Showing papers by "Olivier Bernard published in 2019"
TL;DR: Results show that encoder-decoder-based architectures outperform state-of-the-art non-deep learning methods and faithfully reproduce the expert analysis for the end-diastolic and end-systolic left ventricular volumes, which open the door for accurate and fully-automatic analysis of 2D echocardiographic images.
Abstract: Delineation of the cardiac structures from 2D echocardiographic images is a common clinical task to establish a diagnosis. Over the past decades, the automation of this task has been the subject of intense research. In this paper, we evaluate how far the state-of-the-art encoder-decoder deep convolutional neural network methods can go at assessing 2D echocardiographic images, i.e segmenting cardiac structures as well as estimating clinical indices, on a dataset especially designed to answer this objective. We therefore introduce the Cardiac Acquisitions for Multi-structure Ultrasound Segmentation (CAMUS) dataset, the largest publicly-available and fully-annotated dataset for the purpose of echocardiographic assessment. The dataset contains two and four-chamber acquisitions from 500 patients with reference measurements from one cardiologist on the full dataset and from three cardiologists on a fold of 50 patients. Results show that encoder-decoder based architectures outperform state-of-the-art non-deep learning methods and faithfully reproduce the expert analysis for the end-diastolic and end-systolic left ventricular volumes, with a mean correlation of 0.95 and an absolute mean error of 9.5 ml. Concerning the ejection fraction of the left ventricle, results are more contrasted with a mean correlation coefficient of 0.80 and an absolute mean error of 5.6 %. Although these results are below the inter-observer scores, they remain slightly worse than the intra-observer's ones. Based on this observation, areas for improvement are defined, which open the door for accurate and fully-automatic analysis of 2D echocardiographic images.
241 citations
TL;DR: In this article, the authors evaluate how far the state-of-the-art encoder-decoder deep convolutional neural network methods can go at assessing 2D echocardiographic images, i.e., segmenting cardiac structures and estimating clinical indices.
Abstract: Delineation of the cardiac structures from 2D echocardiographic images is a common clinical task to establish a diagnosis. Over the past decades, the automation of this task has been the subject of intense research. In this paper, we evaluate how far the state-of-the-art encoder-decoder deep convolutional neural network methods can go at assessing 2D echocardiographic images, i.e., segmenting cardiac structures and estimating clinical indices, on a dataset, especially, designed to answer this objective. We, therefore, introduce the cardiac acquisitions for multi-structure ultrasound segmentation dataset, the largest publicly-available and fully-annotated dataset for the purpose of echocardiographic assessment. The dataset contains two and four-chamber acquisitions from 500 patients with reference measurements from one cardiologist on the full dataset and from three cardiologists on a fold of 50 patients. Results show that encoder-decoder-based architectures outperform state-of-the-art non-deep learning methods and faithfully reproduce the expert analysis for the end-diastolic and end-systolic left ventricular volumes, with a mean correlation of 0.95 and an absolute mean error of 9.5 ml. Concerning the ejection fraction of the left ventricle, results are more contrasted with a mean correlation coefficient of 0.80 and an absolute mean error of 5.6%. Although these results are below the inter-observer scores, they remain slightly worse than the intra-observer’s ones. Based on this observation, areas for improvement are defined, which open the door for accurate and fully-automatic analysis of 2D echocardiographic images.
114 citations
13 Oct 2019
TL;DR: With this method, CNNs can now produce results that are both within the inter-expert variability and always anatomically plausible, and can accommodate any cardiac segmentation method and convert its anatomical implausible results to plausible ones without affecting its overall geometric and clinical metrics.
Abstract: Recent publications have shown that the segmentation accuracy of modern-day convolutional neural networks (CNN) applied on cardiac MRI can reach the inter-expert variability, a great achievement in this area of research. However, despite these successes, CNNs still produce anatomically inaccurate segmentations as they provide no guarantee on the anatomical plausibility of their outcome, even when using a shape prior. In this paper, we propose a cardiac MRI segmentation method which always produces anatomically plausible results. At the core of the method is an adversarial variational autoencoder (aVAE) whose latent space encodes a smooth manifold on which lies a large spectrum of valid cardiac shapes. This aVAE is used to automatically warp anatomically inaccurate cardiac shapes towards a close but correct shape. Our method can accommodate any cardiac segmentation method and convert its anatomically implausible results to plausible ones without affecting its overall geometric and clinical metrics. With our method, CNNs can now produce results that are both within the inter-expert variability and always anatomically plausible.
56 citations
01 Feb 2019
TL;DR: This work synthesizes the range of model structures that have been leveraged for algae and cyanobacteria modeling and core model features that are required to enable reliable process modeling in the context of water resource recovery facilities.
Abstract: Microalgal and cyanobacterial resource recovery systems could significantly advance nutrient recovery from wastewater by achieving effluent nitrogen (N) and phosphorus (P) levels below the current limit of technology. The successful implementation of phytoplankton, however, requires the formulation of process models that balance fidelity and simplicity to accurately simulate dynamic performance in response to environmental conditions. This work synthesizes the range of model structures that have been leveraged for algae and cyanobacteria modeling and core model features that are required to enable reliable process modeling in the context of water resource recovery facilities. Results from an extensive literature review of over 300 published phytoplankton models are presented, with particular attention to similarities with and differences from existing strategies to model chemotrophic wastewater treatment processes (e.g., via the Activated Sludge Models, ASMs). Building on published process models, the core requirements of a model structure for algal and cyanobacterial processes are presented, including detailed recommendations for the prediction of growth (under phototrophic, heterotrophic, and mixotrophic conditions), nutrient uptake, carbon uptake and storage, and respiration.
55 citations
Institut Gustave Roussy1, Boston Children's Hospital2, University of Paris3, Paris Diderot University4, University of Cambridge5, Paris Descartes University6, French Institute of Health and Medical Research7, Friedrich Miescher Institute for Biomedical Research8, University of Basel9, University of Bologna10, Sapienza University of Rome11, University of Oxford12
TL;DR: Aggression and phenotypes in pediatric acute myeloid leukemia result from an ontogeny-related differential susceptibility to transformation by fusion oncogenes, as well as key transcription factor activities, including ERG, SPI1, GATA1 and CEBPA.
Abstract: Fusion oncogenes are prevalent in several pediatric cancers, yet little is known about the specific associations between age and phenotype. We observed that fusion oncogenes, such as ETO2-GLIS2, are associated with acute megakaryoblastic or other myeloid leukemia subtypes in an age-dependent manner. Analysis of a novel inducible transgenic mouse model showed that ETO2-GLIS2 expression in fetal hematopoietic stem cells induced rapid megakaryoblastic leukemia whereas expression in adult bone marrow hematopoietic stem cells resulted in a shift toward myeloid transformation with a strikingly delayed in vivo leukemogenic potential. Chromatin accessibility and single-cell transcriptome analyses indicate ontogeny-dependent intrinsic and ETO2-GLIS2-induced differences in the activities of key transcription factors, including ERG, SPI1, GATA1, and CEBPA. Importantly, switching off the fusion oncogene restored terminal differentiation of the leukemic blasts. Together, these data show that aggressiveness and phenotypes in pediatric acute myeloid leukemia result from an ontogeny-related differential susceptibility to transformation by fusion oncogenes. SIGNIFICANCE: This work demonstrates that the clinical phenotype of pediatric acute myeloid leukemia is determined by ontogeny-dependent susceptibility for transformation by oncogenic fusion genes. The phenotype is maintained by potentially reversible alteration of key transcription factors, indicating that targeting of the fusions may overcome the differentiation blockage and revert the leukemic state.See related commentary by Cruz Hernandez and Vyas, p. 1653.This article is highlighted in the In This Issue feature, p. 1631.
33 citations
TL;DR: The use of photovoltaic panels triggers a synergetic effect, sourcing local electricity and reducing climate change impacts, and it is expected that significant improvements in microalgae productivity or more advanced production processes should rapidly enhance these performances.
Abstract: 13 Background: Microalgae are 10 to 20 times more productive than the current agricultural biodiesel 14
33 citations
TL;DR: colourimetric assays (sensor assays based on coloured dyes) provide a stable, multivariate system for the detection of Volatile Fatty Acids (VFAs), but also provide a much deeper insight into the process by assessing other parameters, which, to date have never been assessed.
Abstract: There is currently an increasing requirement for renewable fuel alternatives to replace fossil-based fuels as an energy source. Although biogas is not a new approach to producing renewable fuel, it could further be developed to improve its potential as an alternative energy source. To achieve this, vast improvements in the efficiency and cost of biogas production are essential. These enhancements require detailed systematic monitoring to attain a near-optimal biogas production process. To date, there is a striking imbalance between the inherent biological complexity of anaerobic digestion, and the minimal information currently measured on-line. Improvements in availability and cost of sensor technology used for determining the key compounds and their dynamics within the biogas processing plant will facilitate the further understanding of the biogas production process, preventing the biological process failure. The objective of this review is to assess colourimetric assays for variable detection in anaerobic digestion. Colourimetric assays (sensor assays based on coloured dyes) provide a stable, multivariate system for the detection of Volatile Fatty Acids (VFAs), but also provide a much deeper insight into the process by assessing other parameters, which, to date have never been
29 citations
TL;DR: A dynamic, adaptive model is developed and forecast simulations are run, exploring a range of adaptation time scales, to probe the likely responses to climate change and stress how biodiversity erosion depends on the ability of organisms to adapt rapidly to temperature increase.
Abstract: Photosynthetic picoeukaryotesx in the genus Micromonas show among the widest latitudinal distributions on Earth, experiencing large thermal gradients from poles to tropics. Micromonas comprises at least four different species often found in sympatry. While such ubiquity might suggest a wide thermal niche, the temperature response of the different strains is still unexplored, leaving many questions as for their ecological success over such diverse ecosystems. Using combined experiments and theory, we characterize the thermal response of eleven Micromonas strains belonging to four species. We demonstrate that the variety of specific responses to temperature in the Micromonas genus makes this environmental factor an ideal marker to describe its global distribution and diversity. We then propose a diversity model for the genus Micromonas, which proves to be representative of the whole phytoplankton diversity. This prominent primary producer is therefore a sentinel organism of phytoplankton diversity at the global scale. We use the diversity within Micromonas to anticipate the potential impact of global warming on oceanic phytoplankton. We develop a dynamic, adaptive model and run forecast simulations, exploring a range of adaptation time scales, to probe the likely responses to climate change. Results stress how biodiversity erosion depends on the ability of organisms to adapt rapidly to temperature increase.
26 citations
06 Oct 2019
TL;DR: A combination of two U-Nets is used to derive a region of interest in the image before the segmentation of the endocardium and epicardium in 2D echocardiography, and the reduction in outlier predictions supports the interest of such approach.
Abstract: In this work, we present a novel attention mechanism to refine the segmentation of the endocardium and epicardium in 2D echocardiography. A combination of two U-Nets is used to derive a region of interest in the image before the segmentation. By relying on parameterised sigmoids to perform thresholding operations, the full pipeline is trainable end-to-end. The Refining U-Net (RU-Net) architecture is evaluated on the CAMUS dataset, comprising 2000 annotated images from the apical 2 and 4 chamber views of 500 patients. Although geometrical scores are only marginally improved, the reduction in outlier predictions (from 20% to 16%) supports the interest of such approach.
22 citations
13 Sep 2019
TL;DR: The results revealed that the architecture of microalgae biofilms is species-specific, however, time similarly affects the structural and biochemical parameters.
Abstract: Microalgae biofilms have been proposed as an alternative to suspended cultures in commercial and biotechnological fields. However, little is known about their architecture that may strongly impact biofilm behavior, bioprocess stability, and productivity. In order to unravel the architecture of microalgae biofilms, four species of commercial interest were cultivated in microplates and characterized using a combination of confocal laser scanning microscopy and FTIR spectroscopy. In all the species, the biofilm biovolume and thickness increased over time and reached a plateau after seven days; however, the final biomass reached was very different. The roughness decreased during maturation, reflecting cell division and voids filling. The extracellular polymeric substances content of the matrix remained constant in some species, and increased over time in some others. Vertical profiles showed that young biofilms presented a maximum cell density at 20 μm above the substratum co-localized with matrix components. In mature biofilms, the maximum density of cells moved at a greater distance from the substratum (30–40 μm), whereas the maximum coverage of matrix components remained in a deeper layer. Carbohydrates and lipids were the main macromolecules changing during biofilm maturation. Our results revealed that the architecture of microalgae biofilms is species-specific. However, time similarly affects the structural and biochemical parameters.
21 citations
01 Oct 2019
TL;DR: By training from scratch the neural network was able to segment ALAX views, but with a lower accuracy to that of A2C/A4C views, and study how a single network can learn to segment all three views.
Abstract: It has been shown that deep neural networks can accuratly segment the left ventricle (LV), myocardium and left atrium in apical two and four chamber (A2C and A4C) views. While segmentation of apical long-axis (ALAX) views is quite similar to A2C and A4C, there is one major difference; the left ventricular outflow tract (LVOT) which restricts the myocardium. The objectives of this work were to accurately segment ALAX views, investigate if transfer learning from A2C/A4C improves accuracy, and study how a single network can learn to segment all three views.The CAMUS dataset of 500 patients together with an additional dataset of 106 patients with ALAX views were used for training and testing using 10-fold cross-validation. The results showed that by training from scratch the neural network was able to segment ALAX views, but with a lower accuracy to that of A2C/A4C views. Transfer learning only slightly improved mycoardium accuracy (0.77 to 0.78), but was statistically significant (p-value 0.001). Multi-view segmentation with the baseline network showed a reduction in accuracy, resulting in 38 cases of incorrect segmentations in terms of LVOT. The proposed network reduced the number of incorrect segmentations to 8, and achieved the best overall accuracy in terms of dice score where the improvement in myocardium segmentation accuracy (0.776 to 0.786) was statistically significant (p-value 0.005).
TL;DR: The demonstration that a somatic point mutation tips the balance of genome-binding pattern provides a mechanistic paradigm for how missense mutations in transcription factor genes may be oncogenic in human tumors.
Abstract: The ETS-domain transcription factors divide into subfamilies based on protein similarities, DNA-binding sequences, and interaction with cofactors. They are regulated by extracellular clues and contribute to cellular processes, including proliferation and transformation. ETS genes are targeted through genomic rearrangements in oncogenesis. The PU.1/SPI1 gene is inactivated by point mutations in human myeloid malignancies. We identified a recurrent somatic mutation (Q226E) in PU.1/SPI1 in Waldenstrom macroglobulinemia, a B-cell lymphoproliferative disorder. It affects the DNA-binding affinity of the protein and allows the mutant protein to more frequently bind and activate promoter regions with respect to wild-type protein. Mutant SPI1 binding at promoters activates gene sets typically promoted by other ETS factors, resulting in enhanced proliferation and decreased terminal B-cell differentiation in model cell lines and primary samples. In summary, we describe oncogenic subversion of transcription factor function through subtle alteration of DNA binding leading to cellular proliferation and differentiation arrest. Significance: The demonstration that a somatic point mutation tips the balance of genome-binding pattern provides a mechanistic paradigm for how missense mutations in transcription factor genes may be oncogenic in human tumors. This article is highlighted in the In This Issue feature, p. 681
TL;DR: In this paper, an adversarial variational autoencoder (aVAE) is used to warp anatomically inaccurate cardiac shapes towards a close but correct shape, which can accommodate any cardiac segmentation method.
Abstract: Recent publications have shown that the segmentation accuracy of modern-day convolutional neural networks (CNN) applied on cardiac MRI can reach the inter-expert variability, a great achievement in this area of research. However, despite these successes, CNNs still produce anatomically inaccurate segmentations as they provide no guarantee on the anatomical plausibility of their outcome, even when using a shape prior. In this paper, we propose a cardiac MRI segmentation method which always produces anatomically plausible results. At the core of the method is an adversarial variational autoencoder (aVAE) whose latent space encodes a smooth manifold on which lies a large spectrum of valid cardiac shapes. This aVAE is used to automatically warp anatomically inaccurate cardiac shapes towards a close but correct shape. Our method can accommodate any cardiac segmentation method and convert its anatomically implausible results to plausible ones without affecting its overall geometric and clinical metrics. With our method, CNNs can now produce results that are both within the inter-expert variability and always anatomically plausible.
TL;DR: This work focuses on the shape optimization and optimal control of an innovative process where the microalgae are fixed on a support, and proposes an adjoint-based gradient method to identify the optimal (constant) process folding and the (time varying) velocity of the biofilm.
TL;DR: A promising way to grow microalgae is explored, examining a biofilm developed on a moving conveyor belt, which seems to deal with photoinhibition better than when the biofilm is exposed to permanent illumination.
Abstract: The production of microalgae using biofilm-based processes is becoming popular because of their higher productivity compared to traditional culture systems. Another advantage of microalgal biofilms is the straightforward harvesting procedure achieved by scraping off the biofilm, significantly reducing the energy demand required when concentrating liquid culture. Here, a promising way to grow microalgae is explored, examining a biofilm developed on a moving conveyor belt. Algae are then successively exposed to light and dark periods as the conveyer belt rotates. A lab-scale biofilm-based reactor mimicking the light pattern of the moving system was first used to study the effect of light/dark cycles on a Chlorella autotrophica biofilm. The succession of light and dark phases (in the order of minutes) effectively dilutes the light over a given time period and mitigates over-exposure of light, which can lead to photoinhibition. When the illumination time represents one-third of the cycle period (light dilution factor of 3), the biofilm seems to deal with photoinhibition better than when the biofilm is exposed to permanent illumination. Extrapolations for a rotating conveyer belt in such conditions points out twofold productivity compared to a static biofilm exposed to continuous light. However, when the periods in the dark extend too long, respiration decreases the carbon pool, hindering the benefit of photosynthesis, and a trade-off must be achieved.
TL;DR: This review intends to assess the feasibility of online, cost‐effective, rapid, and efficient detection of dissolved H2, as well as briefly assessing H2S, acetic acid, ammonia, and methane in AD by SPR.
Abstract: Biogas production is becoming significantly viable as an energy source for replacing fossil-based fuels. The further development of the biogas production process could lead to significant improvements in its potential. Wastewater treatment currently accounts for 3% of the electrical energy load in developed countries, while it could be developed to provide a source of nitrogen and phosphorus, in addition to energy. The improvement of anaerobic digestion (AD) detection technologies is the cornerstone to reach higher methane productivities and develop fully automatized processes to decrease operational costs. New sensors are requested to automatically obtain a better interpretation of the complex and dynamical internal reactor environment. This will require detailed systematic detection in order to realize a near-optimal production process. In this review, optical fiber-based sensors will be discussed to assess their potential for use in AD. There is currently a disparity between the complexity of AD, and online detection. By improving the durability, sensitivity, and cost of dissolved H2 (as well as H2S, acetic acid, ammonia, and methane) sensor technology, further understanding of the AD process may allow the prevention of process failure. The emergence of surface plasmon resonance (SPR) sensing with optical fibers coupled with the H2-sensitive metal palladium, allows detection of dissolved hydrogen in liquid. By implementing these SPR sensors into AD, improvements to the biogas production process, even at small scales, may be achieved by guiding the process in the optimum direction, avoiding the collapse of the biological process. This review intends to assess the feasibility of online, cost-effective, rapid, and efficient detection of dissolved H2, as well as briefly assessing H2S, acetic acid, ammonia, and methane in AD by SPR.
TL;DR: A thorough analysis of the optimizer strategy revealed that the increase of productivity in summer was achieved by finding a trade-off between algal concentration to optimally distribute light and pond temperature to get closer to optimal growth temperature.
Abstract: Outdoor biofuel production from microalgae is a complex dynamical process submitted to climatic variations. Controlling and optimizing such a nonlinear process strongly influenced by weather conditions is therefore tricky, but it is crucial to make this process economically sustainable. The strategy investigated in this study uses weather forecast coupled to a detailed predictive model of algal productivity for online optimization of the rates of fresh medium injection and culture removal into and from the pond. This optimization strategy was applied at various climatic conditions and significantly increased productivity compared to a standard operation with constant pond depth and dilution rate, by up to a factor of 2.2 in a Mediterranean climate in summer. A thorough analysis of the optimizer strategy revealed that the increase of productivity in summer was achieved by finding a trade-off between algal concentration to optimally distribute light and pond temperature to get closer to optimal growth temperature. This study also revealed that maintaining the temperature as high as possible is the best strategy to maximize productivity in cold climatic conditions.
TL;DR: In this paper, a model was developed, considering a system composed of a bubble column connected with an open photobioreactor, to evaluate the operation of a potential large-scale system.
TL;DR: A mathematical approach to reduce high dimensional linearized metabolic models, which relies on time scale separation and the Quasi Steady State Assumption, and depends on a small system of differential equations which represents the slow variables dynamics.
Abstract: Metabolic modeling has gained accuracy in the last decades, but the resulting models are of high dimension and difficult to use for control purpose. Here we propose a mathematical approach to reduce high dimensional linearized metabolic models, which relies on time scale separation and the Quasi Steady State Assumption. Contrary to the Flux Balance Analysis assumption that the whole system reaches an equilibrium, our reduced model depends on a small system of differential equations which represents the slow variables dynamics. Moreover, we prove that the concentration of metabolites in Quasi Steady State is one order of magnitude lower than the concentration of metabolites with slow dynamics (under some flux conditions). Also, we propose a minimization strategy to estimate the reduced system parameters. The reduction of a toy network with the method presented here is compared with other approaches. Finally, our reduction technique is applied to an autotrophic microalgae metabolic network.
TL;DR: In this article, a rotating algal biofilm (RAB) model is introduced, which is based on the Han model and it is shown that taking into consideration light dilution factor can increase productivity.
TL;DR: Since a model should be tailored to the objectives, which will depend on applications and environment, a universal model representing any possible situation is probably not the best option.
Abstract: Because of the inherent complexity of bioprocesses, mathematical models are more and more used for process design, control, optimization, etc. These models are generally based on a set of biochemical reactions. Model equations are then derived from mass balance, coupled with empirical kinetics. Biological models are nonlinear and represent processes, which by essence are dynamic and adaptive. The temptation to embed most of the biology is high, with the risk that calibration would not be significant anymore. The most important task for a modeler is thus to ensure a balance between model complexity and ease of use. Since a model should be tailored to the objectives, which will depend on applications and environment, a universal model representing any possible situation is probably not the best option.
TL;DR: In this article, the authors investigate a minimal-time control problem in a chemostat continuous photo-bioreactor model that describes the dynamics of two distinct microalgae populations and develop a dilution-based control strategy that steers the model trajectories to a suitable target in minimal time.
TL;DR: Surgical shunt for severe portal hypertension in biliary atresia may delay the need for liver transplantation, however complications are indications for transplantation.
17 Apr 2019
TL;DR: In this study, segmentation of quadriceps muscle heads of ultra-endurance athletes was done using a multi- atlas segmentation and corrective leaning framework where the registration based multi-atlas segmentations step was replaced with weakly supervised U-Net.
Abstract: In this study, segmentation of quadriceps muscle heads of ultra-endurance athletes was done using a multi-atlas segmentation and corrective leaning framework where the registration based multi-atlas segmentation step was replaced with weakly supervised U-Net. For the case with remarkably different morphology, our method produced improved accuracy, while reduced significantly the computation time.
TL;DR: In this paper, the authors studied the long-term behavior of a continuous culture of microalgae exposed to a periodic source of light and showed that the microalgabe population is forced to a periodically regime.
10 Apr 2019
TL;DR: An extension of the evaluation criteria to anatomical assessment is proposed, as traditional geometric and clinical metrics in cardiac segmentation do not take into account the anatomical correctness of the predicted shapes.
Abstract: We recently published a deep learning study on the potential of encoder-decoder networks for the segmentation of the 2D CAMUS ultrasound dataset. We propose in this abstract an extension of the evaluation criteria to anatomical assessment, as traditional geometric and clinical metrics in cardiac segmentation do not take into account the anatomical correctness of the predicted shapes. The completed study sheds a new light on the ranking of models.
TL;DR: In this article, a simplified dynamical system to represent the competition between two species of microalgae in a chemostat was considered, and an optimal control problem was formulated with the objective of finding the substrate concentration which would maximize the fraction of the species of interest over a fixed finite time-window.
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TL;DR: In this article, an extension of the evaluation criteria to anatomical assessment is proposed, as traditional geometric and clinical metrics in cardiac segmentation do not take into account the anatomical correctness of the predicted shapes.
Abstract: We recently published a deep learning study on the potential of encoder-decoder networks for the segmentation of the 2D CAMUS ultrasound dataset. We propose in this abstract an extension of the evaluation criteria to anatomical assessment, as traditional geometric and clinical metrics in cardiac segmentation do not take into account the anatomical correctness of the predicted shapes. The completed study sheds a new light on the ranking of models.
TL;DR: Based on the theory of the light limited chemostat, the variable cell quota approach, and photoacclimation models, this paper built a mathematical model for describing microalgae growth under limitation by these resources.