Coordinated force production in multi-finger tasks: finger interaction and neural network modeling

During maximal voluntary contraction (MVC) with several fingers, the following three phenomena are observed: (1) the total force produced by all the involved fingers is shared among the fingers in a specific manner (sharing); (2) the force produced by a given finger in a multi-finger task is smaller than the force generated by this finger in a single-finger task (force deficit); (3) the fingers that are not required to produce any force by instruction are involuntary activated (enslaving). We studied involuntary force production by individual fingers (enslaving effects, EE) during tasks when (an)other finger(s) of the hand generated maximal voluntary pressing force in isometric conditions. The subjects (n = 10) were instructed to press as hard as possible on the force sensors with one, two, three and four fingers acting in parallel in all possible combinations. The EE were (A) large, the slave fingers always producing a force ranging from 10.9% to 54.7% of the maximal force produced by the finger in the single-finger task; (B) nearly symmetrical; (C) larger for the neighboring fingers; and (D) non-additive. In most cases, the EE from two or three fingers were smaller than the EE from at least one finger (this phenomenon was coined occlusion). The occlusion cannot be explained only by anatomical musculo-tendinous connections. Therefore, neural factors contribute substantially to the EE. A neural network model that accounts for all the three effects has been developed. The model consists of three layers: the input layer that models a central neural drive; the hidden layer modeling transformation of the central drive into an input signal to the muscles serving several fingers simultaneously (multi-digit muscles); and the output layer representing finger force output. The output of the hidden layer is set inversely proportional to the number of fingers involved. In addition, direct connections between the input and output layers represent signals to the hand muscles serving individual fingers (uni-digit muscles). The network was validated using three different training sets. Single digit muscles contributed from 25% to 50% of the total finger force. The master matrix and the enslaving matrix were computed; they characterize the ability of a given finger to enslave other fingers and its ability to be enslaved. Overall, the neural network modeling suggests that no direct correspondence exists between neural command to an individual finger and finger force. To produce a desired finger force, a command sent to an intended finger should be scaled in accordance with the commands sent to the other fingers. Received: 17 October 1997 / Accepted in revised form: 12 May 1998     

Effects of age and gender on finger coordination in MVC and submaximal force-matching tasks.

The objective of the study is to examine the effects of age and gender on finger coordination. Twelve young (24 +/- 8 yr; 6 men and 6 women) and 12 elderly (75 +/- 5 yr; 6 men and 6 women) subjects performed single-finger maximal contraction [maximal voluntary contraction (MVC)], four-finger MVC, and four-finger ramp force production tasks by pressing on individual force transducers. A drop in the force of individual fingers during four-finger MVC tasks compared with single-finger MVC tasks (force deficit) was larger, whereas unintended force production by other fingers during single-finger MVC tasks (enslaving) was smaller, in elderly than in young subjects and in women than in men. Force deficit was smaller and enslaving was larger in subjects with higher peak force. During the ramp task, the difference between the variance of total force and the sum of variances of individual forces showed a logarithmic relation to the level of total force, across all subject groups. These findings suggest that indexes of finger coordination scale with force-generating capabilities across gender and age groups.     

Force and torque production in static multifinger prehension: biomechanics and control. II. Control

 The coordination of digits during combined force/torque production tasks was further studied using the data presented in the companion paper [Zatsiorsky et al. Biol Cybern this issue, Part I]. Optimization was performed using as criteria the cubic norms of (a) finger forces, (b) finger forces normalized with respect to the maximal forces measured in single-finger tasks, (c) finger forces normalized with respect to the maximal forces measured in a four-finger task, and (d) finger forces normalized with respect to the maximal moments that can be generated by the fingers. All four criteria failed to predict antagonist finger moments when these moments were not imposed by the task mechanics. Reconstruction of neural commands: The vector of neural commands c was reconstructed from the equation c=W ⁻¹ F, where W is the finger interconnection weight matrix and F is the vector of finger forces. The neural commands ranged from zero (no voluntary force production) to one (maximal voluntary contraction). For fingers producing moments counteracting the external torque (`agonist' fingers), the intensity of the neural commands was well correlated with the relative finger forces normalized to the maximal forces in a four-finger task. When fingers produced moments in the direction of the external torque (`antagonist' fingers), the relative finger forces were always larger than those expected from the intensity of the corresponding neural commands. The individual finger forces were decomposed into forces due to `direct' commands and forces induced by enslaving effects. Optimization of the neural commands resulted in the best correspondence between actual and predicted finger forces. The antagonist moments are, at least in part, due to enslaving effects: strong commands to agonist fingers also activated antagonist fingers. Received: 8 August 2001 / Accepted in revised form: 7 February 2002     

Force and torque production in static multifinger prehension: biomechanics and control. I. Biomechanics

 We studied the coordinated action of fingers during static tasks involving exertion of force and torque on a handheld object. Subjects were asked to keep a handle with an attachment that allowed for independent change of the suspended load (0.5–2.0 kg) and external torque (0.375–1.5 N m) in a vertical position while applying minimal effort. Normal and shear forces were measured from the thumb; normal forces only were measured from the four fingers. Experimental results: (1) the thumb shear force increased during supination efforts and decreased during pronation efforts; (2) the total moment of the normal finger forces only counterbalanced approximately 50% of the external torque, hence shear forces accounted for approximately one-half of the total torque exerted on the object; (3) the total normal force increased with external torque, and the total force magnitude did not depend on the torque direction; (4) the forces of the `peripheral' (index and little) fingers depended mainly on the torque while the forces exerted by the `central' (middle and ring) fingers depended both on the load and torque; (5) there was a monotonic relationship between the mechanical advantage of a finger (i.e., its moment arm during torque production) and the force produced by that finger; and (6) antagonist finger moments acting opposite to the intended direction of the total moment were always observed – at low torques the antagonist moments were as high as 40–60% of the agonist moments. Modeling: A three-zone model of coordinated finger action is suggested. In the first zone of load/torque combinations, activation of antagonist fingers (i.e., fingers that generate antagonist moments) is necessary to prevent slipping. In the second zone, the activity of agonist fingers is sufficient for preventing slips. In the third zone, the performer has freedom to choose between either activating the antagonist fingers or redistributing activities amongst the agonist fingers. The findings of this study provide the foundation for neural network and optimization modeling described in the companion paper [Zatsiorsky et al. (2002) Biol Cybern DOI 10.1007/s00422-002-0320-7]. Received: 8 August 2001 / Accepted in revised form: 7 February 2002     

Spike synchronization and firing rate in a population of motor cortical neurons in relation to movement direction and reaction time

 We studied the dynamics of precise spike synchronization and rate modulation in a population of neurons recorded in monkey motor cortex during performance of a delayed multidirectional pointing task and determined their relation to behavior. We showed that at the population level neurons coherently synchronized their activity at various moments during the trial in relation to relevant task events. The comparison of the time course of the modulation of synchronous activity with that of the firing rate of the same neurons revealed a considerable difference. Indeed, when synchronous activity was highest, at the end of the preparatory period, firing rate was low, and, conversely, when the firing rate was highest, at movement onset, synchronous activity was almost absent. There was a clear tendency for synchrony to precede firing rate, suggesting that the coherent activation of cell assemblies may trigger the increase in firing rate in large groups of neurons, although it appeared that there was no simple parallel shifting in time of these two activity measures. Interestingly, there was a systematic relationship between the amount of significant synchronous activity within the population of neurons and movement direction at the end of the preparatory period. Furthermore, about 400 ms later, at movement onset, the mean firing rate of the same population was also significantly tuned to movement direction, having roughly the same preferred direction as synchronous activity. Finally, reaction time measurements revealed a directional preference of the monkey with, once again, the same preferred direction as synchronous activity and firing rate. These results lead us to speculate that synchronous activity and firing rate are cooperative neuronal processes and that the directional matching of our three measures – firing rate, synchronicity, and reaction times – might be an effect of behaviorally induced network cooperativity acquired during learning. Received: 16 January 2002 / Accepted in revised form: 26 November 2002 / Published online: 7 April 2003 RID="*" ID="*" Present address: Istituto di Fisiologia Umana, Università di Parma, Via Volturno 39, 43100 Parma, Italy Correspondence to: A. Riehle (e-mail: ariehle@lnf.cnrs-mrs.fr, Tel.: +33-491-164329, Fax: +33-491-774969) Acknowledgements. We wish to thank Sonja Grün, Markus Diesmann, and Bill MacKay for many helpful and exciting discussions and one anonymous referee for her/his helpful comments. Special thanks go to Annette Bastian for her help in data collection, Michèle Coulmance for writing data acquisition and parts of data analysis software, and Marc Martin for animal welfare. This research was supported in part by the CNRS, GIS (Sciences de la Cognition), and ACI Cognitique (Invariants and Variability). FG was supported by the French government (MENRT).     

A numerical method for renal models that represent tubules with abrupt changes in membrane properties

 The urine concentrating mechanism of mammals and birds depends on a counterflow configuration of thousands of nearly parallel tubules in the medulla of the kidney. Along the course of a renal tubule, cell type may change abruptly, resulting in abrupt changes in the physical characteristics and transmural transport properties of the tubule. A mathematical model that faithfully represents these abrupt changes will have jump discontinuities in model parameters. Without proper treatment, such discontinuities may cause unrealistic transmural fluxes and introduce suboptimal spatial convergence in the numerical solution to the model equations. In this study, we show how to treat discontinuous parameters in the context of a previously developed numerical method that is based on the semi-Lagrangian semi-implicit method and Newton's method. The numerical solutions have physically plausible fluxes at the discontinuities and the solutions converge at second order, as is appropriate for the method. Received: 13 November 2001 / Revised version: 28 June 2002 / Published online: 26 September 2002 This work was supported in part by the National Institutes of Health (National Institute of Diabetes and Digestive and Kidney Diseases, grant DK-42091.) Mathematics Subject Classification (2000): 65-04, 65M12, 65M25, 92-04, 92C35, 35-04, 35L45 Keywords or phrases: Mathematical models – Differential equations – Mathematical biology – Kidney – Renal medulla – Semi-Lagrangian semi-implicit     

Dynamics of annual influenza A epidemics with immuno-selection

 The persistence of Influenza A in the human population relies on continual changes in the viral surface antigens allowing the virus to reinfect the same hosts every few years. The epidemiology of such a drifting virus is modeled by a discrete season-to-season map. During the epidemic season only one strain is present and its transmission dynamics follows a standard epidemic model. After the season, cross-immunity to next year's virus is determined from the proportion of hosts that were infected during the season. A partial analysis of this map shows the existence of oscillations where epidemics occur at regular or irregular intervals. Received: 16 February 2001 / Revised version: 11 June 2002 / Published online: 28 February 2003 Key words or phrases: Infectious disease – Influenza drift – Cross-immunity – Seasonal epidemics – Iterated map     

On the dynamics of discrete food chains: low- and high-frequency behavior and optimality of chaos

 In this paper we derive and analyze a discrete version of Rosenzweig's (Am. Nat. 1973) food-chain model. We provide substantial analytical and numerical evidence for the general dynamical patterns of food chains predicted by De Feo and Rinaldi (Am. Nat. 1997) remaining largely unaffected by this discretization. Our theoretical analysis gives rise to a classification of the parameter space into various regions describing distinct governing dynamical behaviors. Predator abundance has a local optimum at the edge of chaos. Received: 13 August 1999 / Revised version: 12 March 2002 / Published online: 17 October 2002 Mathematics Subject Classification (1991): 92D40 Keywords or phrases: Discrete food-chain – Discrete Hopf (Neimark-Sacker) bifurcation – Pulsewise birth processes – Mean yield maximization – Nicholson-Bailey model     

A nonlinear dynamical mechanism for bruit generation by an intracranial saccular aneurysm

 Intracranial saccular aneurysms have been clinically observed to emit a transient sound, a bruit, on each heartbeat. The mechanism causing the bruits has been a matter of contention. A qualitative analysis of the nonlinear dynamical properties of the Shah-Humphrey model for periodic pressure forcing of a thin-necked saccular aneurysm, using the Fung nonlinear constitutive model for the aneurysm material, shows that a small blood pressure jump on each beat, whether the pressure is weakly aperiodic or periodic, induces transients in the radial deformation response of the aneurysmal wall on each heartbeat. These transient vibrations, which have a component with frequency near the natural frequency of the system but are not resonant phenomena and which decay rapidly to a limit cycle during each distinct forcing pressure cycle, can generate the bruits. Received: 21 November 2000 / Revised version: 9 August 2001 / Published online: 23 August 2002 Mathematics Subject Classification (2000): 92B99, 70K40, 70K05 Key words or phrases: Intracranial saccular aneurysm – Bruit – Spectrum – Nonlinear dynamics – Transients – Vortex shedding – Fung model     

The isometric force that induces maximal surface muscle deoxygenation

To determine the external force that induces maximal deoxygenation of brachioradialis muscle 32 trained male subjects maintained isometric contractions using the elbow flexor muscles up to the limit time (isotonic part of the isometric contraction, IIC) and beyond that time for 120 s (anisotonic part of the isometric contraction). During IIC each subject maintained relative forces of either 25% and 70% maximal voluntary contraction (MVC), 50% and 100% MVC, or 40% and 60% MVC. Muscle oxygenation was assessed using a near infrared spectroscope, and expressed as a percentage of the reference value (ΔO_2rest) which was the difference between the minimal oxygenation obtained after 6 min of ischaemia at rest and the maximal reoxygenation following the release of the tourniquet. During IIC at 25% MVC, muscle oxygenation decreased to 17 (SEM 3)% ΔO_2rest, then it levelled off [25 (SEM 1)% ΔO_2rest]. After the point at which target force could not be maintained, reoxygenation was very weak. During IIC at 40%, 50%, 60%, and 70% MVC, the lowest muscle oxygenation values were obtained after 15–20 s of contraction and corresponded to −18 (SEM 6), −59 (SEM 12) −31 (SEM 6), and −29 (SEM 6)% ΔO_2rest, respectively. For the contraction at 100% MVC, the lowest oxygenation [−19 (SEM 9)% ΔO_2rest] was obtained while force was decreasing (69% MVC). During the anisotonic part of the isometric contractions, the greatest reoxygenation rate was obtained after 50% MVC IIC (P < 0.001). Our results showed that during isometric elbow flexions between 25% and 100% MVC, there was no linear relationship between external force and muscle oxygenation, and that the maximal deoxygenation of the brachioradialis muscle was obtained at 50% MVC. Accepted: 16 February 1998     

Exact sampling formulas for multi-type Galton-Watson processes

 Exact formulas for the mean and variance of the proportion of different types in a fixed generation of a multi-type Galton-Watson process are derived. The formulas are given in terms of iterates of the probability generating function of the offspring distribution. It is also shown that the sequence of types backwards from a randomly sampled particle in a fixed generation is a non-homogeneous Markov chain where the transition probabilities can be given explicitly, again in terms of probability generating functions. Two biological applications are considered: mutations in mitochondrial DNA and the polymerase chain reaction. Received: 10 June 2001 / Revised version: 21 November 2001 / Published online: 23 August 2002 Mathematics Subject Classification (2000): Primary 60J80, Secondary 92D10, 92D25 Key words or phrases: Multi-type Galton-Watson process – sampling formula – PCR – mitochondrial DNA     

Age effects on force produced by intrinsic and extrinsic hand muscles and finger interaction during MVC tasks.

Finger-pressing forces are produced by activation of the intrinsic hand muscles, which are finger specific, and the extrinsic muscles that connect to multiple fingers. We tested a hypothesis of greater weakening of intrinsic hand muscles with age and quantified associated indexes of finger interaction such as enslaving (force production by unintended fingers) and force deficit (loss of finger force in multifinger tasks compared with single-finger tasks). Twelve young (23-35 yr old) and 12 elderly (70-95 yr old) men and women performed single-finger and four-finger maximal pressing tasks, in which force was applied at the proximal phalanges (PP, the intrinsic muscles are major focal force generators) and at the distal phalanges (DP, the extrinsic muscles are focal force generators). The decline in the peak force with age was greater at PP (30%) than at DP (19%). Larger indexes of finger interaction were observed at PP (enslaving = 17.2 +/- 9.4%, force deficit = 36.1 +/- 11.1%) than at DP (enslaving = 14.9 +/- 8.8%, force deficit = 27.7 +/- 10.8%) across ages and genders. We conclude that intrinsic hand muscles show disproportionate weakening with age. The greater indexes of finger interaction in PP tests with greater involvement of intrinsic hand muscles suggest that the finger interactions are predominantly of a central origin across ages and genders.     

Genetic susceptibility to ischemic stroke in Russians

The frequencies of alleles and genotypes for ten functionally significant single-nucleotide polymorphisms were determined in the FGA, FGB, APOE, LPL, ACE, and CMA1 genes for Russian ischemic stroke (IS) patients and for a control group of Russians similar in gender and age distribution. The groups showed no significant differences in the frequencies of individual alleles or genotypes for any polymorphism studied. However, complex analysis of genetic susceptibility by the APSampler algorithm demonstrated that carriership of the APOE (−491A) allele predisposed to IS (p = 0.044, OR 3.8, 95% CI 1.0–15.1). Correspondingly, the APOE (−491T/T) genotype was associated with resistance to IS (p = 0.044, OR 0.26, 95% CI 0.07–1.0). The carriership of FGB (−249C) allele together with this genotype enhanced its protective potential, reducing the p value of the combination twofold (OR 0.17, 95% CI 0.04–0.8). Two more protective combinations were identified: biallelic APOE (−427C) + LPL (1595G) and triallelic APOE (−491C) + LPL (1595G) + CMA1 (−1903G). In both cases, p = 0.0052, OR 0.18, and 95% CI 0.05–0.66. Altogether, involvement in the formation of IS risk in Russians was evidenced for alleles of four genes: APOE, FGB, LPL, and CMA1; the APOE involvement was demonstrated for alleles of two polymorphic loci: −491T and −427C. Linkage analysis suggested that these loci were involved in IS resistance independently of each other.     

Transient dynamics in multilocus invasions by transgenic organisms

 With recent advances in molecular genetics, it is likely that releases of genetically modified organisms will be used for a variety of purposes. In many cases, such systems would utilize organisms that have been modified on multiple genetic loci. Predicting the effect of such releases will require an understanding of the transient dynamics in the system. However, theoretical understanding of transient dynamics in multilocus systems is limited, particularly for early generations when gametic disequilibrium is still high. I derive approximate expressions for marginal allele frequency and marginal two-locus disequilibrium that are applicable in this initial period, assuming infinite population size, two alleles per locus, and weak viability selection. I then apply these results to exploring the effect of parameters on the frequency of the resident gamete type in a release of organisms carrying an autocidal allele on multiple loci. This leads to simple approximate expressions for the optimal number of loci carrying the autocidal allele (as a function of release size and the degree of natural selection against the alleles) and the size of release needed to overcome a given level of selection against the released alleles. Received: 5 March 2001 / Revised version: 10 July 2002 / Published online: 18 December 2002 Current address: Department of Statistics, 204 Statistics Building, University of Georgia, Athens, GA 30602-1952, USA. e-mail: pdschlie@stat.uga.edu Key words or phrases: Multilocus – Selection – Transgenic – Pest control – Genetic control Acknowledgements. I thank Steve Ellner for insight and guidance throughout this project. This research was partially funded by a fellowship from the College of Agricultural and Life Sciences Foundation of North Carolina State University.     

Progression age enhanced backward bifurcation in an epidemic model with super-infection

 We consider a model for a disease with a progressing and a quiescent exposed class and variable susceptibility to super-infection. The model exhibits backward bifurcations under certain conditions, which allow for both stable and unstable endemic states when the basic reproduction number is smaller than one. Received: 11 October 2001 / Revised version: 17 September 2002 / Published online: 17 January 2003 Present address: Department of Biological Statistics and Computational Biology, 434 Warren Hall, Cornell University, Ithaca, NY 14853-7801 This author was visiting Arizona State University when most of the research was done. Research partially supported by NSF grant DMS-0137687. This author's research was partially supported by NSF grant DMS-9706787. Key words or phrases: Backward bifurcation – Multiple endemic equilibria – Alternating stability – Break-point density – Super-infection – Dose-dependent latent period – Progressive and quiescent latent stages – Progression age structure – Threshold type disease activation – Operator semigroups – Hille-Yosida operators – Dynamical systems – Persistence – Global compact attractor     

A discrete,size-structured model of phytoplankton growth in the chemostat: introduction of inhomogeneous cell division size

 We introduce inhomogeneous, substrate dependent cell division in a time discrete, nonlinear matrix model of size-structured population growth in the chemostat, first introduced by Gage et al. [8] and later analysed by Smith [13]. We show that mass conservation is verified, and conclude that our system admits one non zero globally stable equilibrium, which we express explicitly. Then we run numerical simulations of the system, and compare the predictions of the model to data related to phytoplankton growth, whose obtention we discuss. We end with the identification of several parameters of the system. Received: 9 February 2000 / Revised version: 10 October 2001 / Published online: 23 August 2002 RID="*" ID="*" Present address: Department of Mathematics and Statistics, University of Victoria, B.C., Canada. e-mail: jarino@math.uvic.ca Key words or phrases: Chemostat – Structured population models – Discrete model – Inhomogeneous division size     

A temperature-sensitive DNA adenine methyltransferase mutant of Salmonella typhimurium

A temperature-sensitive mutant of Salmonella typhimurium was isolated earlier after transposon mutagenesis with Tn10d Tet. The mutant D220 grows well at 28 °C but has a lower growth rate and forms filaments at 37 °C. Transposon-flanking fragments of mutant D220 DNA were cloned and sequenced. The transposon was inserted in the dam gene between positions 803 and 804 (assigned allele number: dam-231 : : Tn10d Tet) and resulted in a predicted ten-amino-acid-shorter Dam protein. The insertion created a stop codon that led to a truncated Dam protein with a temperature-sensitive phenotype. The insertion dam-231 : : Tn10d Tet resulted in a dam“leaky” phenotype since methylated and unmethylated adenines in GATC sequences were present. In addition, the dam-231 : : Tn10d Tet insertion rendered dam mutants temperature-sensitive for growth depending upon the genetic background of the S. typhimurium strain. The wild-type dam gene of S. typhimurium exhibited 82% identity with the Escherichia coli dam gene.     

Pressure and temperature effects on growth and viability of the hyperthermophilic archaeon Thermococcus peptonophilus

We studied the effects of high temperatures and elevated hydrostatic pressures on the physiological behavior and viability of the extremely thermophilic deep-sea archaeon Thermococcus peptonophilus. Maximal growth rates were observed at 30 and 45 MPa although no significant increases in cell yields were detected. Growth at 60 MPa was slower. The optimal growth temperature shifted from 85° C at 30 MPa to 90–95° C at 45 MPa. Cell viability during the stationary phase was also enhanced under high pressure. A trend towards barophily at pressures greater than those encountered in situ at the sea floor was demonstrated at increasing growth temperatures. The viability of cells during starvation, at high temperature (90, 95° C), and at low temperature (10° C) was enhanced at 30 and 45 MPa as compared to atmospheric pressure. These results show that the extremely thermophilic archaeon T. peptonophilus is a barophile. Received: 21 October 1996 / Accepted: 5 February 1997     

The onset of oscillatory dynamics in models of multiple disease strains

 We examine a generalised SIR model for the infection dynamics of four competing disease strains. This model contains four previously-studied models as special cases. The different strains interact indirectly by the mechanism of cross-immunity; individuals in the host population may become immune to infection by a particular strain even if they have only been infected with different but closely related strains. Several different models of cross-immunity are compared in the limit where the death rate is much smaller than the rate of recovery from infection. In this limit an asymptotic analysis of the dynamics of the models is possible, and we are able to compute the location and nature of the Takens–Bogdanov bifurcation associated with the presence of oscillatory dynamics observed by previous authors. Received: 5 December 2001 / Revised version: 5 May 2002 / Published online: 17 October 2002 Keywords or phrases: Infection – Pathogen – Epidemiology – Multiple strains – Cross-immunity – Oscillations – Dynamics – Bifurcations     

Characterization of a three-phase response in gloved cold-stressed fingers

Seven gloves were studied worn by eight sedentary subjects (six men and two women) exposed to cold–dry, C–D, (mean dry bulb temperature −17.2^∘C; mean dew point temperature ), and cold–wet, C–W, ( 0^∘C; ) conditions. Mean endurance times were 75 min for the C–D and 162 min for the C–W conditions. A three-phase response pattern of the temperature in the fingers was characterized. Phase I comprised an initial period during which finger temperature remained close to the pre-exposed level, due to delayed vasoconstriction in the finger. Phase II involved an exponential-like decrease of finger temperature indicative of the onset of vasoconstriction in the finger. Phase III manifested periodic finger temperature changes due to cold induced vasodilatation (CIVD). Mean wave patterns for phase III indicated approximately 3.5 waves · h⁻¹ in the C–D but only about 2 waves · h⁻¹ in the C–W condition. Extension of endurance time, due to CIVD, was defined as the difference in time between the actual end of the experiment and the time the finger-tip would have reached the set temperature endurance limit as extrapolated by a continued exponential drop. Three overall response patterns of fingers in the cold were characterized: type A exhibiting all 3 phases; type B₁ or B₂ exhibiting either phases I+II or phases II+III; and type C showing only phase II. Considerable inter- and intra-subject variability was found. In both test conditions the final physiological thermal states of the subjects were between comfortable and slightly uncomfortable but acceptable and thus did not correlate with the responses in the fingers. Accepted: 5 January 1998