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PubMed2005

Sources of uncertainty in model predictions: lessons learned from the IAEA Forest and Fruit Working Group model intercomparisons.

The International Atomic Energy Agency (IAEA), through the BIOMASS program, has provided a unique international forum for assessing the relative contribution of different sources of uncertainty associated with environmental modeling. The methodology and guidance for dealing with parameter uncertainty have been fairly well developed and quantitative tools such as Monte-Carlo modeling are often recommended. The issue of model uncertainty is still rarely addressed in practical applications and the use of several alternative models to derive a range of model outputs (similar to what was done in IAEA model intercomparisons) is one of a few available techniques. This paper addresses the often overlooked issue of what we call 'modeler uncertainty,' i.e., differences in problem formulation, model implementation and parameter selection originating from subjective interpretation of the problem at hand. This study uses results from the Fruit and Forest Working Groups created under the BIOMASS program (BIOsphere Modeling and ASSessment). The greatest uncertainty was found to result from modelers' interpretation of scenarios and approximations made by modelers. In scenarios that were unclear for modelers, the initial differences in model predictions were as high as seven orders of magnitude. Only after several meetings and discussions about specific assumptions did the differences in predictions by various models merge. Our study shows that the parameter uncertainty (as evaluated by a probabilistic Monte-Carlo assessment) may have contributed over one order of magnitude to the overall modeling uncertainty. The final model predictions ranged between one and three orders of magnitude, depending on the specific scenario. This study illustrates the importance of problem formulation and implementation of an analytic-deliberative process in fate and transport modeling and risk characterization.

Fruit↗
PubMed2006

Economic evaluation of duloxetine for the treatment of women with stress urinary incontinence: a Markov model comparing pharmacotherapy with pelvic floor muscle training.

BACKGROUND: Duloxetine is a serotonin and norepinephrine reuptake inhibitor and may be useful for treating women with stress urinary incontinence (SUI) in general practice. OBJECTIVE: The objective of this study was to examine the cost-effectiveness of 2 duloxetine strategies (duloxetine alone and duloxetine after inadequate response to pelvic floor muscle training [PFMT]) compared with PFMT or no treatment for women aged>or=50 years with SUI. METHODS: A Markov model with a 3-month cycle length was developed, with a time horizon of 5 years. Incontinence severity was based on incontinence episode frequency per week (IEF/week). Four SUI health states were distinguished in the model: no SUI (0 incontinence episode [IE] per week), mild SUI (19 IEs/week), moderate SUI (10-25 IEs/week), and severe SUI (>or=26 IEs/week). Transition probabilities were calculated, based on published evidence, expert opinion, and demographic data. Outcomes were expected total societal costs and expected IEs. The analysis was performed from the societal perspective of The Netherlands, and all costs were reported in year-2002 euros. One-way sensitivity and probabilistic sensitivity analyses were performed. RESULTS: In the model, providing PFMT cost euro0.03/IE avoided, compared with no treatment. Duloxetine after inadequate PFMT cost euro3.81/IE avoided, compared with PFMT One-way sensitivity analyses indicated that these results were robust regarding variation in age, IEF/week, and discount rate. Below the ceiling ratio of euro3.65/IE avoided, PFMT had the highest probability of being cost-effective. With higher ceiling ratios, duloxetine after inadequate PFMT had the highest cost-effectiveness probability. CONCLUSIONS: Treating patients with duloxetine after inadequate PFMT response yielded additional health effects in the model, but would require society in The Netherlands to pay euro3.81/IE avoided for women aged>or=50 years with SUI being treated in general practice. It is up to policy-makers to determine whether this ratio would be acceptable.

Adrenergic Uptake Inhibitors↗
PubMedDate not supplied

Large-sample Bayesian posterior distributions for probabilistic sensitivity analysis.

In probabilistic sensitivity analyses, analysts assign probability distributions to uncertain model parameters and use Monte Carlo simulation to estimate the sensitivity of model results to parameter uncertainty. The authors present Bayesian methods for constructing large-sample approximate posterior distributions for probabilities, rates, and relative effect parameters, for both controlled and uncontrolled studies, and discuss how to use these posterior distributions in a probabilistic sensitivity analysis. These results draw on and extend procedures from the literature on large-sample Bayesian posterior distributions and Bayesian random effects meta-analysis. They improve on standard approaches to probabilistic sensitivity analysis by allowing a proper accounting for heterogeneity across studies as well as dependence between control and treatment parameters, while still being simple enough to be carried out on a spreadsheet. The authors apply these methods to conduct a probabilistic sensitivity analysis for a recently published analysis of zidovudine prophylaxis following rapid HIV testing in labor to prevent vertical HIV transmission in pregnant women.

Bayes Theorem↗
PubMed2006

Surveillance of Barrett's oesophagus: exploring the uncertainty through systematic review, expert workshop and economic modelling.

OBJECTIVES: To assess what is known about the effectiveness, safety, affordability, cost-effectiveness and organisational impact of endoscopic surveillance in preventing morbidity and mortality from adenocarcinoma in patients with Barrett's oesophagus. In addition, to identify important areas of uncertainty in current knowledge for these programmes and to identify areas for further research. DATA SOURCES: Electronic databases up to March 2004. Experts in Barrett's oesophagus from the UK. REVIEW METHODS: A systematic review of the effectiveness of endoscopic surveillance of Barrett's oesophagus was carried out following methodological guidelines. Experts in Barrett's oesophagus from the UK were invited to contribute to a workshop held in London in May 2004 on surveillance of Barrett's oesophagus. Small group discussion, using a modified nominal group technique, identified key areas of uncertainty and ranked them for importance. A Markov model was developed to assess the cost-effectiveness of a surveillance programme for patients with Barrett's oesophagus compared with no surveillance and to quantify important areas of uncertainty. The model estimates incremental cost--utility and expected value of perfect information for an endoscopic surveillance programme compared with no surveillance. A cohort of 1000 55-year-old men with a diagnosis of Barrett's oesophagus was modelled for 20 years. The base case used costs in 2004 and took the perspective of the UK NHS. Estimates of expected value of information were included. RESULTS: No randomised controlled trials (RCTs) or well-designed non-randomised controlled studies were identified, although two comparative studies and numerous case series were found. Reaching clear conclusions from these studies was impossible owing to lack of RCT evidence. In addition, there was incomplete reporting of data particularly about cause of death, and changes in surveillance practice over time were mentioned but not explained in several studies. Three cost--utility analyses of surveillance of Barrett's oesophagus were identified, of which one was a further development of a previous study by the same group. Both sets of authors used Markov modelling and confined their analysis to 50- or 55-year-old white men with gastro-oesophageal reflux disease (GORD) symptoms. The models were run either for 30 years or to age 75 years. As these models are American, there are almost certainly differences in practice from the UK and possible underlying differences in the epidemiology and natural history of the disease. The costs of the procedures involved are also likely to be very different. The expert workshop identified the following key areas of uncertainty that needed to be addressed: the contribution of risk factors for the progression of Barrett's oesophagus to the development of high-grade dysplasia (HGD) and adenocarcinoma of the oesophagus; possible techniques for use in the general population to identify patients with high risk of adenocarcinoma; effectiveness of treatments for Barrett's oesophagus in altering cancer incidence; how best to identify those at risk in order to target treatment; whether surveillance programmes should take place at all; and whether there are clinical subgroups at higher risk of adenocarcinoma. Our Markov model suggests that the base case scenario of endoscopic surveillance of Barrett's oesophagus at 3-yearly intervals, with low-grade dysplasia surveyed yearly and HGD 3-monthly, does more harm than good when compared with no surveillance. Surveillance produces fewer quality-adjusted life-years (QALYs) for higher cost than no surveillance, therefore it is dominated by no surveillance. The cost per cancer identified approaches pound 45,000 in the surveillance arm and there is no apparent survival advantage owing to high recurrence rates and increased mortality due to more oesophagectomies in this arm. Non-surveillance continues to cost less and result in better quality of life whatever the surveillance intervals for Barrett's oesophagus and dysplastic states and whatever the costs (including none) attached to endoscopy and biopsy as the surveillance test. The probabilistic analyses assess the overall uncertainty in the model. According to this, it is very unlikely that surveillance will be cost-effective even at relatively high levels of willingness to pay. The simulation showed that, in the majority of model runs, non-surveillance continued to cost less and result in better quality of life than surveillance. At the population level (i.e. people with Barrett's oesophagus in England and Wales), a value of pound 6.5 million is placed on acquiring perfect information about surveillance for Barrett's oesophagus using expected value of perfect information (EVPI) analyses, if the surveillance is assumed to be relevant over 10 years. As with the one-way sensitivity analyses, the partial EVPI highlighted recurrence of adenocarcinoma of the oesophagus (ACO) after surgery and time taken for ACO to become symptomatic as particularly important parameters in the model. CONCLUSIONS: The systematic review concludes that there is insufficient evidence available to assess the clinical effectiveness of surveillance programmes of Barrett's oesophagus. There are numerous gaps in the evidence, of which the lack of RCT data is the major one. The expert workshop reflected these gaps in the range of topics raised as important in answering the question of the effectiveness of surveillance. Previous models of cost-effectiveness have most recently shown that surveillance programmes either do more harm than good compared with no surveillance or are unlikely to be cost-effective at usual levels of willingness to pay. Our cost--utility model has shown that, across a range of values for the various parameters that have been chosen to reflect uncertainty in the inputs, it is likely that surveillance programmes do more harm than good -- costing more and conferring lower quality of life than no surveillance. Probabilistic analysis shows that, in most cases, surveillance does more harm and costs more than no surveillance. It is unlikely, but still possible, that surveillance may prove to be cost-effective. The cost-effectiveness acceptability curve, however, shows that surveillance is unlikely to be cost-effective at either the 'usual' level of willingness to pay ( pound 20,000-30,000 per QALY) or at much higher levels. The expected value of perfect information at the population level is pound 6.5 million. Future research should target both the overall effectiveness of surveillance and the individual elements that contribute to a surveillance programme, particularly the performance of the test and the effectiveness of treatment for both Barrett's oesophagus and ACO. In addition, of particular importance is the clarification of the natural history of Barrett's oesophagus.

Adenocarcinoma↗
PubMed2005

Deterministic vs. probabilistic analyses to identify sensitive parameters in dose assessment using RESRAD.

The dose assessments for sites containing residual radioactivity usually involve the use of computer models that employ input parameters describing the physical conditions of the contaminated and surrounding media and the living and consumption patterns of the receptors in analyzing potential doses to the receptors. The precision of the dose results depends on the precision of the input parameter values. The identification of sensitive parameters that have great influence on the dose results would help set priorities in research and information gathering for parameter values so that a more precise dose assessment can be conducted. Two methods of identifying site-specific sensitive parameters, deterministic and probabilistic, were compared by applying them to the RESRAD computer code for analyzing radiation exposure for a residential farmer scenario. The deterministic method has difficulty in evaluating the effect of simultaneous changes in a large number of input parameters on the model output results. The probabilistic method easily identified the most sensitive parameters, but the sensitivity measure of other parameters was obscured. The choice of sensitivity analysis method would depend on the availability of site-specific data. Generally speaking, the deterministic method would identify the same set of sensitive parameters as the probabilistic method when 1) the baseline values used in the deterministic method were selected near the mean or median value of each parameter and 2) the selected range of parameter values used in the deterministic method was wide enough to cover the 5th to 95th percentile values from the distribution of that parameter.

Agriculture↗
PubMed2006

Rapid object indexing using locality sensitive hashing and joint 3D-signature space estimation.

We propose a new method for rapid 3D object indexing that combines feature-based methods with coarse alignment-based matching techniques. Our approach achieves a sublinear complexity on the number of models, maintaining at the same time a high degree of performance for real 3D sensed data that is acquired in largely uncontrolled settings. The key component of our method is to first index surface descriptors computed at salient locations from the scene into the whole model database using the Locality Sensitive Hashing (LSH), a probabilistic approximate nearest neighbor method. Progressively complex geometric constraints are subsequently enforced to further prune the initial candidates and eliminate false correspondences due to inaccuracies in the surface descriptors and the errors of the LSH algorithm. The indexed models are selected based on the MAP rule using posterior probability of the models estimated in the joint 3D-signature space. Experiments with real 3D data employing a large database of vehicles, most of them very similar in shape, containing 1,000,000 features from more than 365 models demonstrate a high degree of performance in the presence of occlusion and obscuration, unmodeled vehicle interiors and part articulations, with an average processing time between 50 and 100 seconds per query.

Algorithms↗
PubMed2005

Orientation in manhattan: equiprojective classes and sequential estimation.

The problem of inferring 3D orientation of a camera from video sequences has been mostly addressed by first computing correspondences of image features. This intermediate step is now seen as the main bottleneck of those approaches. In this paper, we propose a new 3D orientation estimation method for urban (indoor and outdoor) environments, which avoids correspondences between frames. The scene property exploited by our method is that many edges are oriented along three orthogonal directions; this is the recently introduced Manhattan world (MW) assumption. The main contributions of this paper are: the definition of equivalence classes of equiprojective orientations, the introduction of a new small rotation model, formalizing the fact that the camera moves smoothly, and the decoupling of elevation and twist angle estimation from that of the compass angle. We build a probabilistic sequential orientation estimation method, based on an MW likelihood model, with the above-listed contributions allowing a drastic reduction of the search space for each orientation estimate. We demonstrate the performance of our method using real video sequences.

Algorithms↗
PubMed2006

Hidden Markov multiple event sequence models: A paradigm for the spatio-temporal analysis of fMRI data.

This paper presents a novel, completely unsupervised fMRI brain mapping method that addresses the three problems of hemodynamic response function (HRF) variability, hemodynamic event timing, and fMRI response non-linearity. Spatial and temporal information are directly taken into account into the core of the activation detection process. In practice, activation detection at voxel v is formulated in terms of temporal alignment between sequences of hemodynamic response onsets (HROs) detected in the fMRI signal at v and in the spatial neighborhood of v, and the input sequence of stimuli or stimulus onsets. Event-related and epoch paradigms are considered. The multiple event sequence alignment problem is solved within the probabilistic framework of hidden Markov multiple event sequence models (HMMESMs), a new class of hidden Markov models. Results obtained on real and synthetic data significantly outperform those obtained with the popular statistical parametric mapping (SPM2) method without requiring any prior definition of the expected activation patterns, the HMMESM mapping approach being completely unsupervised.

Adolescent↗
PubMedDate not supplied

Extracting the principal behavior of a probabilistic supervisor through neural networks ensemble.

In this paper, we propose a model of a neural network ensemble that can be trained with a supervisor having two kinds of input-output functions where the occurrence probability of each function is not even. This condition can be likened to a learning condition, in which the learning data are hampered by noise. In this case, the neural network has the impression that the learning supervisor (object) has a probabilistic behavior in which the supervisor generates correct learning data most of the time but occasionally generates erroneous ones. The objective is to train the neural network to approximate the greatest distributed input-output relation, which can be considered to be the principal nature of the supervisor, so that we can obtain a neural network that is able, to some extent, to suppress the ill effect of erroneous data encountered during the learning process.

Algorithms↗
PubMed2006

Soft mixer assignment in a hierarchical generative model of natural scene statistics.

Gaussian scale mixture models offer a top-down description of signal generation that captures key bottom-up statistical characteristics of filter responses to images. However, the pattern of dependence among the filters for this class of models is prespecified. We propose a novel extension to the gaussian scale mixture model that learns the pattern of dependence from observed inputs and thereby induces a hierarchical representation of these inputs. Specifically, we propose that inputs are generated by gaussian variables (modeling local filter structure), multiplied by a mixer variable that is assigned probabilistically to each input from a set of possible mixers. We demonstrate inference of both components of the generative model, for synthesized data and for different classes of natural images, such as a generic ensemble and faces. For natural images, the mixer variable assignments show invariances resembling those of complex cells in visual cortex; the statistics of the gaussian components of the model are in accord with the outputs of divisive normalization models. We also show how our model helps interrelate a wide range of models of image statistics and cortical processing.

Animals↗
PubMed2006

Kernel representations for flux and concentration in ion channel models with time-varying concentrations.

This paper explores stochastic models for the study of ion transport in biological cells. It considers one-dimensional models with time-varying concentrations at the boundaries. The average concentration and flux in the channel are obtained as kernel representations, where the kernel functions have a probabilistic interpretation which contributes to a better understanding of the models. In particular, the kernel representation is given for the flux at a boundary point, providing a correct version of a representation found in the literature. This requires special attention because one of the kernel functions exhibits a singularity. This kernel representation is feasible due to the linearity of the system that arises from the assumed independence between ions.

Diffusion↗
PubMedDate not supplied

A method for risk assessment for three contaminated sites in northern Italy.

A stepwise human health risk assessment procedure carried out using American Society for Testing and Materials methodology was applied to three contaminated sites located in northern Italy: an uncontrolled landfill, an abandoned industrial site and an industrial waste contaminated land. Two different tiers of analysis were performed by means of the analytical model RBCA Tool Kit and the numerical model API-DSS, respectively. The latter was applied according to both a deterministic and a probabilistic risk analysis. The comparison of the two approaches highlighted the great benefit provided by probabilistic analysis for the risk assessment based on site specific parameters and more complex models, in particular for groundwater exposure route. Finally, the risk-based site specific target levels were compared to the generic regulatory threshold limits fixed by the Italian regulation. The comparison showed the regulatory limits generally too restrictive for non-carcinogenic substances but less protective for carcinogenic chemicals, outlining the need of a site-specific risk assessment especially for carcinogenic substances.

Carcinogens, Environmental↗
PubMed1982

Stochastic information processing biological systems.

We propose a simple, biochemically-based model for stochastic information processing in brain, genetic, and, consequently, evolutionary modelling. The essential features of reaction-diffusion processes are realized by intrinsically stochastic probabilistic automata (Shannon and Weaver, 1948; see also Ashby, 1958, von Neumann, 1966; Burks, 1970; Paz, 1971) whose definition extends that of classical automata. (Classical automata are deterministic; earlier work on probabilistic automata focused on error correction and at least approximating deterministic behavior.) We call these probabilistic automata biochemical to emphasize the role of intrinsically stochastic process in biological information processing. Our model yields descriptions of gradualism (Conrad, 1974), learning, and apparent inefficiencies in the brain, and partially resolves the near impossibility of simultaneous point mutations (Conrad, 1972, 1978) in genetics. The genetic model implies an evolutionary dynamics of punctuated equilibria (Gould and Eldredge, 1977).

Animals↗
PubMed2003

ELISA: structure-function inferences based on statistically significant and evolutionarily inspired observations.

UNLABELLED: The problem of functional annotation based on homology modeling is primary to current bioinformatics research. Researchers have noted regularities in sequence, structure and even chromosome organization that allow valid functional cross-annotation. However, these methods provide a lot of false negatives due to limited specificity inherent in the system. We want to create an evolutionarily inspired organization of data that would approach the issue of structure-function correlation from a new, probabilistic perspective. Such organization has possible applications in phylogeny, modeling of functional evolution and structural determination. ELISA (Evolutionary Lineage Inferred from Structural Analysis, http://romi.bu.edu/elisa) is an online database that combines functional annotation with structure and sequence homology modeling to place proteins into sequence-structure-function "neighborhoods". The atomic unit of the database is a set of sequences and structural templates that those sequences encode. A graph that is built from the structural comparison of these templates is called PDUG (protein domain universe graph). We introduce a method of functional inference through a probabilistic calculation done on an arbitrary set of PDUG nodes. Further, all PDUG structures are mapped onto all fully sequenced proteomes allowing an easy interface for evolutionary analysis and research into comparative proteomics. ELISA is the first database with applicability to evolutionary structural genomics explicitly in mind. AVAILABILITY: The database is available at http://romi.bu.edu/elisa.

Amino Acid Sequence↗
PubMed2002

Products of gaussians and probabilistic minor component analysis.

Recently, Hinton introduced the products of experts architecture for density estimation, where individual expert probabilities are multiplied and renormalized. We consider products of gaussian "pancakes" equally elongated in all directions except one and prove that the maximum likelihood solution for the model gives rise to a minor component analysis solution. We also discuss the covariance structure of sums and products of gaussian pancakes or one-factor probabilistic principal component analysis models.

Neural Networks, Computer↗
PubMed2003

Systematic review of the clinical effectiveness and cost-effectiveness of tension-free vaginal tape for treatment of urinary stress incontinence.

OBJECTIVES: To evaluate the effectiveness and cost-effectiveness of tension-free vaginal tape (TVT) in comparison with the standard surgical interventions currently used. DATA SOURCES: Literature searches were carried out on electronic databases and websites for data covering the period 1966--2002. Other sources included references lists of relevant articles; selected experts in the field; abstracts of a limited number of conference proceedings titles; and the Internet. REVIEW METHODS: A systematic review of studies including comparisons of TVT with any of the comparators was conducted. Alternative treatments considered were abdominal retropubic colposuspension (including both open and laparoscopic colposuspension), traditional suburethral sling procedures and injectable agents (periurethral bulking agents). The identified studies were critically appraised and their results summarised. A Markov model comparing TVT with the comparators was developed using the results of the review of effectiveness and data on resource use and costs from previously conducted studies. The Markov model was used to estimate costs and quality-adjusted life-years for up to 10 years following surgery and it incorporated a probabilistic analysis and also sensitivity analysis around key assumptions of the model. RESULTS: Based on limited data from direct comparisons with TVT and from systematic reviews, laparoscopic colposuspension and traditional slings have broadly similar cure rates to TVT and open colposuspension, whereas injectable agents appear to have lower cure rates. TVT is less invasive than colposuspension and traditional sling procedures, and is also usually performed under regional or local anaesthesia. The principal operative complication is bladder perforation. There are currently no randomised controlled trial (RCT) data beyond 2 years post-surgery, and long-term effects are therefore currently not known reliably. TVT was more likely to be considered cost-effective compared with the other surgical procedures. Increasing the absolute probability of cure following TVT reduced the likelihood that TVT would be considered cost-effective. CONCLUSIONS: The long-term performance of TVT in terms of both continence and unanticipated adverse effects is not known reliably at the moment. Despite relatively few robust comparative data, it appears that in the short to medium term TVT's effectiveness approaches that of alternative procedures currently available, and is of lower cost. As TVT is a less invasive procedure, it is possible that some women who would currently be managed non-surgically will be considered eligible for TVT. Increased adoption of TVT will require additional surgeons proficient in the technique. It is likely that some of the higher rates of complications, e.g. bladder perforation, reported for TVT are associated with a 'learning curve'. Appropriate training will therefore be needed for surgeons new to the operation, in respect of both the technical aspects of the procedure and the choice of women suitable for the operation. Further research suggestions include unbiased assessments of longer term performance from follow-up of controlled trials or population-based registries; more data from methodologically sound RCTs using standard outcome measures; a surveillance system to detect longer term complications, if any, associated with the use of tape; and rigorous evaluation before extending the use of TVT to women who are currently managed non-surgically.

Colposcopy↗
PubMed2003

Assessment of food intake input distributions for use in probabilistic exposure assessments of food additives.

A key component of a food chemical exposure assessment using probabilistic analysis is the selection of the most appropriate input distribution to represent exposure variables. The study explored the type of parametric distribution that could be used to model variability in food consumption data likely to be included in a probabilistic exposure assessment of food additives. The goodness-of-fit of a range of continuous distributions to observed data of 22 food categories expressed as average daily intakes among consumers from the North-South Ireland Food Consumption Survey was assessed using the BestFit distribution fitting program. The lognormal distribution was most commonly accepted as a plausible parametric distribution to represent food consumption data when food intakes were expressed as absolute intakes (16/22 foods) and as intakes per kg body weight (18/22 foods). Results from goodness-of-fit tests were accompanied by lognormal probability plots for a number of food categories. The influence on food additive intake of using a lognormal distribution to model food consumption input data was assessed by comparing modelled intake estimates with observed intakes. Results from the present study advise some level of caution about the use of a lognormal distribution as a mode of input for food consumption data in probabilistic food additive exposure assessments and the results highlight the need for further research in this area.

Eating↗
PubMed1999

A probabilistic rule of mixtures for elastic moduli.

A novel approach is developed for mathematically modeling the variability observed in experimentally determined elastic moduli of longitudinally oriented fibrous tissues such as ligaments and tendons. The elastic modulus of these tissues is modeled with a rule of mixtures (ROM) where each parameter (fibril and matrix moduli and fibril volume fraction) is assumed to be an independent random variable. A joint density function formed from the independent densities results in a probabilistic ROM (pROM). This pROM is used to generate a distribution of moduli which agrees well with moduli determined from tests of rabbit medial collateral ligaments (Woo and Ohland, 1994, Unpublished experimental data as gift). Minimizing the error between the pROM and experimental distributions resulted in an integrated error of 9% for a constrained set of independent distribution parameters derived from the literature. This pROM thus incorporates microstructural observations (fibril and matrix moduli and fibril volume fraction) to partially explain the experimentally observed variability in a macroscopic property (tissue modulus).

Animals↗