Systems science methods in public health: what can they contribute to our understanding of and response to the cost-of-living crisis?

BACKGROUND

Many complex public health evidence gaps cannot be fully resolved using only conventional public health methods. We aim to familiarise public health researchers with selected systems science methods that may contribute to a better understanding of complex phenomena and lead to more impactful interventions. As a case study, we choose the current cost-of-living crisis, which affects disposable income as a key structural determinant of health.

METHODS

We first outline the potential role of systems science methods for public health research more generally, then provide an overview of the complexity of the cost-of-living crisis as a specific case study. We propose how four systems science methods (soft systems, microsimulation, agent-based and system dynamics models) could be applied to provide more in-depth understanding. For each method, we illustrate its unique knowledge contributions, and set out one or more options for studies that could help inform policy and practice responses.

RESULTS

Due to its fundamental impact on the determinants of health, while limiting resources for population-level interventions, the cost-of-living crisis presents a complex public health challenge. When confronted with complexity, non-linearity, feedback loops and adaptation processes, systems methods allow a deeper understanding and forecasting of the interactions and spill-over effects common with real-world interventions and policies.

CONCLUSIONS

Systems science methods provide a rich methodological toolbox that complements our traditional public health methods. This toolbox may be particularly useful in early stages of the current cost-of-living crisis: for understanding the situation, developing solutions and sandboxing potential responses to improve population health.

Testing and refining middle-range theory in evaluations of public-health interventions: evidence from recent systematic reviews and trials

Evaluations of public-health interventions might potentially be used to test and refine middle-range theory (ie, theory about the mechanisms, which generate outcomes that is analytically generalisable enough to span a range of contexts, interventions or outcomes, but specific enough to be salient in a given application). This approach has been suggested as one means of developing more informed assessments of how different interventions work and whether mechanisms might transfer across contexts. However, we have noticed that studies included in some of our recent systematic reviews are not oriented towards helping test middle-range theory because interventions draw on multiple middle-range theories (so that it is difficult to draw any conclusions about each middle-range theory based on their results) and these middle-range theories are insufficiently clear (with vague constructs) or parsimonious (with too many constructs) to be readily testable. Some studies might in future better contribute to testing and refining middle-range theory via focusing on interventions informed by one middle-range theory and focused on one mechanism at a time. Such 'proof-of-principle' studies should draw on middle-range theory that is sufficiently clear and parsimonious to allow such testing. These evaluations might facilitate more rigorous testing of middle-range theory and hence refinement of scientific knowledge. They might inform broader assessments of how mechanisms transfer across contexts aiding the development of future public-health interventions. Such studies would be a complement not an alternative to pragmatic studies of scalable complex interventions, often informed by more than one middle-range theory.

Mapping clinical outcomes to generic preference-based outcome measures: development and comparison of methods

BACKGROUND

Cost-effectiveness analysis using quality-adjusted life-years as the measure of health benefit is commonly used to aid decision-makers. Clinical studies often do not include preference-based measures that allow the calculation of quality-adjusted life-years, or the data are insufficient. 'Mapping' can bridge this evidence gap; it entails estimating the relationship between outcomes measured in clinical studies and the required preference-based measures using a different data set. However, many methods for mapping yield biased results, distorting cost-effectiveness estimates.

OBJECTIVES

Develop existing and new methods for mapping; test their performance in case studies spanning different preference-based measures; and develop methods for mapping between preference-based measures.

DATA SOURCES

Fifteen data sets for mapping from non-preference-based measures to preference-based measures for patients with head injury, breast cancer, asthma, heart disease, knee surgery and varicose veins were used. Four preference-based measures were covered: the EuroQoL-5 Dimensions, three-level version (n = 11), EuroQoL-5 Dimensions, five-level version (n = 2), Short Form questionnaire-6 Dimensions (n = 1) and Health Utility Index Mark 3 (n = 1). Sample sizes ranged from 852 to 136,327. For mapping between generic preference-based measures, data from FORWARD, the National Databank for Rheumatic Diseases (which includes the EuroQoL-5 Dimensions, three-level version, and EuroQoL-5 Dimensions, five-level version, in its 2011 wave), were used.

MAIN METHODS DEVELOPED

Mixture-model-based approaches for direct mapping, in which the dependent variable is the health utility value, including adaptations of methods developed to model the EuroQoL-5 Dimensions, three-level version, and beta regression mixtures, were developed, as were indirect methods, in which responses to the descriptive systems are modelled, for consistent multidirectional mapping between preference-based measures. A highly flexible approach was designed, using copulas to specify the bivariate distribution of each pair of EuroQoL-5 Dimensions, three-level version, and EuroQoL-5 Dimensions, five-level version, responses.

RESULTS

A range of criteria for assessing model performance is proposed. Theoretically, linear regression is inappropriate for mapping. Case studies confirm this. Flexible, direct mapping methods, based on different variants of mixture models with appropriate underlying distributions, perform very well for all preference-based measures. The precise form is important. Case studies show that a minimum of three components are required. Covariates representing disease severity are required as predictors of component membership. Beta-based mixtures perform similarly to the bespoke mixture approaches but necessitate detailed consideration of the number and location of probability masses. The flexible, bi-directional indirect approach performs well for testing differences between preference-based measures.

LIMITATIONS

Case studies drew heavily on EuroQoL-5 Dimensions. Indirect methods could not be undertaken for several case studies because of a lack of coverage. These methods will often be unfeasible for preference-based measures with complex descriptive systems.

CONCLUSIONS

Mapping requires appropriate methods to yield reliable results. Evidence shows that widely used methods such as linear regression are inappropriate. More flexible methods developed specifically for mapping show that close-fitting results can be achieved. Approaches based on mixture models are appropriate for all preference-based measures. Some features are universally required (such as the minimum number of components) but others must be assessed on a case-by-case basis (such as the location and number of probability mass points).

FUTURE RESEARCH PRIORITIES

Further research is recommended on (1) the use of the monotonicity concept, (2) the mismatch of trial and mapping distributions and measurement error and (3) the development of indirect methods drawing on methods developed for mapping between preference-based measures.

FUNDING

This project was funded by the National Institute for Health Research (NIHR) Health Technology Assessment programme and will be published in full in Health Technology Assessment; Vol. 24, No. 34. See the NIHR Journals Library website for further project information. This project was also funded by a Medical Research Council grant (MR/L022575/1).

UNSTABLE GENETIC TRANSFORMATION IN BACILLUS SUBTILIS AND THE MODE OF INHERITANCE IN UNSTABLE CLONES

Iyer, V. N. (Canada Department of Agriculture, Ottawa, Ont., Canada). Unstable genetic transformation in Bacillus subtilis and the mode of inheritance in unstable clones. J. Bacteriol. 90:495-503. 1965.-An ultraviolet-induced mutant has been isolated from the double auxotroph of Bacillus subtilis (bearing the linked mutations try(2) and his(2)). This mutant has the property of yielding unstable transformants which, in the case of transformation to prototrophy, can be recognized by reduced colony size on minimal agar. Unstable transformant clones usually become stabilized early during the development of the clone (within 12 generations). Analyses of genotypes emerging from such clones on stabilization indicate that in some of these clones the exogenote is transmitted linearly; its integrity is sufficiently preserved that it can participate in two independent recombination events in two different cells. Genetic markers on the exogenote are expressed in situations where genetic integration has not occurred.

A THEORETICAL ANALYSIS OF NEURONAL VARIABILITY

A simple neuronal model is assumed in which, after a refractory period, excitatory and inhibitory exponentially decaying inputs of constant size occur at random intervals and sum until a threshold is reached. The distribution of time intervals between successive neuronal firings (interresponse time histogram), the firing rate as a function of input frequency, the variability in the time course of depolarization from trial to trial, and the strength-duration curve are derived for this model. The predictions are compared with data from the literature and good qualitative agreement is found. All parameters are experimentally measurable and a direct test of the theory is possible with present techniques. The assumptions of the model are relaxed and the effects of such experimentally found phenomena as relative refractory and supernormal periods, adaptation, potentiation, and rhythmic slow potentials are discussed. Implications for gross behavior studies are considered briefly.

A STUDY OF SOME THIOL ESTER HYDROLYSES AS MODELS FOR THE DEACYLATION STEP OF PAPAIN-CATALYSED HYDROLYSES

1. The self-catalysed hydrolyses of the thiol esters, S-hippurylthioglycollic acid and S-ethyl monothiolsuccinate, have been shown to be slower than the deacylation step for the papain-catalysed hydrolysis of hippuric esters, by a factor approx. 10(5). This difference in rate constants largely reflects a difference in activation energy, which together with other evidence drawn from the literature make it unlikely that a carboxylate ion could be the nucleophile responsible for the deacylation of acyl-papain. 2. The imidazole-catalysed hydrolysis of S-hippurylthioglycollic acid and ethyl thiolacetate have activation energies similar to that for the deacylation step in papain-catalysed hydrolyses. This, together with other evidence drawn from the literature, suggests that the imidazole of a histidine residue is the nucleophile responsible for the deacylation of acyl-papain.

ON THE ACTION OF COLCHICINE, THE MELANOCYTE MODEL

The effect of colchicine was studied on the rapid, reversible darkening of frog skin under the influence of melanocyte-stimulating hormone (MSH). Darkening is due to dispersion of melanin granules in melanocytes and is thought to be accompanied by a gel-to-sol cytoplasmic transformation. After subsequent washing, the skin lightens, with aggregation of melanin granules and cytoplasmic gelation. Preincubation of skin with colchicine had the following effects: 1. Darkening induced by MSH was increased in comparison to control skins, and on removal of MSH, lightening was inhibited. Inhibition was a function of both concentration (1 x 10^–5 to 9 x 10^–5M) and exposure time (2 to 30 minutes). Once established, inhibition was maintained throughout the remainder of the experiment. 2. The same effects were noted (a) when darkening was effected by agents other than MSH (ATP) 0.9 x 10^–3M; caffeine, 5.2 x 10^–3M; ethyl acetate, 0.8 x 10^–2M), and (b) when lightening was effected by addition of chemical agents (melatonin, 4.3 x 10^–10M; hydrocortisone, 1 x 10^–3M; norepinephrine, 1 x 10^–3M), instead of by washing. 3. Colchicine alone produced a gradual, irreversible, dosage-dependent darkening over several hours. This darkening was inhibited by melatonin, 4.3 x 10^–10M. The melanocyte model is used to construct a general theory of colchicine action on living cells, an action resulting in decreased protoplasmic viscosity. In this formulation colchicine lowers the potential limit of protoplasmic gelation, and does it rapidly, reversibly, in low concentration, in a dosage-dependent manner, and without killing the cell. The theory allows interpretation of "synergism" and "antagonism" to colchicine by other substances. It suggests a tentative approach to the understanding of colchicine action in acute gouty arthritis, where interference with ameboid activities of polymorphonuclear leukocytes is one possible aspect of the anti-inflammatory effect of colchicine. Finally, the colchicine-treated melanocyte is viewed as a good, live physical model that can be used to elucidate some fundamental biological properties.

THE EXTRATHYROIDAL DISTRIBUTION OF 131-I THYROXINE

The elimination of radioactivity from the blood stream has been examined in 6 subjects after intravenous administration of 131I-thyroxine. About 50 per cent of the radioactivity left the blood within 60–90 minutes and 75 per cent within 6 hours. In both in vivo and in vitro experiments there was a rapid linking of the labelled thyroxine to the serum proteins.

The elimination of radioactivity from the blood and the excretion in urine and faeces was followed in 12 subjects for 12 days. To calculate the distribution and exchange of the labelled thyroxine between the various extrathyroidal pools, a model comprising 4 pools was constructed. The working of the model was analysed by means of an analogue computer. There was a close agreement between the curves thus obtained and those yielded by empirical methods. According to the 4-pool model 6 – 7 times the intravascular thyroxine pool was exchanged with the extravascular pool in 24 hours.

VISUAL-REINFORCER COLOR, AND OPERANT BEHAVIOR IN SIAMESE FIGHTING FISH

Male Siamese Fighting Fish (Betta splendens) were conditioned to emit an operant response sequence reinforced by presentation of a model of a male Siamese Fighting Fish in aggressive display. Operant response rate varied as a function of the color of the model with respect to the color of the subject.

INVESTIGATION OF AN OPERATOR METHOD IN THE ANALYSIS OF BIOLOGICAL TRACER DATA

Some factors affecting the usefulness of a linear operator in the analysis of tracer data were evaluated. Application of the operator to a sum of two exponential components resulted in the separation of the rate constants with an accuracy of 10 to 15 per cent if they differed by a factor of at least 2 and the error in the data was about 2 per cent. A factor of 4 was necessary if the error in the data was 6 per cent, and of 6 if the error was 10 per cent. The ratio of amplitudes varied from near unity to equality with the ratio of rate constants. However, if the ratio of amplitudes was greater than the ratio of rate constants the method would not resolve the rate constants. Application of the operator to a sum of three exponential components was also considered.

LEUKOCYTES AND INTERFERON IN THE HOST RESPONSE TO VIRAL INFECTIONS. I. MOUSE LEUKOCYTES AND LEUKOCYTE-PRODUCED INTERFERON IN VACCINIA VIRUS INFECTION IN VITRO

1. Investigation of the role of leukocytes in vaccinia virus infection is reported in an in vitro model, in the absence of an immune response. 2. Mouse leukocytes were shown to be capable of inhibiting the progression of vaccinia virus infection in primary mouse embryo fibroblast cultures. The degree of protection varied from slowing of spread of infection to complete control of the infection with eventual elimination of detectable virus and recovery of the culture. 3. Interferon production by leukocytes is thought to be an important factor in the observed protective effect.

ON THE CONCENTRATION GRADIENT ACROSS A SPHERICAL SOURCE WASHED BY SLOW FLOW

A model has been numerically analyzed to help interpret the orienting effects of flow upon cells. The model is a sphere steadily and uniformly emitting a diffusible stuff into a medium otherwise free of it and moving past with Stokes flow. Its properties depend primarily upon the Peclet number, Pe, equal to a . v(infinity)/D, i.e., the sphere's radius, a, times the free stream speed, v(infinity), over the stuff's diffusion constant, D. As Pe rises, and washing becomes more effective, the average surface concentration, C(s a) falls (Figs. 2 and 5) and the residual material becomes relatively concentrated on the sphere's lee pole (Figs. 2 and 4). Specifically, as Pe rises from 0.1 to 1, the relative concentration gradient, G, rises from 0.7 to 5.0 per cent and to the point where it is rising at about 8 per cent per decade; by Pe 1000, G = 22.1 per cent. From Pe 1 through 1000, G/(1 - C(s a)), or the gradient per concentration deficiency remains at about 26 per cent suggesting that G approaches a ceiling of about 26 per cent. Also from Pe 1 through 1000, the average mass transfer co-efficient nearly equals that previously calculated for spheres maintaining constant surface concentration instead of flux. The complete differential equation without approximations, the Gauss-Seidel method, and an approximation for the outer boundary condition were used.

Different types of sympathomimetic alpha-receptors. ACTA ACUST UNITED AC. 1965;17:202-216. [PMID: 14327707 DOI: 10.1111/j.2042-7158.1965.tb07646.x]

Sympathomimetic effects have been studied on the isolated vas deferens of the rat, in the isolated jejunum of the rabbit and on the cardiovascular system of the cat. (–)-Noradrenaline (1-R configuration), (+)-noradrenaline (1-S configuration) and dopamine as well as a number of homologues were used as agonists. The adrenergic blocking drugs piperoxan, phentolamine, yohimbine, aceperone and the tranquillising drugs chlorpromazine, (–)-mepromazine, haloperidol, droperidol and spiramide as well as bulbocapnine were used as antagonists. The results obtained with both agonists and antagonists provide evidence that the structural requirements for drugs to react with and to activate α-receptors in the vas deferens and the rabbit intestine are different; epinine and dopamine have an identical mechanism of action.

THE NUMERICAL SOLUTION OF THE TIME-DEPENDENT NERNST-PLANCK EQUATIONS

Calculations are reported of the time-dependent Nernst-Planck equations for a thin permeable membrane between electrolytic solutions. Charge neutrality is assumed for the time-dependent case. The response of such a membrane system to step current input is measured in terms of the time and space changes in concentration, electrical potential, and effective conductance. The report also includes discussion of boundary effects that occur when charge neutrality does not hold in the steady-state case.

AUTOIMMUNE DISEASE IN NZB/BL MICE. I. PATHOLOGY AND PATHOGENESIS OF A MODEL SYSTEM OF SPONTANEOUS GLOMERULONEPHRITIS

This study, based upon 528 laboratory examinations and 16 complete autopsies of NZB/Bl mice, deals with autoimmune manifestations (as shown by hypergammaglobulinemia, Coombs positive hemolytic anemia, and the occasional presence of lupus- and rheumatoid-like factors) and mainly with the pathology and the pathogenesis of glomerulonephritis in these mice, a model system of membranous glomerulonephritis with spontaneous and insidious onset, progression through chronic stages, and almost certainly induced by immunological, and autoimmune, mechanisms. The earliest and lasting histological change was hyaline thickening of the capillary walls and adjacent intercapillary regions of the glomerular tufts, corresponding in location to polysaccharide-rich capillary basement membrane and mesangial materials. Distributed focally and diffusely in the glomerular tuft and eventually sparing no glomerulus, hyaline, granular, and fibrillar ("spongy fiber") materials produced narrowing of capillary lumens by concentric or eccentric encroachment upon them. In the later stages hyaline lobulation and sclerosis of the glomerular tufts occurred. Thus the lesions corresponded to those seen in human focal and diffuse membranous, chronic lobular, and lastly (intracapillary) sclerosing glomerulonephritis. In all instances of glomerulonephritis the glomerular tufts contained selective localizations of mouse immunoglobulins corresponding in distribution to that of the hyaline and (PAS-positive) polysaccharide-rich materials in the focal and diffuse membranous and lobular lesions and in amounts increasing with the severity of glomerular disease. The mouse immunoglobulins were extracted from frozen sections of glomerulonephritic kidneys and were then capable of recombination with glomerular tufts in sections of autologous or isologous glomerulonephritic kidneys from which in vivo localized immunoglobulins had been extracted. The pattern of recombination with glomerular tufts was similar to that of in invo localized immunoglobulins. The extracted immunoglobulins did not show affinity for mouse red cells (in the indirect Coombs test) nor for autologous or isologous cell nuclei (in the immunofluorescence test). The serum of mice with severe glomerulonephritis contained immunoglobulins with in vitro affinity for extracted autologous or isologous glomerular tufts. Thus circulating as well as localized antibodies were demonstrated. The immunogenic materials (autoantigens) may have been formed in the glomerular tufts or accumulated in them from some other source, such as the circulating plasma; however they corresponded in location to polysaccharide-rich capillary basement membrane and mesangial materials. The spleen was identified at the cellular level as the main site of formation of autoantibodies to red cells, as well as the main site of red cell destruction. Some evidence was brought forth suggesting that these autoantibodies were "heavy" or γM-globulins. More studies are in progress.

MODELS AND THEORY FOR UREA METABOLISM

1. Theories have been developed to try to interpret the effects of finite time of equilibration between plasma and body water, and the mechanism of renal function, on the variations of activity and specific activity of urea in plasma and urine after initial injection. 2. The magnitudes of errors likely to arise through approximations made in estimating the pool of body urea etc. have been derived. 3. Experimental results do not fit exactly with extreme models postulated, but are usually intermediate.

A MATHEMATICAL MODEL OF THE HUMAN RESPIRATORY CONTROL SYSTEM

The respiratory system exhibits the properties of a control system of the regulator type. Equations describing this biological control system have been derived. Transient and steady-state solutions for various CO(2) and O(2) step input disturbances were obtained utilizing a digital computer and are compared with experimental results. The effectiveness of the respiratory system as a regulator is investigated. Further extensions of the model are suggested.

STEADY-STATE PHOTOTROPISM IN PHYCOMYCES

The steady-state phototropic bending of Phycomyces sporangiophores was studied using apparatus designed to keep the growing zone vertical and the angle of illumination constant over long periods of time. The bending speed is quite constant if the intensity and angle of illumination are fixed. A phototropic inversion occurs in response to a sudden change in intensity, either an increase or a decrease. A bending component lateral to the illumination direction is strongly evident at normal incidence. It is shown that this component is due to a rotation between the stimulus and response loci about the axis of the growing zone, which is probably related to the spiral growth of the cell. The steady-state bending speed is at a maximum value for illumination directions ranging from normal incidence to about 45 degrees . From 45 to 14 degrees the bending speed decreases linearly with angle, reaching zero at 14 degrees . Angles less than 14 degrees elicit a weak negative phototropic response. Using an optical model of the growing zone, the intracellular intensity distribution was determined as a function of the angle of illumination. Several hypotheses relating the intensity distribution to the phototropic response are discussed.

AUTOMATIC CLASSIFICATION OF STAPHYLOCOCCI BY PRINCIPAL-COMPONENT ANALYSIS AND A GRADIENT METHOD

Hill, L. R. (Università Statale, Milano, Italy), L. G. Silvestri, P. Ihm, G. Farchi, and P. Lanciani. Automatic classification of staphylococci by principal-component analysis and a gradient method. J. Bacteriol. 89:1393-1401. 1965.-Forty-nine strains from the species Staphylococcus aureus, S. saprophyticus, S. lactis, S. afermentans, and S. roseus were submitted to different taxometric analyses; clustering was performed by single linkage, by the unweighted pair group method, and by principal-component analysis followed by a gradient method. Results were substantially the same with all methods. All S. aureus clustered together, sharply separated from S. roseus and S. afermentans; S. lactis and S. saprophyticus fell between, with the latter nearer to S. aureus. The main purpose of this study was to introduce a new taxometric technique, based on principal-component analysis followed by a gradient method, and to compare it with some other methods in current use. Advantages of the new method are complete automation and therefore greater objectivity, execution of the clustering in a space of reduced dimensions in which different characters have different weights, easy recognition of taxonomically important characters, and opportunity for representing clusters in three-dimensional models; the principal disadvantage is the need for large computer facilities.

ENERGY SUPPLY FOR THE CHEMOAUTOTROPH FERROBACILLUS FERROOXIDANS

Dugan, Patrick R. (Syracuse University, Syracuse, N.Y.), and Donald G. Lundgren. Energy supply for the chemoautotroph Ferrobacillus ferrooxidans. J. Bacteriol. 89:825-834. 1965.-A working model is proposed to explain dissimilatory ferrous iron oxidation by Ferrobacillus ferrooxidans, that is, oxidation linked to an energy source. The model is supported by experimental evidence reported here as well as in the literature. Polarographic assays of the culture medium demonstrated an iron "complex" involving oxygen. The initial "complex" would be oxygenated, but not oxidized because no electron transport has taken place. The "complex" is formed in solution or on the cell surface and is somehow reacted with iron oxidase (or oxygenase), resulting in the release of an electron. Either sulfate or a flavoprotein is suggested as involved in the initial electron-transfer link between iron and the cell. The electron is transported in the cell through a typical electron-transport system involving coenzyme Q(6), cytochrome c, and cytochrome a; oxygen is the final electron acceptor. Electron micrographs of intact and sectioned cells are included to show structural detail in support of the model.

OXYGEN-HEMOGLOBIN SYSTEM: A MODEL FOR FACILITATED MEMBRANOUS TRANSPORT

Enhanced transport of oxygen in a Millipore filter containing a solution of hemoglobin can be accounted for by the diffusion of free oxygen as well as of hemoglobin-bound oxygen. A model shows that, at oxygen tensions at which the hemoglobin is fully saturated in a portion of the membrane, the enhanced transport is due to a steeper gradient for free oxygen, whereas in the rest of the membrane an "(oxy)hemoglobin shuttle" operates. A similar model may be useful for explaining facilitated diffusion in other systems.

ELECTRON MICROSCOPY OF LEPTOSPIRES. I. ANATOMICAL FEATURES OF LEPTOSPIRA POMONA

Ritchie, A. E. (National Animal Disease Laboratory, Ames, Iowa), and Herman C. Ellinghausen. Electron microscopy of leptospires. I. Anatomical features of Leptospira pomona. J. Bacteriol. 89:223-233. 1965.-Anatomical features of Leptospira pomona are described. Most cells in the logarithmic phase of growth, when examined in whole cell "negative-stained" preparations, display a homogeneous finely granular protoplasmic cylinder. Some cells contain discrete or complex lamellar structures. The cell termini are attached to the protoplasmic cylinder by a membrane system. Each organism appears to have two independent axial filaments originating from opposite ends of the cell. The axial filaments are composed of a closely knit bundle of some 12 to 15 individual strands. A simple model suggesting a locomotory function for the axial filaments is presented. A superficial callouslike mass is occasionally observed in the cell's terminal region. The enveloping sheath is similar to the cytoplasmic membrane; both are triple-layered and ca. 50 A thick. The sheath preferentially forms blebs at the cell termini and midway along the protoplasmic cylinder. Septal-wall formation occurs at the mid region of the cell, and it is concluded that simple transverse binary fission is the predominant mode of reproduction.

A STATISTICAL ANALYSIS OF THE CONTINUAL ACTIVITY OF SINGLE CORTICAL NEURONES IN THE CAT UNANAESTHETIZED ISOLATED FOREBRAIN

Statistical analyses are applied to records obtained under conditions of spontaneous activity. These demonstrate that all the cells examined are similar in the respect that their signals are composed of an approximately Poissonian shower gated on and off at random instants. A mathematical model is developed on this basis which characterises the signal of any one neurone with a number of simple parameters. The manner in which these parameters change under various types of stimulation is studied. It is found that the average frequency inside the sections of Poisson shower remains unchanged in all cases examined. Implications as to the types of network involved are discussed.