The invention relates to a method for determining an indicator which is dependent on respiratory data and defines the transition from the aerobic to the anaerobic metabolism of a person, with said person being subjected to physical stress, as well as an apparatus to perform the method,
The physical performance capacity of an organism constitutes an integrative and imprecisely described value which is to quantify the ability to tolerate physical stress.  As a result of physical stress several subsystems of the organism are loaded in different forms and intensities depending on the respective state of training.  The most important of said subsystems are, in addition to the neuromuscular systems for initiating the sequence of motions, the oxygen transport system (respiration, diffusion of the respiratory gases, oxygen binding to hemoglobin, cardiovascular system) and the metabolic system of the working skeletal muscles. 
Since the metabolic system of the skeletal muscle constitutes the performance-limiting system in the healthy person, the muscular metabolism is given primary attention in exercise-resp.  work physiology. 
In order to perform physical activities it is necessary that the muscle is able to rely on a pool of adenosine triphosphate (ATP) as a direct source of energy (see FIG.  1).  With the exception of short-time work for which only phosphate stores are used, two metabolic ways are available for its resynthesis which are used depending on the respective requirements concerning intensity of work and duration of work.  The most important and energetically most favourable way is the aerobic metabolism in which the substrates glycogen and glucose and also free fatty acids are degraded into carbon dioxide and water, provided an adequate supply of oxygen via respiration and circulation. 
The aerobic pathway, however, can only provide moderately high energy flow rates, therefore the second metabolic variant, the anaerobic pathway, is additionally activated for performance of higher work load intensities (also at the beginning of physical work).  This mechanism of providing energy uses glycogen and glucose as a substrate, but supplies lactate as an end product.  It is usually produced more rapidly than it can be degraded and therefore accumulates in the organism.  At the same time hydrogen ions are produced, so that termination of the activities occurs by muscular exhaustion due to the local acidosis in connection with the rise in lactate. 
Physical stress in which primarily the aerobic metabolic pathway is used is the ideal and desirable form of health training, e.g. endurance training, because an economisation of the cardiovascular system is achieved on the one hand and mobilization of metabolism and the lipocatabolism are promoted on the other hand. 
In exercise physiology the idealized assumption as illustrated in FIG.  2 is frequently made that the energy needs (by taking into account the mechanical efficiency) as predetermined by the exercise protocol are covered by way of the biochemical energy liberation as long as the demanded strain is lower than the individually determined maximum strain.  In the exercise protocol illustrated the total expenditure of energy increases according to an approximately quadratic function. 
The maximum share to be covered via the aerobic metabolism is illustrated by a straight line whose slope depends on the maximum aerobic capacity of the test person (which among other things is a function of the state of training). 
Once the total expenditure exceeds the maximum expenditure that can be provided aerobically, the differential share to the total expenditure must be provided by way of the anaerobic metabolism. 
The time Tan, namely the moment of the transition from aerobic to anaerobic, in which the aerobic provision of energy is exceeded is stated (with a defined exercise protocol) in units of stress (e.g. watts). 
When implemented practically, however, the transition from aerobic to anaerobic metabolism cannot be defined precisely by a moment or a stress value, so that frequently a transition area is defined at the lower limit (aerobic threshold) of which the change of the energetic metabolism begins and at the upper limit (anaerobic threshold) of which the same is completed. 
Since the intensity of stress at which the organism switches from the energetically more favourable aerobic metabolism to the anaerobic metabolism depends on the respective state of training and thus on the physical work capacity, various indicators are defined within the scope of ergometric tests or performance tests which are based on various physiological indicators or variables of the involved subsystems of the organism and their changes as a consequence of standardized exercise protocols. 
Depending on their assignment to the various subsystems the following indicators are known:
Lactate-oriented indicators
Heart-rate-oriented indicators
Indicators dependent on respiratory variables
The lactate concentration in the blood is used as a biological variable in the case of lactate-oriented indicators.  In order to obtain a numerical value in terms of physical work, the functional relation between lactate concentration and work load on the ergometer is determined empirically using a standardized protocol with stepwise increasing work load.  The work load at two defined lactate concentrations, namely 2 mmol/l and 4 mmol/l is used as a characteristics for the physical performance capacity.  The 2 mmol/l value is defined as the aerobic threshold and the 4 mmol/l value as the anaerobic threshold.  The intermediate range is designated as aerobic-to-anaerobic transition. 
Where heart-rate-oriented criteria are concerned, either absolute values of the heart rate (e.g. 60% of the maximum heart rate) or specifics of the time course of the heart rate (discontinuities or deflection points) in an increasing work load protocol are used as an indicator for the transition from the aerobic to the anaerobic metabolism.  The best known example of this test method is the so-called CONCONI test. 
Respiratory-oriented criteria are based on the physiological fact that when using the anaerobic metabolism in addition to lactate hydrogen ions are formed which lead to a metabolic acidosis.  The hydrogen ions are buffered by the bicarbonate buffer-system of the blood, with CO2 being liberated.  It is expired via the respiratory system.  Caused by respiratory control, a compensatory hyperventilation is initiated, so that carbon dioxide is expired more intensively.  Therefore one frequently puts the oxygen consumption in relationship with the carbon dioxide output (e.g. by calculating the so-called xe2x80x9crespiratory exchange ratio xe2x80x94RERxe2x80x9d) and tries this way to derive the indicators for the transition from the aerobic to the anaerobic metabolism. 
The indicators used most frequently in performance diagnostics are the lactate-oriented ones, namely the so-called lactate thresholds.  Their advantage is the ability to be determined precisely by measurements.  Their disadvantage is the necessity to take blood from the hyperemisized ear lobe and the required instrumentation for the chemical analysis. 
Heart-rate-oriented indicators are easy to be determined non-invasively.  As a result of the indirect representation of muscular metabolism with respect to a cardiovascular variable, they show a lack of precision and reproducibility, however. 
Respiratory-oriented indicators have the advantage of a direct relation to the muscular metabolism (metabolic acidosis).  Their determination, however, relies on conventional methods of ergospirometry, and on extensive equipment. 
From U.S. Pat.  No.  5,297,558 for example an algorithm is known for the determination of an indicator for the xe2x80x9cfat burning pointxe2x80x9d.  This point substantially corresponds to the aforementioned aerobic-to-anaerobic transition and is determined conventionally on the basis of respiratory variables.  The so-called respiratory exchange ratio (RER) is determined by means of an ergospirometry system known from U.S. Pat.  No.  4,463,764 on the basis of oxygen consumption (volume/time) and carbon dioxide output (volume/time).  The heart rate at the work load intensity at which said RER exceeds the numerical value of 0.9 is used as an indicator value and percentage mark-ups and mark-downs on said heart rate value form the optimal intensity range (now stated on the basis of the heart rate) for the training.  The disadvantageous aspect is the required determination of the respiratory flow (ventilation).  Moreover, the determination of the respiratory flow is frequently subject to errors due to the required breathing masks and mouthpieces (leakage problems), with the use of tightly fitting masks and the breathing through mouthpieces generally being regarded as unpleasant. 
From U.S. Pat.  No.  5,782,772 A a method and an apparatus are further known for determining the individual anaerobic threshold, with the respiratory flow (ventilation) VE, the carbon dioxide output VCO2, and the oxygen consumption VO2, being determined as primary variables.  All aforementioned variables are so-called xe2x80x9cflow variablesxe2x80x9d with the physical dimension of volume/time (unit: l/min, ml/min, etc.).  The determination of these values necessitates in all cases a gas-tight breathing mask, with the disadvantages occurring as explained in connection with U.S. Pat.  No.  4,463,764.  The respective gas concentrations need to be measured to determine the carbon dioxide output and the oxygen consumption. 
It is the goal of the present invention to provide a method and an apparatus to perform the method in order to enable a simple determination of the aerobic-to-anaerobic transition on the basis of respiratory criteria, with unpleasant circumstantial conditions being substantially avoided for the test person in the application of the method or apparatus. 
This objective is achieved in accordance with the invention in such a way that the O2 and CO2 concentrations are measured directly in the person""s respiratory gas stream or in a partial stream derived there from, with the time course of the concentration values being acquired within at least one period of respiration, and that the indicator defining the aerobic-to-anaerobic transition is derived by using a mathematical model from the time course of the concentration values. 
As an alternative it is possible that discrete O2 and CO2 concentration values are measured at predetermined times (e.g. by using a thermistor probe) in the course of at least one respiration period, with the indicator defining the aerobic-to-anaerobic transition being derived from the discrete O2 and CO2 concentration values by using a mathematical model. 
In contrast to the conventional determination of respiratory flow, reference is made exclusively to the time course or determination at certain points of the concentration values of oxygen and carbon dioxide in the course of at least one respiration period.  An indicator value is calculated on the basis of these by using an empirical mathematical model (cf.  FIGS.  5 and 6 for example) or one that is derived from physiological-medical basic information. 
The indicator characterizing the transition from the aerobic to the anaerobic metabolism can be used as a guideline for controlling the intensity of training within the scope of stationary institutions such as fitness centers or individual outdoor training measures such as jogging for example.  It can also be used for purposes of diagnosis of physical performance, namely to determine physical performance capacity.  In the latter case it is necessary to measure the performance provided by the person subjected to a physical stress in addition to the concentration values in order to be able to assign the calculated indicator to a specific work load. 
An apparatus in accordance with the invention for the determination of an indicator which defines the transition from the aerobic to anaerobic metabolism of a person is characterized in such a way that positionable sensors for the measurement of the O2 and CO2 concentration are positioned directly in the respiratory gas stream or a partial stream gained from the respiratory gas stream, which sensors are suitable for detecting the time course of the concentration values or discrete concentration values within at least one respiratory cycle.  Measurement is thus performed either quasi-continuously or in form of discrete values (e.g. minimum or maximum values).  Preferably, measurement can be performed directly in the respiratory gas stream, with the sensors being positioned on a fixing device similar to a hands-free kit in front of the mouth, or a partial stream can be gained from the respiratory gas stream by means of a mask- or funnel-like apparatus which rests loosely on the person""s mouth and nose.  In the latter case a device for drying the respiratory gases can be provided between the mask-like apparatus for gaining the partial stream and the sensors for measuring the O2 and CO2 concentration. 
It is advantageous when the time course of the O2 and CO2 concentration is determined over several respiratory cycles under similar stress and the result is preferably stored in digitized form. 
It is provided in a preferable embodiment of the invention that the final expiratory values for O2 and CO2 are calculated from the time course of the O2 and CO2 concentration values and are used for the derivation of the indicator. 
It is provided further in accordance with the invention that the work load intensities and the heart rate of the person are measured in addition and are displayed as diagnostic values or used as control values, or that values are considered in the mathematical model which describe the mixing characteristics of the respiratory system, the compartmentalization of the muscular metabolism and the buffer system of the blood and/or the gas transport and signal characteristics of the measurement system. 
In accordance with the invention it is also possible to use shape criteria of the expiratory part of the time course of the O2 and CO2 concentration values for determining the indicator.  Representative is thus not only the calculated end expiratory concentration value, but also the shape of the time course (rise, discontinuities, etc.)  in the expiratory phase.