Apparatus and method for the analysis of the change of body composition and hydration status and for dynamic indirect individualized measurement of components of the human energy metabolism

One embodiment of an apparatus for analysis of body composition and hydration status by detecting resistance of the human subject at zero and infinite frequency including a method for measuring indirectly extracellular water mass, intracellular water mass, lean body mass, and body fat mass; daily changes of extracellular water mass, intracellular water mass, lean body mass, and body fat mass; and acute changes of extracellular water mass and intracellular water mass; and for individualized calibration of these indirect measurements.In addition, a method for fitting mathematical models to serial measurements of indirectly measured lean body mass and fat mass and for dynamic indirect individualized measurement using minimum variance estimation and prediction of daily changes of the body composition defined as change of glycogen store, change of fat store and change of protein store; daily utilized macronutrient energy intake defined as utilized carbohydrate, fat, and protein caloric intake; daily macronutrient oxidation rate defined as rate of carbohydrate oxidation, fat oxidation, and protein oxidation; daily resting metabolic rate; daily unknown forms of energy losses or gains; daily rate of endogenous lipolysis; daily nitrogen excretion; daily gluconeogenesis from protein; daily determination of extracellular water mass; daily determination of intracellular water mass; and acute change of extracellular water mass and intracellular water mass.

BACKGROUND OF INVENTION

Field

My apparatus and methods for the analysis of the change of body composition and hydration status and individualized mathematical modeling of the human energy metabolism relates generally to the measurement of the resistance and reactance of the human subject, to fitting mathematical models to serial measurements of indirectly measured lean body mass and fat mass, and to performing minimum variance estimation and prediction of variables of the human energy metabolism.

Prior Art

Biomedical engineering tools and multiple patented inventions of bioimpedance spectroscopy have been concerned with the problems of measuring the resistance and reactance of the human body at a multitude of frequencies in order to determine body composition and hydration status. Advancements in mathematical modeling of the human energy metabolism have provided tools to describe the relationship between energy balance, which is the difference of the energy intake and the total energy expenditure, and body composition changes. State space modeling coupled with the use of time variant minimum variance Kalman filtering or prediction has been successfully used in control engineering for over 50 years to observe and control state variables of complex dynamic systems. This technology holds great potential in monitoring difficult to measure daily body composition changes along with other essential components of the human energy metabolism in order to maximize capabilities of controlling them.

1. Background and problem identification with bioimpedance spectroscopy.

Bioimpedance spectroscopy has become a widely used technique in body composition and hydration status analysis in recent decades. The measurement of impedance, which is measuring resistance and reactance at frequencies from 1 to 1000 kHz, is purported to assist in the determination of extracellular and intracellular water mass. According to the Cole model of body impedance as interpreted by Cornish (Cornish, DOI: 10.1088/0031-9155/38/3/001), a current at low frequency flows through the extracellular water mass while at higher frequencies it flows through both the extracellular and intracellular water mass, allowing for extracellular and total water mass measurements. The Cole model fitted to resistances and reactances of the human subject at various frequencies can be extrapolated to the resistance values at zero and infinite frequencies. Using the resistance values at zero and infinite frequency, Moissl developed equations corrected with body mass index to calculate extracellular and intracellular water mass (Moissl, DOI: 10.1088/0967-3334/27/9/012). The problem with Moissl's equations was that they contained errors in the references, which accounted for the errors in the body mass index corrected extracellular and intracellular water mass calculation's accuracy (Moissl, DOI: 10.1088/0967-3334/27/9/012).

The errors in bioimpedance measurements of extracellular and intracellular water have hampered their accuracy and reliability. When using bioimpedance instruments, artefactual errors occur everywhere along the path of the flowing current around the entire electric circuit, which consists of current sources, a human subject, measurement electrodes, cable connections from subject to measuring instrument, and calibration elements. A disadvantage of the prior art, for example U.S. Pat. No. 5,280,429 (1994), is that the errors due to offset voltage and voltage noise at nodal junction points of the circuit elements cannot be determined, analyzed, and mitigated.

Moreover, at higher frequencies in bioimpedance spectroscopy, unexpected phase shifts in the results occur due to human subject stray capacitance and the instrument introduces distortions in the results due to nonlinearity. Errors due to stray capacitance are unavoidable in practice, uncontrollable to a large degree, and likely to be more pronounced where other devices are also attached to the subject, but they are measurable. A disadvantage of the prior art, for example U.S. Pat. No. 5,280,429 (1994), is that the errors due to stray capacitances and other measuring errors are neither determined, nor analyzed, nor reduced.

Another problem with the current bioimpedance spectroscopy technology is the variation in measurement results among machines due to the systemic errors introduced by the techniques, the instrumentation used, and other errors. The disadvantage of the prior art, for example U.S. Pat. No. 5,280,429 (1994), is that no effort was made to measure quality and inform the user about the size of the detectable error during measurement and about the reliability of the measurement results.

Another problem with bioimpedance measurements could be the placement of the preamplifier and the drivers of the shielded cables far away from the sensing electrodes. The disadvantage of such arrangements is that the magnitude of the interference from outside electromagnetic sources and the capacitive load from the shielded cables could cause suboptimal results. The prior art, for example U.S. Pat. No. 5,280,429 (1994), uses Fast Fourier Transformation, substituting summation for integration and evaluating only two wavelengths. These simplifications would be allowed if the analog to digital conversation were accurate, which it is not.

Advantages—Apparatus and Method for the Analysis of Change of Body Composition and Hydration Status

Accordingly, several advantages of one or more aspects over the prior art in the field of bioimpedance spectroscopy are as follows:a. Measuring and correcting for stray capacitance:

I measure all capacitances including stray capacitances. I measure the voltage at 6 measuring points along the current path. I apply Kirchhoff's first and second rule and Ohm's rule. All measurements have amplitude, offset, and phase value and I compare them to the zero phase value measured at reference resistances. The advantage of measuring voltage at nodal junctions and applying Kirchhoff's rules and Ohm's rule is that I am able to calculate the stray capacitance and measure its influence on the results.b. Positioning the preamplifiers and the shield drivers close to the sensing electrodes: The advantage of positioning the preamplifiers and the shield drivers close to the sensing electrodes is that the input noise will be kept low and no additional noise or capacitive load will be added.c. Analyzing and removing errors and noise in the measuring circuit by using an input logic circuit:

I use switches to isolate or short circuit or leave intact parts of the measuring circuit without or with excitation at various frequencies. This allows for determining errors due to offset voltage and voltage noise due to various sources. The offset voltage is eliminated by subtracting the measured values at nodal junctions from the measured signal via a software algorithm. Hardware and/or software filtering remove voltage noise. The advantage of using an input logic circuit is that the apparatus will sense the offset voltage and voltage noise in the environment of operation and this allows for reduction of offset voltage and voltage noise.d. A current source designed for high output resistance and low output reactance:

I use two mirrored Howland current sources which are fine tuned for their passive components to achieve high output resistance and low output reactance (Bertemes-Filho, DOI:10.4236/cs.2013.47059). This mirrored arrangement has the advantage that the output reactance is cut in half. I use two reference resistances for each current source. Using two reference resistances for each current source has the advantage that the current generated or sunk into the circuit will be known for each current source, allowing for precise network analysis. Using two mirrored Howland current sources has the advantage also that it creates a virtual floating earth potential, avoiding electric charge build up on the sensing electrodes.e. Use of a sine wave fitting algorithm:

Sine wave fitting has the advantage of providing a priori knowledge of the exact value of the applied frequency of excitation, reducing the number of unknown variables. In statistical terms, sine fitting provides the minimum variance linear estimation for amplitude, phase, and offset. Sine fitting compensates better for the errors of the analog digital conversion than the Fast Fourier Transformation, which remains sensitive to such errors (Bertocco, DOI:10.1109/19.571881). Using a sine wave fitting algorithm over 6 to 16 wavelengths minimizes sampling error of the analog to digital converter. The sine fitting algorithm also gives a residual value, which I use to measure quality. The advantage of the use of the sine fitting algorithm is better overall noise reduction, allowing for elimination of offset voltage, minimization of voltage noise, and the ability to measure quality.f. Non-linear curve fitting algorithm:

A Cole model with unknown resistance at zero and infinite frequency and unknown membrane capacitance is fitted to the resistance and reactance values at each examined frequency. The residual value, calculated as the difference between the measured and the model predicted value, is used to measure the quality of each individual measurement at each frequency. The sum of squared residual values measures the overall performance of the first embodiment of my apparatus. The advantage of measuring performance using the sum of squared residual values is that the user obtains quantified information of performance and of reliability of the function of the apparatus.g. Creating individualized references for the measurement of body composition and hydration status change:

I overcome the problem that the equations corrected with body mass index contain errors in the references by establishing individual references for extracellular and intracellular water mass. The advantage of creating individualized references is that all of my measurements are individualized, referenced to individual reference values.

2. Background and problem identification with the prior art for measuring variables of the human energy metabolism.

Decades of research into the causes of the obesity epidemic and related scientific research for the cause of it led to the creation of mathematical models of obesity. These models were based on the first law of thermodynamics and proffered that imbalance between energy intake and energy expenditure lead to changes in energy storage, primarily in lipids. The effort to quantify changes of the lipid store led Hall to construct mathematical models describing body composition changes matched to group averages (Hall, DOI: 10.1152/ajpendo.00523; DOI: 10.1109/MEMB.2009.935465; DOI: 10.1152/ajpendo.00559.2009). However, everyone's metabolism has unique characteristics, and individualized modeling is needed. Further, there is a need for real time metabolic modeling and tracking. The Hall models (Hall, DOI: 10.1152/ajpendo.00523; DOI: 10.1152/ajpendo.00559.2009) work off line when all data are available for retrospective analysis. Differential equations with infinitesimal time resolution are used in the Hall models, requiring significant software capacity to solve and knowledge of how the system changes during the 24 hour time period, when neither is needed for real time use and for measuring changes every 24 hour period. Importantly, the Hall model equations do not succeed in satisfying the constraint of conservation of energy i.e. the First Law of Thermodynamics, at the end of each day, which is essential for individualized real time modeling. Further, Hall does not consider the constraint that the model calculated body composition with its daily change together with changes of hydration status have to add up to the measured body weight and its daily change to allow for individualized real time modeling.

A long-felt but unsolved need for accurate and simplified tracking of body composition change, energy expenditure, and especially energy intake exists. The imprecision of current methods for determining these variables have precluded accurate quantification of the energy balance and thus precluded definitive statements regarding the cause of the obesity epidemic. The currently accepted method for tracking calorie intake in scientific studies of energy balance is self-reported calorie intake counting. For example, the daily ingested calories broken down into the three macronutrient groups are needed every day for the calculations in the Hall models. However, self-reported calorie intake counting is fraught with systemic errors (Hebert, DOI: 10.1016/S1047-2797(01)00297-6).

Model calculations of the macronutrient oxidation rate are an essential component of the modeling of the human energy metabolism. Hall (Hall, DOI: 10.1152/ajpendo.00523; DOI: 10.1152/ajpendo.00559.2009) created models for the macronutrient oxidation rates. However, Hall's equations are ad-hoc and are inherently nonlinear and not suitable for inverse calculations when model input is sought from known model output.

I have also found that problems of prediction and noise filtering exist in the dynamic modeling of the metabolism. The estimation or prediction of the state variables of a dynamic system model poses the challenges of ensuring accuracy and stability of estimations.

Advantages—Dynamic Indirect Individualized Measurement of Components of the Human Energy Metabolism

Accordingly, several advantages of one or more aspects are as follows:a. Individualized self correcting and self adaptive modeling:

Individualized self correcting and self adaptive modeling is achieved through serial measurements of body composition changes and adjustment of the model parameters in a way that the model calculations approach the indirectly measured body composition changes or a target trajectory. Individualized self correcting and self adaptive modeling has the advantage that it reflects the state of the individual energy metabolism better than previous models, which were adjusted to grouped or averaged data points of a population.b. Real time calculations with recursive formulas and daily updates:

My models use recursive formulas which are updated daily with new data, eliminating the need to know all previous data points except for the last day's data during update and allowing for real time calculations of changes of body composition as they occur. The recursive method preserves the information gained from the last day's data without the need to store the information in the memory for calculations. The advantage of an algorithm using a recursive structure is that it is easy to use on portable computer devices and allows for making indirect measurements in freely moving human subjects.c. Applying linear invertible models:

The nonlinear equations used in the Hall model are very difficult or sometimes impossible to invert in order to calculate an unidentified input, the utilized energy intake, from a known output, the body composition change and energy expenditure. Also, the thermic effect of feeding is calculated implicitly in the Hall models, making inverse calculations to determine utilized energy intake rather difficult. I have also found that adaptive thermogenesis, as modeled by Hall with an ad-hoc formula, requires unnecessary assumptions and model parameter determinations when indirect measurement of the body composition can provide this information.

My model equations are linear and structured to support inverse calculations for unknown input variables, allowing for calculating the unknown macronutrient energy intake. The advantage of a linear invertible model is that by measuring the body composition change and using an inverse calculation, I determine the difficult to measure utilized macronutrient intake which was necessary to produce the measured body composition change in a freely moving human subject.d. Using difference equations:

Rather than using differential equations, which require continuous measurements and elaborate integration methods to solve, I use difference equations with 24 hour time resolution requiring model calculations only every 24 hours. The calculations require only matrix operations, eliminating the need for the knowledge of the exact course of changes during the 24 hour period. The advantage of using difference equations is that the explicit knowledge of how the metabolism arrived at the measured new state of body composition after a 24 hour time span is not required.e. State space method:

The state space method allows for interfacing error containing measurements through the use of a measurement model to a process model describing the metabolic process. The state-space method provides a convenient framework for the implementation of the time variant minimum variance Kalman estimation or prediction method.f. Calculating macronutrient oxidation rates:

I have found that macronutrient oxidation of carbohydrate, fat, and protein can be modeled for inverse calculation purposes using the principles of indirect calorimetry (Ferrannini, DOI: 10.1016/0026-0495(88)90110-2; Simonson, D. C. and R. A. DeFronzo. Indirect calorimetry: methodological and interpretative problems. American Journal of Physiology—Endocrinology and Metabolism. March 1990; 258(3):E399-E412.). I use the formulas introduced by Livesey, G. and Elia, M. (Livesey, G. and M. Elia. Estimation of energy expenditure, net carbohydrate utilization, and net fat oxidation and synthesis by indirect calorimetry: evaluation of errors with special reference to the detailed composition of fuels. American Journal of Clinical Nutrition. April 1988; 47(4):608-628.) to calculate macronutrient oxidation. The advantage of using these formulas is that they can be directly applied to my self adaptive individualized metabolic model of the human energy metabolism because they are linear and suitable for inverse calculations when model input is sought from known model output.g. Calculating daily utilized macronutrient intake values from ingested macronutrient calorie intake:

The input to my equations is the daily utilized macronutrient energy intake without thermic effect of feeding and the energy losses due to incomplete absorption. I calculate the thermic effect of feeding and the energy losses due to incomplete absorption from tabled values (Food and Nutrition Board, Institute of Medicine. Dietary Reference Intakes for Energy, Carbohydrate, Fiber, Fat, Fatty Acids, Cholesterol, Protein, and Amino Acids (Macronutrients): A Report of the Panel on Macronutrients, Subcommittees on Upper Reference Levels of Nutrients and Interpretation and Uses of Dietary Reference Intakes, and the Standing Committee On the Scientific Evaluation of Dietary Reference Intakes. http://www.nap.edu/books/0309085373/html/). The thermic effect of feeding and the energy losses due to incomplete absorption are subtracted from the ingested calories to obtain the daily utilized carbohydrate, fat, and protein intake. Calculating the daily utilized macronutrient values has the advantage that inverse calculations of the utilized energy intake become independent from the individual thermic effect of feeding or food absorption variables.h. Using the law of conversation of energy:

My energy equations take into account all major known processes of the human energy metabolism and are built to satisfy the law of conservation of energy at the end of a 24 hour period. I accommodate the so far unknown energy forms in the energy balance equation by using a correction factor for unknown energy losses or gains. Including a correction factor for unknown energy losses or gains has the advantage that it balances my energy equations so that they satisfy the law of conservation of energy. The correction factor for unknown energy losses or gains also serves as a measure of performance of my model, since the major components of the energy equation are included in my model and the expectation is that the unknown energy forms remain small.i. Estimating the daily utilized macronutrient intake values from indirectly measured body composition changes:

I use the time variant Kalman prediction method with innovations representation (Ljung, L. and T. Soderstrom. Theory and Practice of Recursive Identification. 1983; MIT Press, Cambridge, Mass., pp. 125.) for prediction and estimation of the unknown utilized macronutrient intake. For estimating the error of estimation I prefer using a reference or nominal trajectory method (Jazwinski, A. W. Stochastic Processes and Filtering Theory. 1970; Academic Press, Inc. New York, pp. 376.). The reference or nominal trajectory method has the advantage of enhancing the accuracy and stability of estimations. The advantage of utilizing the Kalman prediction, innovations representation, and the reference or nominal trajectory method is that I am able to estimate the daily utilized macronutrient intake in a freely moving human subject and require only daily measurement of the physical energy expenditure and determination of the body composition change along with an infrequently used calibration procedure.j. Estimating the daily changes of the body composition and stochastic identification of the unidentified energy losses or gains, correction factor of the de novo lipogenesis, and correction factor for gluconeogenesis:

I use the time variant Kalman filtering method with innovations representation for estimation of the daily body composition change. I calculate the unknown energy losses or gains, the correction factor for de novo lipogenesis, and the correction factor for gluconeogenesis from amino acids with a stochastic identification method (Walter, E. and L. Pronzato. Identification of Parametric Models from Experimental Data. 1997; Springer Verlag Berlin, Paris, New York. pp. 114.). I prefer using a reference or nominal trajectory method (Jazwinski, A. W. Stochastic Processes and Filtering Theory. 1970; Academic Press, Inc. New York, pp. 376.) for estimating the daily body composition changes. My method has the advantage of enhancing accuracy and stability of estimations of daily body composition changes and allowing for dynamic indirect individualized measurement of components of the human energy metabolism in a freely moving human subject requiring only daily measurement of the physical energy expenditure and the determination of the body composition change along with an infrequently used calibration procedure for body composition and hydration status change.

These and other advantages of one or more aspects will become apparent from a consideration of the ensuing description and accompanying drawings.

SUMMARY

In accordance with one embodiment of an apparatus and method for the analysis of change of body composition and hydration status and for dynamic indirect individualized measurement of components of the human energy metabolism, my apparatus measures resistance and reactance of the human body directly at multiple frequencies, and I extrapolate indirectly to zero frequency and infinite frequency using the Cole model. I use individual reference values to calibrate my apparatus and method for the analysis of the change of body composition and hydration status. I calculate the extracellular water mass from the resistance at zero frequency and calculate the intracellular water mass from the resistance at infinite frequency.

My method for dynamic indirect individualized measurement of components of the human energy metabolism is comprised of the Self Correcting Model of the Utilized Energy Intake, the mathematical equations for components of the metabolism, and the Self Adaptive Model of the Human Energy Metabolism.

The input variables of the Self Correcting Model of the Utilized Energy Intake include the indirectly measured daily change of body composition, the directly measured total energy expenditure, and the indirectly calculated time-varying constant energy expenditure. I use the Kalman filtering method, the innovations representation method, and the reference or nominal trajectory method. The output is the estimated daily utilized macronutrient energy intake.

The input variables to the mathematical equations of the components of the human energy metabolism include either the ingested daily macronutrient energy intake comprised of carbohydrate, fat, and protein intake or the estimated daily utilized macronutrient energy intake. I use invertible linear equations. The output is the daily macronutrient oxidation rate, the daily resting metabolic rate, the daily unknown forms of energy losses or gains, the daily rate of endogenous lipolysis, the daily nitrogen excretion, and the daily gluconeogenesis from protein.

The input variables of the Self Adaptive Model of the Human Energy Metabolism include either the ingested daily macronutrient energy intake or the estimated daily utilized macronutrient intake. I use the Kalman filtering method, the innovations representation method, and the reference or nominal trajectory method. The output is the estimated daily change of the glycogen store, the fat store, and protein store; the daily correction factor for de novo lipogenesis; the daily correction factor for gluconeogenesis from amino acids; and the daily correction factor for unidentified energy losses or gains.

My apparatus and methods work in unison to create a noninvasive indirect individualized measurement of components of the human energy metabolism in a freely moving human subject.

GLOSSARY

The following signs were used as an upper index:˜ ingested calorie′ measured quantity and the result comes from an outside source* indirectly calculated value′* indirectly calculated value using directly measured valueT transpose of a vector or matrixCAL calibration valueTR* indirectly calculated trajectory valueRRE* calculated value obtained by using the Retained or Released Energy Model of the Human Energy MetabolismREF reference value from outside source

The following signs were used as a lower index:a value after a sentinel event of hydration status changeb value before a sentinel event of hydration status changei value on calibration day ij value on calibration day jk value on day kk−1 value on day k−1k−2 value on day k−2k+1 value on day k+10 value on initiation day

The following sign was used for an estimated value:{circumflex over ( )} value is estimated with help of the Kalman filter or predictor

The following sign was used to assign a value to a variable::= algorithm step where the right side of the equation is evaluated first and assigned to the left side
Scalar VariablesAGEkage (year)BCM0body cell mass (g) at initiation dayBCMkbody cell mass (g) at end of day kBW0body weight (g) on initiation dayBWkbody weight (g) on day kBWk′ measured body weight (g) on day kBM bone mass (g)CarbOxkrate of carbohydrate oxidation (kcal/day)CarbOxk* calculated rate of carbohydrate oxidation (kcal/day)CI0utilized carbohydrate intake (kcal/day) at initiation dayCIkutilized carbohydrate intake in (kcal/day) on day kCIk−1utilized carbohydrate intake in (kcal/day) on day k−1CIk−2utilized carbohydrate intake in (kcal/day) on day k−2CIkRRE* utilized carbohydrate intake indirectly calculated by the Measurement Model of the Utilized Energy Intake from Body Composition Change on day kestimated indirectly calculated carbohydrate intake by the Self Correcting Model of the Utilized Energy Intake on day kCI0˜ingested carbohydrate intake (kcal/day) at initiation dayCI0˜ingested carbohydrate intake (kcal/day) on day kCIk˜ingested carbohydrate intake (kcal/day) on calibration day jdECWjREFreference value of the adjustable dynamic coefficient to calculate acute change of extracellular water mass on calibration day jdICWjREFreference value of the adjustable dynamic coefficient to calculate acute change of intracellular water mass on calibration day jestimation of the adjustable dynamic coefficient to calculate acute change of extracellular water mass on calibration day jestimation of the adjustable dynamic coefficient to calculate acute change of intracellular water mass on calibration day jDFkrate of endogenous lipolysis (g/day) on day kDFj′ measured rate of endogenous lipolysis (g/day) on calibration day jestimated rate of endogenous lipolysis on day k with calibrationDFF0fat store dependent coefficient for rate of endogenous lipolysis at initiation dayDFFkfat store dependent coefficient for rate of endogenous lipolysis on day kDFFk−1fat store dependent coefficient for rate of endogenous lipolysis on day k−1DFCI0carbohydrate intake dependent coefficient for rate of endogenous lipolysisDF0kbias for rate of endogenous lipolysis on day kDF0k−1bias for rate of endogenous lipolysis on day k−1DGkrate of glycogenolysis (g/day) on day kDGk−1rate of glycogenolysis (g/day) on day k−1DNLkrate of de novo lipogenesis (kcal/day) on day kDNLk−1rate of de novo lipogenesis (kcal/day) on day k−1DNLGkglycogen store dependent coefficient for rate of de novo lipogenesis on day kDNLGk−1glycogen store dependent coefficient for rate of de novo lipogenesis on day k−1DNLCI0carbohydrate intake dependent coefficient for rate of de novo lipogenesisDNL0kbias for rate of endogenous lipolysis on day kDNL0k−1bias for rate of endogenous lipolysis on day k−1DPkrate of proteolysis (g/day) on day kDPk−1rate of proteolysis (g/day) on day k−1Eck* indirectly calculated time-varying constant energy expenditure (kcal) on day kEck−1* indirectly calculated time-varying constant energy expenditure (kcal) on day k−1estimation of the indirectly calculated time-varying constant energy expenditure (kcal) on calibration day iestimation of the indirectly calculated time-varying constant energy expenditure (kcal) on calibration day jEcj* indirectly calculated time-varying constant energy expenditure (kcal) on calibration day jECP extracellular protein mass (g)ECW0extracellular water mass (g) at initiation dayECWkextracellular water mass (g) on day kECWk−1extracellular water mass (g) on day k−1ECWk* indirectly measured extracellular water mass (g) on day kECWjREFreference value for extracellular water mass (g) on calibration day jEFskenergy needed for fat synthesis (kcal/day)EPkenergy production by substrate oxidation (kcal/day)F0body fat mass (g) at initiation dayFkbody fat mass (g) on day kFk+1body fat mass (g) on day k+1Fk−1body fat mass (g) on day k−1FI0utilized fat intake (kcal/day) at initiation dayFk* indirectly calculated body fat mass (g) on day kFk+1* indirectly calculated body fat mass (g) on day k+1{circumflex over (F)}k+1* estimated indirectly calculated fat mass (g) on day k+1Fk−1* indirectly calculated body fat mass (g) on day k−1Fk*′ indirectly measured body fat mass (g) on day kFjREFreference value for fat mass (g) on calibration day jFatOxkrate of fat oxidation (kcal/day)FatOxk* calculated rate of fat oxidation (kcal/day)FIkutilized fat intake (kcal/day) on day kFIk−1utilized fat intake in (kcal/day) on day k−1FIk−2utilized fat intake in (kcal/day) on day k−2FIkRRE* utilized fat intake indirectly calculated by Measurement Model of the Utilized energy Intake from Body Composition Change on day kestimated indirectly calculated fat intake by the Self Correcting Model of the utilized Energy Intake on day kFI0˜ingested fat intake (kcal/day) at initiation dayFIk˜ingested fat intake (kcal/day) on day kFIj˜ingested fat intake (kcal/day) on calibration day jG0glycogen mass (g) at initiation dayGkglycogen mass (g) on day kGk+1glycogen mass (g) on day k+1Gk−1glycogen mass (g) on day k−1Gk* indirectly calculated glycogen mass (g) on day kGk+1* indirectly calculated glycogen mass (g) on day k+1Ĝk+1* estimated indirectly calculated glycogen mass (g) on day k+1Gk−1* indirectly calculated glycogen mass (g) on day k−1G3Pkglycerol 3-phosphate synthesis (kcal/day) on day kGNGFkgluconeogenesis from glycerol in (kcal/day) on day kGNGFk−1gluconeogenesis from glycerol in (kcal/day) on day k−1GNGP0 bias for gluconeogenesis from proteinGNGPkgluconeogenesis from protein (kcal/day) on day kestimated gluconeogenesis from protein on day k with calibrationGNGPk−1gluconeogenesis from protein (kcal/day) on day kGNGPP0protein store dependent coefficient for gluconeogenesis from proteinGNGPCI0carbohydrate intake dependent coefficient for gluconeogenesis from proteinGNGPPI0protein intake dependent coefficient for gluconeogenesis from proteinH body height (cm)i index variable showing the day of the calibration before the lastICW0intracellular water mass (g) at initiation dayICWkintracellular water mass (g) on day kICWk−1intracellular water mass (g) on day k−1ICWk*′ indirectly measured intracellular water mass (g) on day kICWjREFreference value for intracellular water mass (g) on calibration day jj index variable showing day of the last calibrationk index variable for the day kKdEkKalman gain of the adjustable dynamic coefficient to calculate the daily change of the extracellular water mass for day k−1KdIkKalman gain of the adjustable dynamic coefficient to calculate the daily change of the intracellular water mass for day k−1KEcjKalman gain of the indirectly measured constant energy expenditurekECWjREFreference value of the adjustable coefficient to calculate to calculate extracellular water mass on day kkICWjREFreference value of the adjustable coefficient to calculate intracellular water mass on day kestimation of the adjustable coefficient to calculate extracellular water mass on day kestimation of the adjustable coefficient to calculate intracellular water mass on day kKkEkKalman gain of the adjustable coefficient to calculate extracellular water mass on day kKkIkKalman gain of the adjustable coefficient to calculate intracellular water mass on day kKμkKalman gain of the correction factor for de novo lipogenesisKνkKalman gain of the correction factor for gluconeogenesis from amino acidsKφkKalman gain of the correction factor for unknown energy losses or gainsL0lean body mass (g) on initiation dayLklean body mass (g) on day kLk*′ indirectly measured lean body mass (g) on day kNexcrknitrogen excretion on day k (g/day)Nexcrj′ measured nitrogen excretion (g/day) on calibration day jP0protein mass (g) at initiation dayPkprotein mass (g) on day kPk+1protein mass (g) on day k+1{circumflex over (P)}k+1* estimated indirectly calculated protein mass (g) on day k+1Pk−1protein mass (g) on day k−1Pk* indirectly calculated body protein mass (g) on day kPk+1* indirectly calculated body protein mass (g) on day k+1Pk−1* indirectly calculated body protein mass (g) on day k−1ProtOxkrate of protein oxidation (kcal/day)ProtOxk* calculated rate of protein oxidation (kcal/day)PAEk′ physical activity energy expenditure (kcal/day)PI0utilized protein intake (kcal/day) at initiation dayPIkutilized protein intake (kcal/day) on day kPIk−1utilized protein intake (kcal/day) on day k−1PIk−2utilized protein intake (kcal/day) on day k−2PIkRRE* utilized protein intake indirectly calculated by the Measurement Model of the Utilized Energy Intake from Body Composition Change on day kestimated indirectly calculated protein intake by the Self Correcting Model of the Utilized Energy Intake on day kPI0˜ingested protein intake (kcal/day) at initiation dayPIk˜ingested protein intake (kcal/day) on day kPIj˜ingested protein intake (kcal/day) on calibration day jrFFAmolecular weight ratio free fatty acid to triglyceriderGFmolecular weight and energy density ratio glycerol to triglyceriderGFmolecular weight ratio glycerol to triglycerider1kpart of the resting metabolic rate which is dependent on the utilized carbohydrate intake on day kr2kpart of the resting metabolic rate which is dependent on the utilized fat intake on day kr3kpart of the resting metabolic rate which is dependent on the utilized protein intake on day kr1k−1part of the resting metabolic rate which is dependent on the utilized carbohydrate intake on day k−1r2k−1 part of the resting metabolic rate which is dependent on the utilized fat intake on day k−1r3k−1 part of the resting metabolic rate which is dependent on the utilized protein intake on day k−1R0kresistance extrapolated at zero frequencyRinfkresistance extrapolated at infinite frequencyR0a′ resistance extrapolated at zero frequency after a sentinel event of hydration changeR0b′ resistance extrapolated at zero frequency before a sentinel event of hydration changeRinfa′ resistance extrapolated at infinite frequency after a sentinel event of hydration changeRinfb′ resistance extrapolated at infinite frequency before a sentinel event of hydration changeRRkpart of the resting metabolic rate which is independent of the body composition changes and the time-varying constant energy expenditure on day kRRk−1part of the resting metabolic rate which is independent of the body composition changes and the time-varying constant energy expenditure on day k−1RETj* ratio of extracellular to total water mass ratio calculated on calibration day with index mark jRREkretained or released energy from body stores for day kRMRkresting metabolic rate (kcal/day) with filtering formula on day kRMRjresting metabolic rate (kcal/day) with predictive formula on calibration day jRMRj′ measured resting metabolic rate on calibration day jSRMRkresting metabolic rate (kcal/day) with predictive formula on day kSRMRk−1resting metabolic rate (kcal/day) with predictive formula on day k−1TEEk* indirectly calculated total energy expenditure (kcal/day) on day kTBWktotal body water mass (g) Wkbody weight (kg) on day k WCkwaist circumference (cm){circumflex over (μ)}0estimation of the correction factor for de novo lipogenesis at initiation day{circumflex over (μ)}kestimation of the correction factor for de novo lipogenesis on day kμk* indirectly calculated correction factor for de novo lipogenesisμj′* indirectly measured correction factor for de novo lipogenesis on calibration day j{circumflex over (ν)}0estimation of the correction factor for gluconeogenesis from amino acids at initiation day{circumflex over (μ)}kestimation of the correction factor for gluconeogenesis from amino acids on day kνk* indirectly calculated correction factor for gluconeogenesis from amino acidsνj′* indirectly measured correction factor for gluconeogenesis from amino acids on calibration day j{circumflex over (φ)}0estimation of the correction factor for unknown energy losses or gains at initiation day{circumflex over (φ)}kestimation of the unknown energy losses or gains on day kφk* indirectly calculated correction factor for unidentified energy losses or gains
Vector VariablesBCkbody composition vector with elements of size of glycogen, fat, and protein stores on day kBCk* indirectly calculated body composition vector on day kBCiCALbody composition vector with elements of size of glycogen, fat, and protein stores obtained through calibration procedure on day iBCjCALbody composition vector with elements of size of glycogen, fat, and protein stores obtained through calibration procedure on day jBCkSM* smoothed indirectly calculated body composition vector on day kBCiTR* body composition vector with elements of size of glycogen, fat, and protein stores obtained through trajectory calculation procedure on day iBCkTR* body composition vector with elements of size of glycogen, fat, and protein stores obtained through trajectory calculation procedure on day kCkbias vector in the Linear Extended Model of the Human Energy Metabolism on day kEIkutilized energy intake vector with elements of daily metabolized macronutrient intake carbohydrate, fat, and protein on day kδdeviation of the estimated indirectly calculated utilized energy intake from trajectory on day kEIkRRE* indirectly measured utilized energy Intake on day k using the Retained or Released Energy Model of the Human Energy Metabolismestimated indirectly calculated utilized energy intake by the Self Correcting Model of the Utilized Energy Intake on day kestimated indirectly calculated utilized energy intake by the Self Correcting Model of the Utilized Energy Intake on day k−1HEEk* indirectly calculated heat energy equivalent vector on day kOxkmacronutrient oxidation vector with elements of energy obtained from oxidation of carbohydrate, fat, and protein on day kOxk* indirectly calculated macronutrient oxidation vector with elements of energy obtained after oxidation of carbohydrate, fat, and protein on day kUCktime varying bias vector in Self Corrective Model of the Utilized Energy Intake on day k UCk−1time varying bias vector in Self Corrective Model of the Utilized Energy Intake on day k−1δdeviation of the estimated indirectly calculated change of body composition vector from trajectory of day kΔBCkchange of body composition vector of day k−1ΔBCk+1change of body composition vector of day kΔBCk+1* indirectly calculated change of body composition vector of day kΔBCk+1TR* change of trajectory of indirectly calculated change of body composition vector of day kΔestimated indirectly calculated change of body composition vector of day kΔLFPk+1* change of the indirectly calculated Lean-Fat-Protein vector for day kΔLFRk+1* change of the indirectly calculated Lean-Fat-Resting-Metabolic-Rate vector for day k
Matrix VariablesAkdynamic transition matrix of the Linear Extended Model of the Human Energy MetabolismBkinput coupling matrix of the Linear Extended Model of the Human Energy MetabolismHe oxygen caloric heat equivalent constants matrixHe−1inverse matrix of the oxygen caloric heat equivalent constants matrixKHkKalman gain matrix of the Self Adaptive Model of the Human Energy MetabolismKUkKalman gain matrix of the Self Correcting Model of the Utilized Energy IntakeMc energy constant matrix of the Retained or Released Energy Model of the Human Energy MetabolismMMAk* indirectly calculated bias vector of the Retained or Released Energy Model of the Human Energy Metabolism on day kMMAk−1* indirectly calculated bias vector of the Retained or Released Energy Model of the Human Energy Metabolism on day k−1MNB constant matrix of the Measurement Model of Body Composition Change from Lean-Fat-ProteinMMBktime varying utilized energy intake coupling matrix in the Retained or Released Energy Model of the Human Energy Metabolism on day kMMBk−1time varying utilized energy intake coupling matrix in the Retained or Released Energy Model of the Human Energy Metabolism on day k−1MMBk−1inverse matrix of the time varying utilized energy intake coupling matrix in the Retained or Released Energy Model of the Human Energy Metabolism on day kMRB constant matrix of the Measurement Model of Body Composition Change from Lean-Fat-Resting Metabolic RateUBCk−1dynamic coupling matrix in the Self Corrective Model of the Utilized Energy Intake on day k−1UEIk−1dynamic transition matrix in the Self Correcting Model of the Utilized Energy Intake on day k−1
Dynamic System or Process ModelsLEM-HEM Linear Extended Model of the Human Energy Metabolism:
ρC·ΔGk+1:=CIk+{circumflex over (ν)}k·GNGPk+GNGFk−{circumflex over (μ)}k·DNLk−G3Pk−EFsk−CarbOxk*−{circumflex over (φ)}k;
ρF·ΔFk+1:=rFFA·FIk+{circumflex over (μ)}k·DNLk+rG·ΔFk+1−FatOxk*;
ρP·ΔGk+1:=PIk−{circumflex over (ν)}k·GNGPk−ProtOxk*;or the equivalent with matrix notation:
ΔBCk+1:=Ak·BCk+Bk·EIk+Ck;LM-HEM Linear Model of the Human Energy Metabolism:
ρC·ΔGk+1:=CIk+GNGPk+GNGFk·DNLk−G3Pk−EFsk−CarbOxk*;
ρF·ΔFk+1:=rFFA·FIk+DNLk+rG·ΔFk+1−FatOxk*;
ρP·ΔGk+1:=PIk−GNGPk−ProtOxk*;RRE-HEM Retained or Released Energy Model of the Human Energy Metabolism
C·ΔGk+1*+F·ΔFk+1*+P=ΔPk+1*=CIk+FIk+PIk−TEEk;
ηG·ΔGk+1*+ηF·ΔFk+1*+ηP·ΔPk+1*=SRMRk−Eck*−RRk;
ρP·ΔPk+1*:=PIk−6.25·ρP·Nexcrk;or the equivalent with matrix notation:
Mc·ΔBCk+1*:=MMBk·EIkRRE*+MMAk*;F-RMR Filtering Model of the Resting Metabolic Rate
RMRk:=Eck*+RRk+ηG·ΔGk+ηF·ΔFk+ηP·ΔPk;P-RMR Predicting Model of the Resting Metabolic Rate
SRMRk:=Eck*+RRk+ηG·ΔGk+1*+ηF·ΔFk+1*+ηP·ΔPk+1*;LM-UEI Linear Model of the Utilized Energy Intake
EIk:=UEIk−1·EIk−1+UBCk−1·ΔBCk+1*+UCk−1;S-EI Self Correcting Model of the Utilized Energy Intake
:=UEIk−1·+UBCk−1·ΔBCk+1*+UCk−1+KUk·δ;SAM-HEM Self Adaptive Model of the Human Energy Metabolism
Δ:=Ak·k*+Bk·EIk+Ck+KHk·δ;
Measurement ModelsM-LFP Measurement Model of Body Composition Change from Lean-Fat-Protein
ΔLFPk+1*:=MNB·ΔBCk+1*;M-LFR Measurement Model of Body Composition Change from Lean-Fat-Resting-Metabolic-Rate
ΔLFRk+1*:=MRB·ΔBCk+1*;M-RRE Measurement Model of Body Composition Change from the Retained or Released Energy
Mc·ΔBCk+1:=MMBk·EIk+MMAk*;M-UEI Measurement Model of the Utilized Energy Intake from Body Composition Change
EIkRRE*:=MMBk−1·Mc·ΔBCk+1−MMBk−1·MMAk*;M-Ox Measurement Model of the Macronutrient Oxidation Rates
Oxk*=He−1·HEEk*
Model Constants

The following model constants were taken from Hall (Hall, DOI: 10.1152/ajpendo.00523):{circumflex over (D)}F140 g·day−1baseline lipolysis rate before calibration{circumflex over (D)}FNEWnew value for the baseline lipolysis rate after calibration on day j{circumflex over (D)}P300 g·day−1baseline proteolysis rate{circumflex over (D)}G180 g·day−1baseline glycogenolysis rateG{circumflex over (N)}GP100 kcal·day−1basal gluconeogenesis rate before calibrationG{circumflex over (N)}GPNEWnew value for the basal gluconeogenesis rate after calibration on day jkL3.0910 dimensionless normalized lipolysis rateMB1.4 kg brain massMG92 g/mol molecular mass of glycerolMTG860 g/mol molecular mass of triglycerideMFFA273 g/mol molecular mass of free fatty acidsco 0.746 liters of oxygen is needed to burn 1 g glucosefo 2.03 liters of oxygen is needed to burn 1 g fatpo 0.966 liters of oxygen is needed to burn 1 g proteincc 0.746 liters of carbon dioxide is produced when 1 g of glucose is burnedfc 1.43 liters of carbon dioxide is produced when 1 g of fat is burnedpc 0.782 liters of carbon dioxide is produced when 1 g of protein is burnedαc0.075 dimensionless thermal effect of feeding factor for ingested carbohydrateαP0.025 dimensionless thermal effect of feeding factor for ingested fatαP0.25 dimensionless thermal effect of feeding factor for ingested proteinγB240 kcal·kg−1·day−1metabolic rate for the brainγF4.5 kcal·kg−1·day−1metabolic rate for adipose tissueγBCM24 kcal·kg−1·day−1basal metabolic rateεP0.17 kcal/g protein degradation costεd0.8 dimensionless de novo lipogenesis efficiencyεg0.8 dimensionless gluconeogenesis efficiencyηF0.18 kcal/g synthesis cost of fatηP0.86 kcal/g synthesis cost of proteinηG0.21 kcal/g synthesis cost of glycogenF9.4 kcal/g energy density of fatC4.2 kcal/g energy density of glycogenP4.7 kcal/g energy density of protein

The following model constants are from Hall, (Hall, DOI: 10.1152/ajpendo.00559.2009):βC0.95 dimensionless adjustment factor for digestion and absorption of ingested carbohydrateβF0.96 dimensionless adjustment factor for digestion and absorption of ingested fatβP0.90 dimensionless adjustment factor for digestion and absorption of protein

The following model constants are from Livesey, (Livesey, G. and M. Elia. Estimation of energy expenditure, net carbohydrate utilization, and net fat oxidation and synthesis by indirect calorimetry: evaluation of errors with special reference to the detailed composition of fuels. American Journal of Clinical Nutrition. April 1988; 47(4):608-628.):Hc 5.047 kcal·Liter−1heat equivalent of oxygen for carbohydrateHf 4.686 kcal·Liter−1heat equivalent of oxygen for fatHp 4.656 kcal·Liter−1heat equivalent of oxygen for protein

The following model constants are from Simonson, (Simonson, D. C. and R. A. DeFronzo. Indirect calorimetry: methodological and interpretative problems. American Journal of Physiology—Endocrinology and Metabolism. March 1990; 258(3):E399-E412.):Fs 2.32 Kcal/gram energy cost of lipid synthesis

Definitions

The daily change of the glycogen store for day k−1 is defined as:
ΔGk:=Gk+Gk−1;  Def. 1.

The daily change of the fat store for day k−1 is defined as:
ΔFk:=Fk−Fk−1;  Def. 2.

The daily change of the protein store for day k−1 is defined as:
ΔPk:=Pk−Pk−1;  Def. 3.

The daily change of the glycogen store for day k is defined as:
ΔLk+1:=Gk+1−Gk;  Def. 4.

The daily change of the fat store for day k is defined as:
ΔFk+1:=Fk+1−Fk;  Def. 5.

The daily change of the protein store for day k is defined as:
ΔPk+1:=Pk+1−Pk;  Def. 6.

The daily change of the extracellular water mass for day k−1 is defined as:
ΔECWk:=ECWk−ECWk−1;  Def. 7.

The daily change of the intracellular water mass for day k−1 is defined as:
ΔICWk:=ICWk−ICWk−1;  Def. 8.

The total energy expenditure is calculated from the resting metabolic rate and the physical activity energy expenditure as:
TEEk:=RMRk+PAEk;  Def. 9.

The bone mass is calculated as in Hall 2010 (Hall, DOI: 10.1152/ajpendo.00559.2009):
BM=0.04·BW0;  Def. 10.

The extracellular protein mass is calculated with the following regression equation from Hall, (Hall, DOI: 10.1152/ajpendo.00559.2009) after adaptation from Wang, (Wang Z, Shen W, Kotler D P, Heshka S, Wielopolski L, Aloia J F, Nelson M E, Pierson R N Jr, Heymsfield S B. Total body protein: a new cellular level mass and distribution prediction model. The American Journal of Clinical Nutrition 78: 979-984, 2003.):
ECP:=0.732·BM+0.01087·ECW0;  Def. 11.

The lean body mass is calculated from brain mass, extracellular protein, extracellular water mass, intracellular water mass, protein mass, and glycogen mass as:
Lk:=BM+ECP+ECWk+ICWk+Pk+Gk;  Def. 12.

The change of lean body mass is calculated from daily changes of extracellular water mass, intracellular water mass, protein mass, and glycogen mass as:
ΔLk:=ΔECWk+ΔICWk+ΔPk+ΔGk;  Def. 13.

The body weight is calculated from lean body mass and body fat mass as:
BWk:=Lk+Fk;  Def. 14.

The daily change of body weight is calculated from daily change of lean body mass and body fat mass as:
ΔBWk:=ΔLk+ΔFk;  Def. 15.

The change of body weight is calculated from daily changes of extracellular water mass, intracellular water mass, fat mass, protein mass, and glycogen mass as:
ΔBWk:=ΔECWk+ΔICWk+ΔFk+ΔPk+ΔGk;  Def. 16.

The body cell mass is calculated from intracellular water mass, protein mass, glycogen mass, and brain mass as:
BCMk:=ICWk+Pk+Gk−MB;  Def. 17.

The daily change of body cell mass is calculated from daily changes of intracellular water mass, protein mass, and glycogen mass as:
ΔBCMk:=ΔICWk+ΔPk+ΔGk;  Def. 18.

The total energy expenditure TEEkis calculated from rate of carbohydrate oxidation, rate of fat oxidation, rate of protein oxidation, and indirectly calculated correction factor for unidentified energy losses or gains:
TEEk:=CarbOxk+FatOxk+ProtOxk+{circumflex over (φ)}k;  Def. 19.

The retained or released energy is calculated from the daily change of the glycogen store, the daily change of the fat store and the daily change of the protein store as:
RREk:=C·ΔGk+1+F·ΔFk+1+P·ΔPk+1;  Def. 20.

The retained or released energy is calculated from utilized carbohydrate intake, utilized fat intake, utilized protein intake, and the total energy expenditure as:
RREk:=CIk+FIk+PIk−TEEk;  Def. 21.

The total 24 h excretion of nitrogen is calculated from rate of protein oxidation and gluconeogenesis from protein as:
Nexcrk:=(6.25·ρP)−1·(ProtOxk+GNGPk);  Def. 22.

The energy needed for fat synthesis is calculated during net fat loss as:
EFsk:=0;  Def. 23.

The energy needed for fat synthesis is calculated during net fat loss as:
EFsk:=(Fs−rG)·ΔFk+1;  Def. 24.

The rate of de novo lipogenesis is calculated by using the following identity calculation:
DNLk:=DFk;  Def. 25.

The estimated rate of endogenous lipolysis with calibration is calculated using the following calculation:

The estimated gluconeogenesis from protein with calibration is calculated using the following calculation:

The molecular weight ratio free fatty acid to triglyceride is calculated as:

The molecular weight and energy density ratio glycerol to triglyceride is calculated as:

The molecular weight ratio glycerol to triglyceride is calculated as:

The body composition vector with elements of size of macronutrient stores glycogen, fat and protein for day k is constructed as:
BCk:=(GkFkPk)T;  Def. 31.

The utilized energy intake vector with elements of daily metabolized macronutrient intake carbohydrate, fat and protein for day k is constructed as:
EIk:=(CIkFIkPIk)T;  Def. 32.

The macronutrient oxidation vector with elements of energy content obtained after oxidation of carbohydrate, fat and protein for day k is constructed as:
Oxk:=(CarbOxkFatOxkProtOxk)T;  Def. 33.

Change of body composition vector is constructed as:
ΔBCk:=(ΔGkΔFkΔPk)T;  Def. 34.

Change of body composition vector is calculate from body composition vectors of day k+1 and body composition vectors of day k as:
ΔBCk+1:=BCk+1−BCk;  Def. 35.

Change of the estimated indirectly calculated body composition vector on day k+1 is constructed from the estimated indirectly calculated glycogen mass, fat mass, and protein mass on day k+1 as:
Δ:=(ΔĜk+1*Δ{circumflex over (F)}k+1*Δ{circumflex over (P)}k+1*)T;  Def. 36.

The constant matrix of the Measurement Model of Body Composition Change from Lean-Fat-Protein is construed as:

The constant matrix of the Measurement Model of Body Composition Change from Lean-Fat-Resting Metabolic Rate:

The energy constant matrix of the Retained or Released Energy Model of the Human Energy Metabolism:

FIGS. 1A and 1B. illustrates how the measurements of a device for body composition and hydration status analysis109flows into a method130for dynamic indirect individualized measurement of components of the human energy metabolism, and this method130is illustrated in detail in the flowchart inFIGS. 5A-5O.

A human subject105undergoes a body composition change of his or her glycogen store, fat store, and protein store on an examined day k. A total energy expenditure101is produced on day k and leaves the human subject105on day k. Energies enter the human subject105in the form of the ingested carbohydrate intake102, fat intake103, and protein intake104on day k. A device for body composition and hydration status analysis109measures resistance directly at multiple frequencies and I extrapolate indirectly to zero frequency and infinite frequency on day k106. The same device for body composition and hydration status analysis109measures the extracellular water mass on day k126, the intracellular water mass on day k127, and the change of lean body mass and fat mass on day k107. The same device109can optionally measure acute change of extracellular water mass and intracellular water mass108. A measurement of physical activity energy expenditure110is required on day k. Optional measurements of ingested energy in the form of carbohydrate111, fat112, and protein113are taken on day j for calibration purposes. An optional measurement of resting metabolic rate114is taken on day j for calibration purposes. An optional measurement of nitrogen excretion115is taken on day j for calibration purposes and to indirectly measure the daily gluconeogenesis. An optional measurement of the rate of endogenous lipolysis116is taken on day j for calibration purposes and to indirectly measure the daily lipolysis. The method for dynamic indirect individualized measurement of components of the human energy metabolism130comprises a Self Correcting Model of the Utilized Energy Intake131, a Self Adaptive Model of the Human Energy Metabolism132, and a calculation of the components of the human energy metabolism133. The Self Correcting Model of the Utilized Energy Intake131estimates the utilized energy intake, defined as the daily utilized energy of carbohydrate, fat, and protein caloric intake119. The Self Adaptive Model of the Human Energy Metabolism132estimates the daily change of body composition, defined as the change of glycogen store, fat store, and protein store118. The calculation of the components of the human energy metabolism133provides the macronutrient oxidation rate results, defined as the daily rate of carbohydrate oxidation, fat oxidation, and protein oxidation120; daily resting metabolic rate121; daily unknown forms of energy losses or gains122; daily rate of endogenous lipolysis123; daily nitrogen excretion124; and daily gluconeogenesis from protein125.

FIG. 2. illustrates an interface electrical connection between the human subject105and measuring points1,208, measuring point3,211, measuring point4,213, and measuring point5,215. The same figure also shows the lumped circuit diagram equivalent of the human subject105connected to nodal junctions216and217. The lumped circuit diagram is made up of the resistance at zero frequency205connected parallel to the serially connected membrane capacitance207and resistance at infinite frequency206. Nodal junction216is also connected to earth potential202through stray capacitance1,204. Nodal junction216is also connected to measuring point1,208through excitation electrode resistance1,209, and to measuring point3,211, through Sensory electrode resistance1,210. Nodal junction217is also connected to earth potential202through stray capacitance2,203. Nodal junction217is also connected to measuring point5,215through excitation electrode resistance2,214and to measuring point4,213through sensory electrode resistance2,212. I model the human impedance with a Cole circuit model consisting of a resistance at zero frequency205connected parallel to the serially connected membrane capacitance207and resistance at infinite frequency206. This Cole circuit model provides the impedance of the human subject105.

FIG. 3. illustrates an input logic circuit connecting measuring point1,208, measuring point3,211, measuring point4,213, and measuring point5,215, which are in close proximity to the human subject328, with measuring point1,208, measuring point3,211, measuring point4,213, measuring point5,215, and measuring point6,325, inside of a device for body composition and hydration status analysis327. Measuring point1,208, in close proximity to the human subject328, is connected to measuring point1,208, inside of the device for body composition and hydration status analysis327, through on and off switch14,310. Measuring point1,208, in close proximity to the human subject328, is also connected to measuring point6,325, inside of the device for body composition and hydration status analysis327, through reference resistance1,324. Measuring point3,211, in close proximity to the human subject328, is directly connected to measuring point3,211, inside of a device for body composition and hydration status analysis327. Measuring point4,213, in close proximity to the human subject328, is directly connected to measuring point4,213, inside of a device for body composition and hydration status analysis327. Measuring point5,215, in close proximity to the human subject328, is connected to measuring point5,215, inside of the device for body composition and hydration status analysis327, through on and off switch13,322. Measuring point5,215, in close proximity to the human subject328, is connected to measuring point2,320, inside of the device for body composition and hydration status analysis327, through reference resistance2,321. Measuring point5,215, in close proximity to the human subject328, is connected to measuring point0,319, inside of the device for body composition and hydration status analysis327, through on and off switch7,312.

Measuring points1,3,4, and5,208,211,213, and215, respectively, in close proximity to the human subject328, are connected through on and off switches1-6,306,307,305,309,308, and311, respectively. Measuring point1,208, is connected to measuring point3,211, through on and off switch2,307. Measuring point1,208, is connected to measuring point5,215, through on and off switch4,309. Measuring point1,208, is connected to measuring point4,213, through on and off switch5,308. Measuring point3,211, is connected to measuring point4,213, through on and off switch1,306. Measuring point3,211, is connected to measuring point5,215, through on and off switch6,311. Measuring point4,213, is connected to measuring point5,215, through on and off switch3,305.

Measuring points6,1,3,4,5,2, and0,325,208,211,213,215,320, and319, respectively, inside of the device for body composition and hydration status analysis327, are connected through on and off switches7-15,312,313,314,315,316,317,322,310, and323, respectively. Measuring point0,319, is connected to earth potential202. Measuring point6,325, is connected to measuring point0,319, through reference resistance1,324, and on and off switch8,313. Measuring point6,325, is also connected to earth potential202through on and off switch15,323. Measuring point1,208, is connected to measuring point0,319, through on and off switch14,310, and on and off switch8,313. Measuring point3,211, is connected to measuring point0,319, through on and off switch9,314. Measuring point4,213, is connected to measuring point0,319, through on and off switch10,315. Measuring point5,215, is connected to measuring point0,319, through on and off switch11,316. Measuring point2,320, is connected to measuring point0,319, through on and off switch12,317.

FIG. 4. illustrates the measuring circuit of the first embodiment to determine the impedance of a human subject at various frequencies. The measuring circuit consists of the following elements in this order: connecting element427; M6or measuring point6,325; connecting element428; reference resistance1,324; connecting element429; M1or measuring point1,208; connecting element419; current excitation electrode1,410; connecting element420; impedance of the human subject at various frequencies consisting of resistance and reactance,105; connecting element421; current excitation electrode2,408; connecting element422; M5or measuring point5,215; connecting element423; reference resistance2,321; connecting element424; M2or measuring point2,320; connecting element425; current source2,404; connecting element426, which is also connected to earth potential202; current source1,403; and again connecting element427.

The current source driving means consists of a first in first out memory401and a digital-analog converter402, which are connected with each other. The first in first out memory401is connected to the microcontroller unit412also containing memory means and a six-channel programmable gain instrumentation amplifier and filtering circuit. The digital-analog converter402is connected431to current source1,403, and is also connected430to current source2,404.

M1or measuring point1,208, is between reference resistance1,324, and current excitation electrode1,410, on the measuring circuit and is also connected to M1or measuring point1input208inside the microcontroller unit412. M2or measuring point2,320, is between current source2,404, and reference resistance2,321, on the measuring circuit and is also connected to M2or measuring point2input320inside the microcontroller unit412. M3or measuring point3,211, is connected to voltage sensing electrode1,415, and is also connected to M3or measuring point3input211inside the microcontroller unit412. M4or measuring point4,213, is connected to voltage sensing electrode2,418, and is also connected to M4or measuring point4input213inside the microcontroller unit412. M5or measuring point5,215, is between current excitation electrode2,408, and reference resistance2,321, on the measuring circuit and is also connected to M5or measuring point5input215inside the microcontroller unit412. M6or measuring point6,325, is between reference resistance1,324, and current source1,403, on the measuring circuit and is also connected to M6or measuring point6input325inside the microcontroller unit412.

Voltage sensing electrode1,415, is between the human subject with its impedance at various frequencies105and M3or measuring point3,211. Voltage sensing electrode2,418, is between the human subject with its impedance at various frequencies105and M4or measuring point4,213. M0or measuring point0input319inside the microcontroller unit412is connected to earth potential202. The digital signal processor unit of the device for body composition and hydration status analysis413is connected to the microcontroller unit412.

The overview of the operation of the first embodiment of my apparatus and method for the analysis of change of body composition and hydration status and for dynamic indirect individualized measurement of components of the human energy metabolism is depicted onFIGS. 1A and 1B. The GLOSSARY lists the definitions of the upper indices, definitions of lower indices, signs for the estimated value and assigned variable, scalar variables, vector variables, matrix variables, dynamic system and process models, measurement models, and model constants and definitions used in my first embodiment.

The human subject's metabolism105takes up energy in the form of the ingested carbohydrate intake102, fat intake103, and protein intake104on day k. The metabolism uses this energy intake; the human subject105undergoes body composition change of his or her glycogen store, fat store, and protein store on an examined day k; and a total energy expenditure101is produced. My apparatus for the analysis of change of body composition and hydration status109measures resistance directly at multiple frequencies and I extrapolate indirectly to zero frequency and infinite frequency on day k106. Using these results the same device109measures the extracellular water mass126, the intracellular water mass127, the change of lean body mass, and change of fat mass on day k107. The extracellular water mass and intracellular water mass107are calculated as in Eq. 148. and Eq. 149., respectively, in process30,FIGS. 5A-5O. The change of lean body mass and change of body fat mass107are calculated as in Eq. 152. and Eq. 153., respectively, in process30,FIGS. 5A-5O. The same device109can optionally measure acute change of extracellular water mass and intracellular water mass108. The acute change of extracellular and intracellular water mass108are calculated as in Eq. 163. and Eq. 164., respectively, in process34,FIGS. 5A-5O. A measurement of physical activity energy expenditure110is required on day k. Optional measurements of ingested energy in the form of carbohydrate111, fat112, and protein113are taken on day j for calibration purposes. An optional measurement of resting metabolic rate114is taken on day j for calibration purposes. An optional measurement of nitrogen excretion115is taken on day j for calibration purposes to indirectly measure daily gluconeogenesis. An optional measurement of the rate of endogenous lipolysis116is taken on day j for calibration purposes to indirectly measure daily lipolysis. The method for dynamic indirect individualized measurement of components of the human energy metabolism130comprises a Self Correcting Model of the Utilized Energy Intake131, a Self Adaptive Model of the Human Energy Metabolism132, and a calculation of the components of the human energy metabolism133. The Self Correcting Model of the Utilized Energy Intake131estimates the utilized energy intake, defined as the daily utilized energy of carbohydrate, fat, and protein caloric intake119. The Self Adaptive Model of the Human Energy Metabolism132estimates the daily change of body composition, defined as the change of glycogen store, fat store, and protein store118. The calculation of the components of the human energy metabolism133provides the macronutrient oxidation rate results, defined as the daily rate of carbohydrate oxidation, fat oxidation, and protein oxidation120; daily resting metabolic rate121; daily unknown forms of energy losses or gains122; daily rate of endogenous lipolysis123; daily nitrogen excretion124; and daily gluconeogenesis from protein125.

The overview of the operation of one embodiment of my apparatus for the analysis of change of body composition and hydration status109is depicted onFIG. 2,FIG. 3, andFIG. 4. I measure the passive circuit elements of the Cole circuit model representing the impedance of the human subject105. The Cole circuit model consists of a resistance at zero frequency205connected parallel to the serially connected membrane capacitance207and resistance at infinite frequency206. At zero frequency, the Cole circuit model consists of a resistance at zero frequency205and at infinite frequency it reduces to a parallel circuit of a resistance at zero frequency205connected parallel to a resistance at infinite frequency206. For higher frequencies than zero and lower frequencies than the infinite frequency, the Cole circuit model has properties of a complex impedance with a resistance and reactance value. I perform measurements at a multitude of discrete preset frequencies from 1 kilohertz to 1 megahertz. At these frequencies the presence of a membrane capacitance207is also measurable and205,206, and207is detected as a specific resistance and reactance value of an impedance105. For each preset frequency, a particular impedance is found. The digital signal processor unit413calculates205and206by fitting the Cole circuit model to the measured impedance values. In the measuring environment, other passive elements with electrical properties are present as well. These are the stray capacitance1,204, the stray capacitance2,203the excitation electrode resistance1,209, the excitation electrode resistance2,214, the sensory electrode resistance1,210, and the sensory electrode resistance2,212. To determine the value of the unknown circuit elements, an excitation current of sinusoidal form flows through the unknown circuit elements and I take voltage signal measurements at the same time at six measuring points208,320,211,213,215, and325. The excitation current comes from current sources1and2,403and404, where one of the two current sources injects the excitation current and the other sinks the current. The injecting and sinking function alternates between the current sources403and404every half period of the excitation frequency. I measure the voltage signal along the path of the measuring circuit, which starts off at earth potential202, continues with426,403,427,325,428,324,429,208,419,410,420,209, and216, branches off to204,202,222,205, and221, and218,207,219,206,205, and220, merges at217, branches off to203,202,214,421,408,422,215,423,321,424,320,425,404, and ends at202. I use an input logic circuit327and328to isolate or short circuit or leave unchanged preselected parts of the measurement circuit. The determination of the unknown lumped passive elements105,203,204,209,210,212, and214occurs with appropriate setting of the input logic circuit327and328. Before each measurement cycle I measure both offset voltage and voltage noise at six measuring points208,320,211,213,215, and325. These results are used later for elimination of offset error and minimization of voltage noise. The measurement cycle has two steps. With step one I determine the value of stray capacitance1,204, excitation electrode resistance1,209, sensory electrode resistance1,210, stray capacitance2,203, excitation electrode resistance2,214, and sensory electrode resistance2,212, using the input logic circuit328and327with appropriate setting of switches1-15,306,307,305,309,308,311,312,313,314,315,316,317,322,310, and323, respectively, and applying Ohm's law and Kirchhoff's first and second law.

In the second step, I determine the unknown impedance or resistance and reactance of the human subject105at a preset frequency by using the input logic circuit328and327with appropriate setting of switches1-15,306,307,305,309,308,311,312,313,314,315,316,317,322,310, and323, respectively, and applying Ohm's law and Kirchhoff's first and second law. The magnitude of the offset voltage and amplitude as well as the phase angle of the voltage signal from measuring point6,326, measuring point1,208, and measuring point3,211, are referenced to reference resistance1,324, and from measuring point2,320, measuring point5,215, and measuring point4,213, are referenced to reference resistance2,321, respectively. The measurement of resistance and reactance of the human subject at each preset frequency starts with loading a sine function of at least 16 wave lengths to a first in first out memory401by a microcontroller unit412. Upon a trigger by the microcontroller unit412, the train of at least 16 sine waves is sent to a digital-analog converter402at a predetermined rate by the microcontroller unit412. The digital-analog converter402generates an excitation pattern with opposing phase for current source1,403, and current source2,404. Programmable gain instrumentation amplifiers within the microcontroller unit412pick up the voltage signals at the six measuring points208,320,211,213,215, and325and amplify and filter the signal adjusted by the microcontroller within the microcontroller unit412. The microcontroller unit412performs analog-digital conversion of the amplified and filtered voltage signal from the six measuring points208,320,211,213,215and325. The microcontroller unit412then sends the signal first to the memory means of the microcontroller unit412and upon demand sends the signal to a digital signal processor unit413. The digital signal processor unit413uses a sine wave function fitting algorithm to determine amplitude, phase, and offset of the digitized, amplified, and filtered voltage signal from the six measuring points208,320,211,213,215and325by minimizing the sum of the square of the deviations between the measured signal and a mathematical sine function of known frequency. The errors of the filtered voltage signal, defined as the difference between the predicted and measured digitalized, amplified, and filtered voltage signal from the six measuring points208,320,211,213,215and325, are used for measurement of quality and to indicate whether a repeat measurement cycle is needed.

The digital processor unit413performs a non-linear curve fitting algorithm of the Cole circuit model to the measured resistances and reactances of human subject105at preset frequencies and extrapolates the best fitting Cole circuit model curve to zero and infinite frequency to obtain resistance of the human subject at zero and infinite frequency. I use the sum of the square of the deviations between Cole circuit model predicted and actually measured impedance values to measure quality and reliability of my apparatus' functioning.

FIGS. 5A-5O. shows the detailed overview of the operation of the first method for the analysis of change of body composition and hydration status and for dynamic indirect individualized measurement of components of the human energy metabolism. The method starts at1. The calculation for subsequent days merges with the start at2. The algorithm branches off at decision point3.

If this is an initiation day then the process continues at5. The index variable for the day k is set to zero as expressed in Eq. 0. The initial values are entered for body cell mass BCM0, extracellular water mass ECW0, lean body mass L0, intracellular water mass ICW0, glycogen mass G0, fat mass F0, protein mass P0, ingested carbohydrate intake CI0˜, ingested fat intake FI0˜, ingested protein intake PIT, estimated correction factor for de novo lipogenesis {circumflex over (μ)}0, estimated correction factor for gluconeogenesis from amino acids {circumflex over (ν)}0, and estimated correction factor for unidentified energy losses or gains {circumflex over (φ)}0.

If this is not an initiation day then the process continues at4where the index variable for day k is set to a chosen value.

The algorithm branches off at decision point6.

If this is a calibration day and the ingested macronutrient calories are available, the process continues at7with Eq. 1. to Eq. 3, which calculate the utilized macronutrient energy intake vector (Hall, DOI: 10.1152/ajpendo.00559.2009) from the ingested macronutrient intake. The process continues at9.

At process9, Eq. 4. calculates the rate of proteolysis and Eq. 5. calculates the rate of glycogenolysis. Eq. 6. calculates the fat store dependent coefficient for rate of endogenous lipolysis on day k. Eq. 7. calculates the carbohydrate intake dependent coefficient for rate of endogenous lipolysis. Eq. 8. calculates the bias for rate of endogenous lipolysis on day k. Eq. 9. calculates the rate of endogenous lipolysis on day k. Eq. 10. calculates the carbohydrate intake dependent coefficient for rate of de novo lipogenesis. Eq. 11. calculates the glycogen store dependent coefficient for rate of de novo lipogenesis on day k. Eq. 12. calculates bias for rate of endogenous lipolysis on day k. Eq. 13. calculates the rate of de novo lipogenesis. Eq. 14. calculates the rate of glycerol gluconeogenesis. Eq. 15. calculates the protein store dependent coefficient for gluconeogenesis from protein. Eq. 16. calculates the carbohydrate intake dependent coefficient for gluconeogenesis from protein. Eq. 17. calculates the protein intake dependent coefficient for gluconeogenesis from protein. Eq. 18. calculates the bias for gluconeogenesis from protein. Eq. 19. calculates the rate of gluconeogenesis from protein. Eq. 20. calculates the glycerol 3-phosphate synthesis. Eq. 21. calculates the resting metabolic rate with a filtering formula on day k. Eq. 22. calculates the indirectly calculated total energy expenditure from the resting metabolic rate with the filtering formula on day k and directly measured physical activity energy expenditure. Eq. 23. calculates the 24 hour nitrogen excretion from utilized protein intake on day k and the daily change of the protein store for day k−1. The process continues at16.

If at decision point6this is not a calibration day and the ingested macronutrient calories are not available, the process continues at decision point8.

If there is no trajectory value ΔBCk+1TR*, called the change of trajectory of indirectly calculated change of body composition vector of day k, available for ΔBCk+1TR*, called the indirectly calculated change of body composition vector of day k, at decision point8, then the algorithm continues with process10.

At process10, Eq. 24. shows the calculation of the rate of proteolysis on day k. Eq. 25. calculates the rate of glycogenolysis on day k. Eq. 26. calculates the fat store dependent coefficient for the rate of endogenous lipolysis on day k. Eq. 27. calculates the carbohydrate intake dependent coefficient for the rate of endogenous lipolysis on day k. Eq. 28. calculates the bias for the rate of endogenous lipolysis on day k. Eq. 29. calculates the rate of endogenous lipolysis on day k. Eq. 30. calculates the carbohydrate intake dependent coefficient for the rate of de novo lipogenesis on day k. Eq. 31. calculates the glycogen store dependent coefficient for the rate of de novo lipogenesis on day k. Eq. 32. calculates the bias for the rate of endogenous lipolysis on day k. Eq. 33. calculates the rate of de novo lipogenesis on day k. Eq. 34. calculates the rate of glycerol gluconeogenesis on day k. Eq. 35. calculates the protein store dependent coefficient for gluconeogenesis from protein on day k. Eq. 36. calculates the carbohydrate intake dependent coefficient for gluconeogenesis from protein on day k. Eq. 37. calculates the protein intake dependent coefficient for gluconeogenesis from protein on day k. Eq. 38. calculates the bias for gluconeogenesis from protein on day k. Eq. 39. calculates the rate of gluconeogenesis from protein on day k. Eq. 40. calculates a part of the resting metabolic rate which is independent of the body composition vector changes and the time-varying constant energy expenditure on day k. Eq. 41. calculates the resting metabolic rate with predictive formula on day k. Eq. 42. calculates a part of the resting metabolic rate which is dependent on the utilized carbohydrate intake on day k. Eq. 43. calculates a part of the resting metabolic rate which is dependent on the utilized fat intake on day k. Eq. 44. calculates a part of the resting metabolic rate which is dependent on the utilized protein intake on day k. The process continues at11.

At process11, Eq. 45. constructs the energy constant matrix of the Retained or Released Energy Model of the Human Energy Metabolism on day k. Eq. 46. constructs the time varying utilized energy intake coupling matrix in the Retained or Released Energy Model of the Human Energy Metabolism on day k. Eq. 47. constructs the indirectly calculated bias vector of the Retained or Released Energy Model of the Human Energy Metabolism on day k. Eq. 48. calculates the utilized energy intake vector indirectly with the Measurement Model of the Utilized Energy Intake from body composition vector change on day k, which I obtain either from Eq. 117. or Eq. 119. where I obtain the lean body mass change and fat mass change from 107, which is part of109, the device and method for body composition and hydration status analysis. Eq. 49. assigns the value of the utilized carbohydrate intake indirectly calculated by the Measurement Model of the Utilized Energy Intake from body composition vector change on day k to the variable for the utilized carbohydrate intake on day k. Eq. 50. assigns the value of the utilized fat intake indirectly calculated by the Measurement Model of the Utilized Energy Intake from body composition vector change on day k to the variable for the utilized fat intake on day k. Eq. 51. assigns the value of the utilized protein intake indirectly calculated by the Measurement Model of the Utilized Energy Intake from body composition vector change on day k to the variable for the utilized protein intake on day k. The process continues at process9.

If there is a trajectory value ΔBCk+1TR*, called the change of trajectory of indirectly calculated change of body composition vector of day k, available for ΔBCk+1TR*, called the indirectly calculated change of body composition vector of day k, at decision point8, then the algorithm continues with process12.

At process12, Eq. 52. shows the calculation of the rate of proteolysis on day k−1. Eq. 53. calculates the rate of glycogenolysis on day k−1. Eq. 54. calculates the fat store dependent coefficient for the rate of endogenous lipolysis on day k−1. Eq. 55. calculates the carbohydrate intake dependent coefficient for the rate of endogenous lipolysis on day k−1. Eq. 56. calculates the bias for the rate of endogenous lipolysis on day k−1. Eq. 57. calculates the rate of endogenous lipolysis on day k−1. Eq. 58. calculates the carbohydrate intake dependent coefficient for the rate of de novo lipogenesis on day k−1. Eq. 59. calculates the glycogen store dependent coefficient for the rate of de novo lipogenesis on day k−1. Eq. 60. calculates the bias for the rate of endogenous lipolysis on day k−1. Eq. 61. calculates the rate of de novo lipogenesis on day k−1. Eq. 62. calculates the rate of glycerol gluconeogenesis on day k−1. Eq. 63. calculates the protein store dependent coefficient for gluconeogenesis from protein on day k−1. Eq. 64. calculates the carbohydrate intake dependent coefficient for gluconeogenesis from protein on day k−1. Eq. 65. calculates the protein intake dependent coefficient for gluconeogenesis from protein on day k−1. Eq. 66. calculates the bias for gluconeogenesis from protein on day k−1. Eq. 67. calculates the rate of gluconeogenesis from protein on day k−1. Eq. 68. calculates a part of the resting metabolic rate which is independent of the body composition vector changes and the time-varying constant energy expenditure on day k−1. Eq. 69. calculates the resting metabolic rate with predictive formula on day k−1. Eq. 70. calculates a part of the resting metabolic rate which is dependent on the utilized carbohydrate intake on day k−1. Eq. 71. calculates a part of the resting metabolic rate which is dependent on the utilized fat intake on day k−1. Eq. 72. calculates a part of the resting metabolic rate which is dependent on the utilized protein intake on day k−1. The process continues at13.

At process13, Eq. 73. shows the calculation of rate of proteolysis on day k. Eq. 74. calculates the rate of glycogenolysis on day k. Eq. 75. calculates the fat store dependent coefficient for rate of endogenous lipolysis on day k. Eq. 76. calculates carbohydrate intake dependent coefficient for rate of endogenous lipolysis on day k. Eq. 77. calculates the bias for rate of endogenous lipolysis on day k. Eq. 78. calculates the rate of endogenous lipolysis on day k. Eq. 79. calculates the carbohydrate intake dependent coefficient for the rate of de novo lipogenesis on day k. Eq. 80. calculates the glycogen store dependent coefficient for the rate of de novo lipogenesis on day k. Eq. 81. calculates the bias for the rate of endogenous lipolysis on day k. Eq. 82. calculates the rate of de novo lipogenesis on day k. Eq. 83. calculates the rate of glycerol gluconeogenesis on day k. Eq. 84. calculates the protein store dependent coefficient for gluconeogenesis from protein on day k. Eq. 85. calculates the carbohydrate intake dependent coefficient for gluconeogenesis from protein on day k. Eq. 86. calculates the protein intake dependent coefficient for gluconeogenesis from protein on day k. Eq. 87. calculates the bias for gluconeogenesis from protein. Eq. 88. calculates the rate of gluconeogenesis from protein on day k. Eq. 89. calculates a part of the resting metabolic rate that is independent of the body composition vector changes and the time-varying constant energy expenditure on day k. Eq. 90. calculates the resting metabolic rate with a predictive formula on day k. Eq. 91. calculates a part of the resting metabolic rate which is dependent on the utilized carbohydrate intake on day k. Eq. 92. calculates a part of the resting metabolic rate which is dependent on the utilized fat intake on day k. Eq. 93. calculates a part of the resting metabolic rate which is dependent on the utilized protein intake on day k. The process continues at14.

At process14, Eq. 94. constructs the time varying utilized energy intake coupling matrix in the Retained or Released Energy Model of the Human Energy Metabolism on day k−1. Eq. 95. constructs the indirectly calculated bias vector of the Retained or Released Energy Model of the Human Energy Metabolism on day k−1. Eq. 96. constructs the time varying utilized energy intake coupling matrix in the Retained or Released Energy Model of the Human Energy Metabolism on day k. Eq. 97. constructs the indirectly calculated bias vector of the Retained or Released Energy Model of the Human Energy Metabolism on day k. Eq. 98. calculates the dynamic transition matrix in the Self Correcting Model of the Utilized Energy Intake on day k−1. Eq. 99. calculates dynamic coupling matrix in the Self Corrective Model of the Utilized Energy Intake on day k−1. Eq. 100. calculates the time varying bias vector in the Self Corrective Model of the Utilized Energy Intake on day k−1. Eq. 101. calculates the utilized energy intake vector, with the elements consisting of the daily metabolized macronutrient intake from carbohydrate, fat and protein on day k. I refer to Eq. 101. as the Linear Model of the Utilized Energy Intake, and this linear model also serves as the process model of the Self Correcting Model of the Utilized Energy Intake. Eq. 102. calculates the indirectly measured utilized energy intake vector on day k using the Retained or Released Energy Model of the Human Energy Metabolism, and I refer to Eq. 102. as the Measurement Model of the Utilized Energy Intake from body composition vector change. The input variable to Eq. 102. is the indirectly calculated change of body composition vector of day k, which I obtain either from Eq. 117. or Eq. 119. where I obtain the lean body mass change and fat mass change from 107, which is part of109, the device and method for body composition and hydration status analysis. The process continues at process15.

At process15, the deviation of the estimated indirectly calculated utilized energy intake vector is evaluated with one of two optional equations, Eq. 103. or Eq. 104. Eq. 103. calculates the deviation of the estimated indirectly calculated utilized energy intake vector from the indirectly measured utilized energy intake vector on day k using the indirectly calculated change of body composition vector of day k and the Measurement Model of the Utilized Energy Intake. Eq. 104. calculates the deviation of the estimated indirectly calculated utilized energy intake vector from a trajectory using the change of trajectory of indirectly calculated change of body composition vector of day k and the Measurement Model of the Utilized Energy Intake. Eq. 105. implements the discrete time Kalman estimator with innovations representation for the daily utilized macronutrient energy intake vector using the Self Correcting Model of the Utilized Energy Intake with innovations representation. The Kalman gain matrix is calculated as in Grewal, (Grewal M. S. and A. P. Andrews. Kalman Filtering: Theory and Practice Using MATLAB. John Wiley & Sons, New Jersey. Third Ed.; September 2011, 136 pp.). Eq. 106. assigns the estimated indirectly calculated utilized energy intake vector by the Self Correcting Model of the Utilized Energy Intake on day k to the utilized energy intake vector vector with elements of daily metabolized macronutrient intake of carbohydrate, fat, and protein on day k. The process continues at9.

At process16, the macronutrient oxidation rates are calculated. Eq. 107. constructs the oxygen caloric heat equivalent constants matrix. Eq. 108. constructs the indirectly calculated heat energy equivalent vector on day k. Eq. 109. calculates the indirectly calculated macronutrient oxidation vector with the elements of energy content obtained after oxidation of carbohydrate, fat, and protein on day k. Eq. 110. assigns the values of the components of the macronutrient oxidation vector to variables of the calculated rate of carbohydrate oxidation, calculated rate of fat oxidation, and calculated rate of protein oxidation. The process continues at17.

The process at17shows the process model of the Linear Extended Model of the Human Energy Metabolism. Eq. 111. calculates the daily energy of the glycogen store change for day k. Eq. 112. calculates the daily energy of fat store change for day k. Eq. 113. calculates the daily energy of protein store change for day k. The calculations in Eq. 111. to Eq. 113. are represented also in Eq. 114. with a matrix representation to calculate the change of body composition vector at the end of day k.

The algorithm branches off at decision point18and reunites again at21. The measurement model can be either the Measurement Model of Body Composition Change from Lean-Fat-Protein as in Eq. 115. to Eq. 117. at process19or the Measurement Model of Body Composition Change from Lean-Fat-Resting Metabolic Rate as in Eq. 118. to Eq. 119. at process20. Eq. 115. calculates daily change of the indirectly calculated body protein mass on day k. Eq. 116. calculates the change of the indirectly calculated lean-fat-protein vector of day k. Eq. 117. calculates the indirectly calculated change of body composition vector for day k, where I obtain the lean body mass change and fat mass change from 107, which is part of109, the device and method for body composition and hydration status analysis. I refer to Eq. 117. as the Measurement Model of Body Composition Change from Lean-Fat-Protein. The algorithm continues at21.

At process20, Eq. 118. is the change of the indirectly calculated lean-fat-resting-metabolic-rate vector of day k. Eq. 119. calculates the indirectly calculated change of body composition vector for day k where I obtain the lean body mass change and fat mass change from 107, which is part of109, the device and method for body composition and hydration status analysis. I refer to Eq. 119. as the Measurement Model of Body Composition Change from Lean-Fat-Resting-Metabolic-Rate. The algorithm continues at21.

At process21, the deviation of the estimated indirectly calculated change of body composition vector is evaluated with one of three optional equations, Eq. 120., Eq. 121., or Eq. 122. Eq. 120. calculates the deviation of the estimated indirectly calculated change of body composition vector of day k from the indirectly measured one using the Measurement Model of Body Composition Change from Lean-Fat-Protein. Eq. 121. calculates the deviation of the estimated indirectly calculated change of body composition vector of day k from the indirectly measured one using the Measurement Model of Body Composition Change from Lean-Fat-Resting-Metabolic-Rate. Eq. 122. calculates the deviation of the estimated indirectly calculated change of body composition vector from a trajectory on day k. Eq. 123. implements the discrete time variant Kalman estimator with innovations representation for the estimation of the indirectly calculated change of body composition of day k. In this equation, I use the Self Adaptive Model of the Human Energy Metabolism and innovations representation technique. The resulting estimates of the daily body composition change of day k allow for stochastic identification of the correction factors for de novo lipogenesis, gluconeogenesis from amino acids, and the correction factor for unidentified energy losses or gains, so that these model parameters become self adaptive. The Kalman gain matrices are calculated as in Grewal, (Grewal M. S. and A. P. Andrews. Kalman Filtering: Theory and Practice Using MATLAB. John Wiley & Sons, New Jersey. Third Ed.; September 2011, pp. 136.). The algorithm continues at22.

At process22, the estimators for the correction factors for de novo lipogenesis, gluconeogenesis from amino acids, and for unidentified energy losses or gains are shown in Eq. 124. to Eq. 126. Eq. 124. sets the a posteriori estimation of the correction factor for de novo lipogenesis of day k equal to the a priori estimation of the correction factor for de novo lipogenesis of day k+1. Eq. 125. sets the a posteriori estimation of the correction factor for gluconeogenesis of day k equal to the a priori estimation of the correction factor for gluconeogenesis of day k+1. Eq. 126. sets the a posteriori estimation of the correction factor for unidentified energy losses or gains of day k equal to the a priori estimation of the correction factor for unidentified energy losses or gains of day k+1. The measurement equations for the correction factors for de novo lipogenesis, gluconeogenesis from amino acids, and for unidentified energy losses or gains are calculated as in Eq. 127. to Eq. 129. The a posteriori estimation of the correction factors for de novo lipogenesis, gluconeogenesis from amino acids, and for unidentified energy losses or gains is performed using the Kalman filter as in Eq. 130. to Eq. 132. The Kalman gains are calculated as a scalar problem as in Grewal, (Grewal M. S. and A. P. Andrews. Kalman Filtering: Theory and Practice Using MATLAB. John Wiley & Sons, New Jersey. Third Ed.; September 2011, pp. 140). The algorithm continues at23.

The algorithm branches off at decision point23.

If no calibrations are desired than the process continues at decision point26.

If this is a calibration day j with known ingested carbohydrate, fat, and protein calories; a known calibration value for body composition vector; and a trajectory calculation for body composition vector changes is desired, then a smoothing procedure of the indirectly calculated body composition vector change is performed and the process continues at24. I prefer optimal smoothers (Grewal M. S. and A. P. Andrews. Kalman Filtering: Theory and Practice Using MATLAB. John Wiley & Sons, New Jersey. Third Ed.; September 2011, pp. 183.). The process continues at25.

At process25, the trajectory calculation is performed. My first embodiment uses the smoothed values of the indirectly measured body composition vector. The time interval for the trajectory is day i, which is the day of the previous calibration, to day j, which is the day of the last calibration. The constraint is that the trajectory starts with a calibration value of day i and ends with a calibration value of day j for the body composition vector. Eq. 133. calculates the trajectory of the body composition vector from day i to day j using the results of the smoothing algorithm. Alternative methods of trajectory creation include using mathematical methods (Venkataraman, P. Applied Optimization with MATLAB Programming. March 2009; John Wiley & Sons, pp. 490) which express the function of the trajectory as a parametric curve. Eq. 134. calculates the trajectory of the body composition vector from day i to day j using a polynomial spline function. Eq. 135. calculates the trajectory of the body composition vector from day i to day j using a B spline function. Eq. 136. calculates the trajectory of the body composition vector from day i to day j using a Bezier function. The algorithm continues at26.

The algorithm branches off at decision point26.

If no calibrations for the adjustable coefficients to calculate extracellular water and intracellular water masses are needed, then the process continues at29.

If a calibration procedure for the adjustable coefficients to calculate extracellular water and intracellular water masses is needed, then the process continues at27and reference values are generated first. The reference value for extracellular water mass on calibration day j is obtained from tabled values (Silva, DOI:10.1088/0967-3334/28/5/004) as shown in Eq. 137., where the values are dependent on weight, height, age, sex and race. The reference value for intracellular water mass on calibration day j is calculated in Eq. 140. (Jaffrin, DOI: 10.1016/j.medengphy.2008.06.009). The formula requires the body weight and the reference value for fat mass on calibration day j. The reference value for fat mass on calibration day j is obtained from the anthropomorphic determination of body fat as in Lean, (Lean, et al. Predicting body composition vector by densitometry from simple anthropometric measurements. American Journal of Clinical Nutrition, January 1996; 63(1):4-14.), as in Eq. 138. for men and Eq. 139. for women. Eq. 141. calculates the reference value for the lean body mass.

The calibration process proceeds to28, where the adjustable coefficients to calculate extracellular water and intracellular water masses are estimated. Eq. 142. sets the a posteriori estimation of the adjustable coefficient to calculate extracellular water on calibration day i equal to the a priori estimation of the adjustable coefficient to calculate extracellular water on day j. Eq. 143. sets the a posteriori estimation of the adjustable coefficient to calculate intracellular water on calibration day i equal to a priori estimation of the adjustable coefficient to calculate intracellular water on day j. The measurement equations for the adjustable coefficients to calculate extracellular water and intracellular water masses are calculated as in Eq. 144. to Eq. 145. The a posteriori estimation of the adjustable coefficients to calculate extracellular water and intracellular water masses is performed using the Kalman filter as in Eq. 146. and Eq. 147. The Kalman gains are calculated as a scalar problem as in Grewal, (Grewal M. S. and A. P. Andrews. Kalman Filtering: Theory and Practice Using MATLAB. John Wiley & Sons, New Jersey. Third Ed.; September 2011, 140 pp.). The algorithm continues at29.

The algorithm branches off at decision point29. If no measurement of the body composition vector and daily change in body composition vector is needed, then the process continues at decision point31.

If measurement of the body composition vector and daily change in body composition vector is needed, then these can be calculated at process30. Eq. 148. calculates the extracellular water mass from the resistance extrapolated at zero frequency. Eq. 149. calculates the intracellular water mass from the resistance extrapolated at infinite frequency. The lean body mass is calculated with Eq. 150. (Jaffrin, DOI: 10.1016/j.medengphy.2008.06.009). The body fat mass is obtained by subtracting the lean body mass from body weight as in Eq. 151. The lean body change from one day to the next day is obtained by subtracting the previous day's lean body mass from the next day's lean body mass as in Eq. 152. The daily fat mass change is obtained by subtracting the daily change of lean body mass from the daily body weight change as in Eq. 153. The algorithm continues at31.

The algorithm branches off at decision point31. If no calibration procedure for the adjustable dynamic coefficients to calculate extracellular water and intracellular water mass changes is needed, then the process continues at decision point33.

If a calibration procedure for the adjustable dynamic coefficients to calculate extracellular water and intracellular water mass changes is needed, then the process continues at32.

At process32, I perform a calibration procedure for the adjustable dynamic coefficients to calculate extracellular water mass and intracellular water mass changes. In calculating dynamic changes of extracellular water and intracellular water, I take advantage of the observation that the ratio of the extracellular and total body water is tightly regulated in normal physiology (Ellis K J, Wong W W (1998) Human hydrometry: comparison of multifrequency bioelectrical impedance with2H2O and bromine dilution. J Appl Physiol 85(3): 1056-1062.). The ratio can be calculate using reference values on day j. The ratio of the extracellular and total body water is determined from reference extra cellular water and intracellular water mass as in Eq. 154.

For the calibration of the acute change of extracellular and intracellular water mass, a known change of the total water mass is needed in a relatively short period of time so as not to affect the body composition vector change. Vigorous perspiration or rapid hydration with fluid can be such a sentinel event when the body loses or gains a measurable weight in a short period of time without any significant change of the body composition. The ensuing body weight change, and equivalently, the total body water change from the beginning to the end of the sentinel event causes the hydration change. The indirectly calculated extracellular water change for this scenario can be calculated as in Eq. 155. Eq. 155. requires the knowledge of the total water change of the body which can be obtained by measuring the weight before and after a sentinel event and calculating the difference. The ensuing change of the intracellular water is calculated in Eq. 156. Eq. 157. sets the a posteriori estimation of the adjustable dynamic coefficient to calculate extracellular water on calibration day i equal to the a priori estimation of the adjustable dynamic coefficient to calculate extracellular water on day j. Eq. 158. sets the a posteriori estimation of the adjustable dynamic coefficient to calculate intracellular water on calibration day i equal to the a priori estimation of the adjustable dynamic coefficient to calculate intracellular water on day j. The measurement equations for the adjustable dynamic coefficients to calculate extracellular and intracellular water masses are calculated in Eq. 159. to Eq. 160. The a posteriori estimation of the adjustable dynamic coefficients to calculate extracellular and intracellular water masses is performed using the Kalman filter in Eq. 161. and Eq. 162. and the Kalman gains are calculated as a scalar problem as in Grewal, (Grewal M. S. and A. P. Andrews. Kalman Filtering: Theory and Practice Using MATLAB. John Wiley & Sons, New Jersey. Third Ed.; September 2011, page 140). The algorithm continues at decision point33.

The algorithm branches off at decision point33. If no measurement of acute change of hydration status is needed, then the process continues at decision point35.

If measurement for acute change of hydration status is needed, then the process continues at34. Eq. 163. calculates dynamic changes of extracellular water indirectly from resistance value changes before and after the acute event causing hydration status change using the resistance extrapolated at zero frequency before and after a sentinel event of hydration status change. Eq. 164. calculates dynamic changes of intracellular water indirectly from resistance value changes before and after the acute event causing hydration status change using the resistance extrapolated at infinite frequency before and after a sentinel event of hydration change. The process continues at decision point35.

The algorithm branches off at decision point35.

If no calibration procedure for the estimation of the time varying constant energy expenditure is needed, the process continues at37.

If a calibration procedure for the estimation of the time varying constant energy expenditure is needed, then the process continues at36. Eq. 165. sets the a posteriori estimation of the time varying constant energy expenditure of the previous calibration day i equal to the a priori estimation of the time varying constant energy expenditure of the last calibration day j. The measurement equation for the time-varying constant energy expenditure for calibration day j is calculated as in Eq. 166. In this equation, the components of the indirectly calculated body composition vector change are entered, taken from the day before the calibration day j. Next, the a posteriori estimation of the time-varying constant energy expenditure is performed using the Kalman filter as in Eq. 167., and the Kalman gains are calculated as a scalar problem as in Grewal, (Grewal M. S. and A. P. Andrews. Kalman Filtering: Theory and Practice Using MATLAB. John Wiley & Sons, New Jersey. Third Ed.; September 2011, page 140). The process continues at decision point37.

At decision point37, if no calibration procedure for the basal gluconeogenesis rate is needed, the process continues at process38. If a new value for the basal gluconeogenesis rate after previous calibration on day j is available than an estimated gluconeogenesis from protein on day k with calibration can be calculated as in Eq. 170. by multiplying the new value for the basal gluconeogenesis rate after calibration on day j with the estimation of the correction factor for gluconeogenesis from amino acids on day k and the gluconeogenesis from protein on day k and dividing the result with the old basal gluconeogenesis rate before calibration. The process continues at decision point40.

At decision point37, if a calibration procedure for the basal gluconeogenesis rate is needed, then the process continues at39. For this calibration procedure the measured nitrogen excretion on calibration day j is required. Eq. 168. calculates the indirectly measured correction factor for gluconeogenesis from amino acids on calibration day j by evaluating a ratio with the numerator being the product of six point twenty-five multiplied with the energy density of protein and multiplied with the measured nitrogen excretion on calibration day j minus the calculated rate of protein oxidation rate on day j, divided by the gluconeogenesis from protein on day j. The indirectly measured correction factor for gluconeogenesis from amino acids on calibration day j could be used for the process equation Eq. 125. allowing for calibrated estimation of the gluconeogenesis from protein. Eq. 169. calculates the new value for the basal gluconeogenesis rate after previous calibration on day j by adding up the product of six point twenty-five multiplied with the energy density of protein, and multiplied with the measured nitrogen excretion on calibration day j minus the calculated rate of protein oxidation rate on day j. The process continues at decision point40.

At decision point40, if no calibration procedure for baseline lipolysis rate is needed, then the process continues at41. If a new value for the baseline lipolysis rate after previous calibration on day j is available than an estimated rate of endogenous lipolysis on day k with calibration can be calculated as in Eq. 173. by multiplying the new value for the baseline lipolysis rate after calibration on day j with the estimation of the correction factor for de novo lipogenesis on day k and the rate of endogenous lipolysis on day k and dividing the result by the old baseline lipolysis rate before calibration. The process continues at decision point43.

At decision point40, if a calibration procedure for baseline lipolysis rate is needed, then the process continues at42. For the calibration procedure, the measured rate of endogenous lipolysis on calibration day j is required. Eq. 171. calculates the indirectly measured correction factor for de novo lipogenesis on calibration day j by calculating the ratio of the baseline lipolysis rate before calibration and the measured rate of endogenous lipolysis on calibration day j. The indirectly measured correction factor for de novo lipogenesis on calibration day j could be used for the process equation Eq. 124. allowing for calibrated estimation of the rate of endogenous lipolysis. Eq. 172. calculates the new value for the baseline lipolysis rate after previous calibration on day j by equating it with the measured rate of endogenous lipolysis on calibration day j. The process continues at decision point43.

At process43, preparations are made to proceed with calculations for the next day. Eq. 173. increases the index variable for day k by one. Eq. 174. calculates the time-varying constant energy expenditure on day k+1.

At process44, the entire calculation for the next day can be performed by proceeding from 44 to 2.

CONCLUSION, RAMIFICATIONS, AND SCOPE

Thus, the reader will see that at least one embodiment of the apparatus and method for the analysis of the change of body composition and hydration status and for dynamic indirect individualized measurement of components of the human energy metabolism provides several advantages. The advantages of the apparatus are that it:a. measures and corrects for stray capacitances,b. minimizes input noise and reduces capacitances of connecting cables,c. measures and eliminates offset voltage at six measuring points and reduces noise by hardware and software means at six measuring points,d. provides high output resistance and low output reactance of the current sources,e. minimizes noise due to analog-digital conversion,f. provides information on performance and reliability of measurements, andg. provides individualized measurements of the extracellular and intracellular water mass and fat and lean body mass.

The advantages of dynamic indirect individualized measurement are that it:a. provides individualized self correcting and self adaptive modeling of the human energy metabolism,b. provides real time calculation of components of the human energy metabolism,c. allows for inverse calculations and for inferring unknown input data from output results,d. allows for real time calculations in a freely moving human subject with the need for measurements only in 24 hour increments,e. allows for dynamic serial measurements of the body composition change where the metabolic model is fitted to the measured data and by using error measurements of the model which becomes individualized and self adaptive,f. allows for calculating the macronutrient oxidation rates,g. allows for estimation of the utilized macronutrient intake,h. allows for detecting the unknown part of the energy metabolism and the error of metabolic model estimations, andi. allows for identification of parameters of lipid degradation and gluconeogenesis from protein.

While my above description contains many specificities, these should not be construed as limitations on the scope, but rather as an illustration of one presently preferred embodiment. For example, the apparatus can:a. have a multiplicity of measuring circuits to allow segmental measurements of the parts of the human body,b. take measurements continuously rather than just daily or intermittently.c. accommodate complex lumped network models of the human body consisting of a multitude of resistances, capacitances, and inductances,d. obtain measurements at a higher frequency than 1 megahertz,e. measure the capacitances of the excitation electrodes and sensory electrodes, andf. measure frequency dependent characteristics of the human tissue.

Further, the dynamic indirect individualized measurement method can, for example, be extended to measure dynamically:a. the de novo lipogenesis,b. the glycerol 3-phosphate synthesis,c. the gluconeogenesis from glycerol,d. synthesis or burning of visceral fat and other segmental fat masses of a body segment,e. building or wasting of segmental muscle masses of a body segment,f. the total energy expenditure, andg. the physical activity energy expenditure.

Accordingly, the scope should be determined not by the embodiment illustrated, but by the appended claims and their legal equivalents.