therefore maximal HPV in normoxia.

Lack of functional information explains the poor performance of 'clot load scores' at predicting outcome in acute pulmonary embolism.

Clot load scores have previously been developed with the goal of improving prognosis in acute pulmonary embolism (PE). These scores provide a simple estimate of pulmonary vascular bed obstruction, however they have not been adopted clinically as they have poor correlation with mortality and right ventricular (RV) dysfunction. This study performed a quantitative analysis of blood flow and gas exchange in 12 patient-specific models of PE, to understand the limitations of current clot load scores and how their prognostic value could be improved. Prediction of hypoxemia in the models when using estimated baseline (non-occluded) minute ventilation and cardiac output correlated closely with clinical metrics for RV dysfunction, whereas the clot load score had only a weak correlation. The model predicts that large central clots have a greater impact on function than smaller distributed clots with the same total clot load, and that the partial occlusion of a vessel only has a significant impact on pulmonary function when the vessel is close to completely occluded. The effect of clot distribution on the redistribution of blood from its normal pattern - and hence the magnitude of the potential effect on gas exchange - is represented in the model but is not included in current clot load scores. Improved scoring systems need to account for the expected normal distribution of blood in the lung, and the impact of clot on redistributing the blood flow.

Quantifying tissue heterogeneity using quadtree decomposition.

Volumetric computed tomography (CT) imaging provides a three-dimensional map of image intensities from which lung soft tissue density distribution can be estimated. The information gained from analyzing these images can prove valuable in diagnosis of conditions where lung tissue is damaged or has degenerated, and it is also necessary for modeling lung tissue mechanics. This paper presents a new technique for quantifying heterogeneity based on individual CT images, and investigates the heterogeneity of lung tissue in a group of healthy young subjects. It is intended that development of this technique leads to a standard model of classifying heterogeneity in lung tissue, while taking into account variables such as different imaging platforms and resolutions, and the position of the patient during imaging.

Blood flow redistribution and ventilation-perfusion mismatch during embolic pulmonary arterial occlusion.

Acute pulmonary embolism causes redistribution of blood in the lung, which impairs ventilation/perfusion matching and gas exchange and can elevate pulmonary arterial pressure (PAP) by increasing pulmonary vascular resistance (PVR). An anatomically-based multi-scale model of the human pulmonary circulation was used to simulate pre- and post-occlusion flow, to study blood flow redistribution in the presence of an embolus, and to evaluate whether reduction in perfused vascular bed is sufficient to increase PAP to hypertensive levels, or whether other vasoconstrictive mechanisms are necessary. A model of oxygen transfer from air to blood was included to assess the impact of vascular occlusion on oxygen exchange. Emboli of 5, 7, and 10 mm radius were introduced to occlude increasing proportions of the vasculature. Blood flow redistribution was calculated after arterial occlusion, giving predictions of PAP, PVR, flow redistribution, and micro-circulatory flow dynamics. Because of the large flow reserve capacity (via both capillary recruitment and distension), approximately 55% of the vasculature was occluded before PAP reached clinically significant levels indicative of hypertension. In contrast, model predictions showed that even relatively low levels of occlusion could cause localized oxygen deficit. Flow preferentially redistributed to gravitationally non-dependent regions regardless of occlusion location, due to the greater potential for capillary recruitment in this region. Red blood cell transit times decreased below the minimum time for oxygen saturation (<0.25 s) and capillary pressures became high enough to initiate cell damage (which may result in edema) only after ~80% of the lung was occluded.

Pulmonary embolism: predicting disease severity.

Pulmonary embolism (PE) is the most common cause of acute pulmonary hypertension, yet it is commonly undiagnosed, with risk of death if not recognized promptly and managed accordingly. Patients typically present with hypoxemia and hypomania, although the presentation varies greatly, being confounded by co-morbidities such as pre-existing cardio-respiratory disease. Previous studies have demonstrated variable patient outcomes in spite of similar extent and distribution of pulmonary vascular occlusion, but the path physiological determinants of outcome remain unclear. Computational models enable exact control over many of the compounding factors leading to functional outcomes and therefore provide a useful tool to understand and assess these mechanisms. We review the current state of pulmonary blood flow models. We present a pilot study within 10 patients presenting with acute PE, where patient-derived vascular occlusions are imposed onto an existing model of the pulmonary circulation enabling predictions of resultant haemodynamic after embolus occlusion. Results show that mechanical obstruction alone is not sufficient to cause pulmonary arterial hypertension, even when up to 65 per cent of lung tissue is occluded. Blood flow is found to preferentially redistribute to the gravitationally non-dependent regions. The presence of an additional downstream occlusion is found to significantly increase pressures.

The interdependent contributions of gravitational and structural features to perfusion distribution in a multiscale model of the pulmonary circulation.

Recent experimental and imaging studies suggest that the influence of gravity on the measured distribution of blood flow in the lung is largely through deformation of the parenchymal tissue. To study the contribution of hydrostatic effects to regional perfusion in the presence of tissue deformation, we have developed an anatomically structured computational model of the pulmonary circulation (arteries, capillaries, veins), coupled to a continuum model of tissue deformation, and including scale-appropriate fluid dynamics for blood flow in each vessel type. The model demonstrates that both structural and the multiple effects of gravity on the pulmonary circulation make a distinct contribution to the distribution of blood. It shows that postural differences in perfusion gradients can be explained by the combined effect of tissue deformation and extra-acinar blood vessel resistance to flow in the dependent tissue. However, gravitational perfusion gradients persist when the effect of tissue deformation is eliminated, highlighting the importance of the hydrostatic effects of gravity on blood distribution in the pulmonary circulation. Coupling of large- and small-scale models reveals variation in microcirculatory driving pressures within isogravitational planes due to extra-acinar vessel resistance. Variation in driving pressures is due to heterogeneous large-vessel resistance as a consequence of geometric asymmetry in the vascular trees and is amplified by the complex balance of pressures, distension, and flow at the microcirculatory level.

The impact of micro-embolism size on haemodynamic changes in the pulmonary micro-circulation.

Embolus occlusion of pulmonary arteries can result in elevated pulmonary blood pressures, often resulting in pulmonary hypertension (PH). Experimental observations have shown that small emboli (diameter <170 µm) can have a disproportionate effect on pulmonary vascular resistance (PVR) compared with larger emboli for the same tissue occlusion. We present an anatomically based theoretical model of perfusion in the acinar blood vessels designed to investigate changes in PVR following occlusion of arteries <500 µm in diameter. The model predicts that emboli lodged near proximal capillary beds have a greater effect on PVR--regardless of their size--than emboli occluding 200 µm diameter arterioles, with PH occurring for 10% less tissue occlusion. Capillary blood pressures are predicted to exceed 24 mmHg (levels initiating capillary wall damage) in regions of the capillary bed at approximately the onset of PH. This study focuses on the effect of mechanical obstruction alone; however, we present simple models of vasoconstriction illustrating an increased impact on PVR.

The role of airway epithelium in replenishment of evaporated airway surface liquid from the human conducting airways.

This article presents a multi-scale computational model describing the transport of water vapor and heat within the human conducting airways and its interaction with cellular fluid transport kinetics. This tight coupling between the cell and the evaporative flux allows the periciliary liquid (PCL) depth to be investigated within the context of a geometric framework of the human conducting airways with spatial and temporal variations. Within the in vivo airway, the epithelium is not the only source of fluid available for hydration of the PCL, and fluid may also be supplied from submucosal glands (SMGs) or via axial transport of the PCL. The model predicts that without fluid supplied by either SMGs or via PCL transport, significant dehydration would occur under normal breathing conditions. Previous studies have suggested that PCL transport from the periphery to the trachea would require absorption of the fluid by the epithelium; here we show that this can theoretically be sustained by the evaporative load under normal breathing conditions. SMGs could also provide a significant supply of fluid for airway hydration, a hypothesis which is corroborated by comparing the distribution of SMGs as a function of airway generation with the distribution of airway evaporative flux.

The effect of intracellular calcium oscillations on fluid secretion in airway epithelium.

Airway epithelium has been shown to elicit fluid secretion after a rise in intracellular calcium. This rise in intracellular calcium has been shown to display complex oscillations in many species after the binding of particular agonists to extracellular receptors. Fluid secreted by the airway epithelium is used to maintain the depth of the periciliary liquid (PCL) above the apical membrane of the epithelial cells lining the bronchial airways. Previous mathematical models have been published which separately consider the electrophysiology involved in regulating periciliary liquid depth, and the transmission of intracellular calcium waves in airway epithelial tissue. In this paper we present a mathematical model that combines these previous models and allows the effect of oscillations in intracellular calcium on fluid secretion by airway epithelial cells to be investigated. We show that an oscillatory calcium response produces different fluid secretion properties to that elicited by a tonic rise in intracellular calcium. These differences are shown to be due to saturation of the Ca(2+) activated ion channels.