Real-time and continuous determination of excess post-exercise oxygen consumption and the estimation of blood lactate

Abstract

The current invention pertains to an apparatus and method for the determination of excess post-exercise oxygen consumption (EPOC) and the estimation of blood lactate levels. While these exercise parameters are traditionally determined using indirect calorimetry and blood sampling, this invention provides a method for the determination of these parameters using heart rate data. A wearable photoplethysmography device for measuring heart rate is included as an exemplary embodiment, however, the method of the current inventions can also be used with heart rate data from any heart rate monitor. In an embodiment of the present invention a supply demand differential equation is used to continuously monitor EPOC in real-time. Furthermore, blood lactate levels can also be estimated as a function of EPOC. Importantly, the process of determining EPOC and blood lactate can be linked to a biomathematical model of human physiology to access additional parameters such as hormonal changes, body composition changes or other physiological fluctuations or transient physiological behavior.

Claims

1. A method for determining excess post-exercise oxygen consumption (EPOC) and an estimated blood lactate level of an individual, the method comprising: (a) capturing PPG light absorbance data from at least one optical sensor in contact with skin of the individual, wherein the at least one optical sensor is within a wearable device; (b) transforming the PPG light absorbance data, via a processor of the wearable device, into raw physiological signals of the individual; (c) determining, via the processor, physiological parameters of the individual from the raw physiological signals, including: i. a continuous heart rate (HR), determined HR, HR.sub.max, and HR.sub.rest; ii. HR.sub.reserve which is the difference between the individual's HR.sub.max and HR.sub.rest; iii. oxygen consumption (VO.sub.2), VO.sub.2max and VO.sub.2rest; iv. VO.sub.2reserve which is the difference between the individual's VO.sub.2max and VO.sub.2rest; and v. exercise intensity; (d) applying a supply-demand differential equation to at least one of the determined physiological parameters to determine the EPOC; (e) calculating the estimated blood lactate level as a function of the EPOC; (f) transmitting the determined EPOC and the estimated blood lactate level to a mobile computing device, a cloud-based platform, or a personal computer; and (g) incorporating a biomathematical model of human physiology to calculate additional parameters from the determined EPOC and the estimated blood lactate level, wherein the biomathematical model comprises biomathematical models of metabolism, body composition change, hormonal changes or any other biomathematical model that describes a physiological process.

2. The method of claim 1, wherein the percentage VO.sub.2max and the exercise intensity are calculated as a function of the relationship between the HR.sub.reserve and the VO.sub.2reserve.

3. The method of claim 1, wherein the determined EPOC is determined by the following supply-demand differential equation, where a supply in reactions increases EPOC (ƒ.sub.supply), and a demand in reactions decreases EPOC (ƒ.sub.demand):
EPOC.sub.(t+1)=EPOC(t)+a*e.sup.b*.sup.v−c*e.sup.d*(1-v)*EPOC(t), wherein V is the Percentage VO.sub.2max, EPOC=0(initialized), a*e.sup.b*v is the ƒ.sub.supply, c*e.sup.d*(1-V) is the ƒ.sub.demand, a, b, c and d are empirically determined parameters, e is the base of the natural logarithm, and t is time.

4. The method of claim 1, wherein the estimated blood lactate level is calculated as a function of the determined EPOC by applying the following equation:
Estimated blood lactate level=lactate.sub.max*(dvar+EPOC), klactate+EPOC wherein lactate.sub.max is the maximal blood lactate achievable (approximately 25 mmol/L), klactate is an empirically derived parameter, and dvar is a parameter that ensures that, at EPOC=0, blood lactate is initialized at a non-zero value.

5. The method of claim 1, wherein the biomathematical model is a cloud-based biomathematical model.

6. The method of claim 1, wherein transmitting the determine EPOC and the estimated blood lactate level further comprises transmitting at least one of the following: the continuous HR data, the determined HR, the raw physiological signals, and the determined physiological parameters.

7. The method of claim 6, wherein at least one of the continuous HR data, the determined HR, the determined EPOC, the raw physiological signals, the determined physiological signals and the estimated blood lactate level is transmitted wirelessly to a platform to be stored, analyzed and viewed on client computing platforms, including a mobile computing device, a personal computer and a wearable electronic device.

8. The method of claim 1, further comprising acquiring accelerometer signals, wherein at least one of the physiological parameters is incorporated with data from the accelerometer signal to further generate the determined physiological parameters.

9. A system for determining excess post-exercise oxygen consumption (EPOC) and an estimated blood lactate level of an individual from a photoplethysmography (PPG) signal, the system comprising a server and a wearable device, the wearable device comprising: at least one optical sensor that collects PPG light absorbance data from the individual when in contact with skin of the individual; and a processor, the processor configured to: (a) acquire the PPG light absorbance data from the at least one optical sensor; (b) determine the individual's heart rate (HR) data, including determined HR, continuous HR, HR.sub.max, and HR.sub.rest from the PPG light absorbance data via the processor of the wearable device; (c) determine additional physiological parameters of the individual from the PPG light absorbance data including HR.sub.reserve which is the difference between the individual's HR.sub.max, HR.sub.rest, oxygen consumption (VO.sub.2), VO2.sub.max, VO2.sub.rest and VO2.sub.reserve which is the difference between the individual's VO2.sub.max and VO2.sub.rest; (d) calculate the individual's exercise intensity from the PPG light absorbance data, the HR, HR.sub.max, HR.sub.rest, or the additional physiological parameters; (e) apply a supply-demand differential equation to at least one of the physiological parameters to determine EPOC; (f) calculate the estimated blood lactate level as a function of the determined EPOC; and (g) transmit the determined EPOC and the estimated blood lactate level to the server, wherein the server is configured to incorporate a biomathematical model of human physiology to calculate additional parameters from the determined EPOC and the estimated blood lactate level, wherein the biomathematical model comprises biomathematical models of metabolism, body composition change, hormonal changes or any other biomathematical model that describes a physiological process.

10. The system of claim 9, wherein the percentage VO.sub.2max and exercise intensity are calculated as a function of the relationship between HR.sub.reserve and VO.sub.2reserve.

11. The system of claim 9, wherein the determined EPOC is determined by the following supply-demand differential equation, where a supply in reactions increases EPOC (ƒ.sub.supply), and a demand in reactions decreases EPOC (ƒ.sub.demand):
EPOC(.sub.t+i)=EPOC(t)+a*e.sup.b*V−c*e.sup.d*(1-V)*EPOC(t), wherein V is the Percentage VO.sub.2max, EPOC=0(initialized), a*e.sup.b*.sup.V is the ƒ.sub.supply, c*e.sup.d*.sup.(1-V) is the ƒ.sub.demand, a, b, c and d are empirically determined parameters, e is the base of the natural logarithm, and t is time.

12. The system of claim 9, wherein the blood lactate level is calculated as a function of the determined EPOC by applying the following equation:
Estimated blood lactate level=lactate.sub.max*(d.sub.var+EPOC) klactate+EPOC wherein lactate.sub.max is the maximal blood lactate achievable (approximately 25 mmol/L), klactate is an empirically derived parameter, dvar is a parameter that ensures that, at EPOC=0, and blood lactate is initialized at a non-zero value.

13. The system of claim 9, wherein the biomathematical model is a cloud-based biomathematical model that runs on the processor of the wearable device.

14. The system of claim 9, wherein the processor is further configured to transmit at least one of the continuous HR, the determined HR, the raw physiological signals, and the determined physiological signals.

15. The system of claim 14, wherein at least one of the continuous HR, the determined HR, the determined EPOC, the raw physiological signals, the determined physiological parameters and the estimated blood lactate level is transmitted wirelessly to a platform where it is stored, analyzed and viewed on at least one of the following client computing devices: a mobile computing device, a personal computer and a wearable electronic device.

16. A wearable device for determining excess post-exercise oxygen consumption (EPOC) and an estimated blood lactate level of an individual comprising: (a) at least one optical sensor in contact with the individual's skin, wherein the optical sensor is configured to capture PPG light absorbance data when in contact with the individual's skin; and (b) a processor, wherein the processor is configured to: (i) generate raw physiological signals from the PPG light absorbance data; (ii) determine the individual's heart rate from the raw physiological signals (iii) determine physiological parameters from the heart rate and the raw physiological signals, including HR.sub.reserve which is the difference between the individual's HR.sub.max and HR.sub.rest, and oxygen consumption (VO.sub.2) reserve, which is the difference between the individual's VO.sub.2max and VO.sub.2rest, (iv) calculate the individual's percentage VO.sub.2max and exercise intensity, (v) apply a supply-demand differential equation to at least one of the physiological parameters to determine EPOC from the determined heart rate and calculate the estimated blood lactate level of the individual as a function of EPOC, and (vi) incorporate a biomathematical model of human physiology to calculate additional parameters from the determined EPOC and the determined heart rate, wherein the biomathematical model comprises biomathematical models of metabolism, body composition change, hormonal changes or any other biomathematical model that describes a physiological process.

17. The device of claim 16, wherein the wearable device is further configured to obtain accelerometer data for the individual and the processor incorporates the accelerometer data with the PPG light absorbance data to generate the biomathematical model.

18. The device of claim 16, wherein at least one of the PPG light absorbance data, the determined physiological parameters, the determined heart rate, the determined EPOC and the estimated blood lactate level is transmitted to at least one of the following client computing devices where it can be stored, analyzed and viewed: a mobile computing device and a personal computer.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The preferred embodiments of the invention will be described by way of example only, with reference to the accompanying drawings:

(2) FIG. 1: Time plot of excess post-exercise oxygen consumption after exercise.

(3) FIG. 2: A basic embodiment of the apparatus of the invention in the context of mobile and internet technologies.

(4) FIG. 3: A schematic representation of the overall method of the current invention illustrated by a flow diagram.

(5) FIG. 4: (A) EPOC and (B) estimated blood lactate determined using the method of the current invention. Estimated blood lactate is compared to measured blood lactate levels.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

(6) The following detailed description and drawings describe different aspects of the current invention. The description and drawings serve to enable one skilled in the art to fully understand the current invention and are not intended to limit the scope of the invention in any manner. Before the present methods and systems are disclosed and described, it is to be understood that the methods and systems are not limited to special methods, special components, or to particular implementations. It is also to be understood that the terminology used herein is for the purpose of describing particular aspects only and is not intended to be limiting. As used in the specification and the appended claims, the word “comprise” and variations of the word, such as “comprising” and “comprises,” means “including but not limited to,” and is not intended to exclude, for example, other components or steps. “Exemplary” means “an example of” and is not intended to convey an indication of a preferred or ideal embodiment. “Such as” is not used in a restrictive sense, but for explanatory purposes. The singular forms “a,” “an,” and “the” also include plural elements unless the context clearly dictates otherwise. “Optional” or “optionally” means that the subsequently described event or circumstance may or may not occur and that the description includes instances where said event or circumstance occurs and instances where it does not.

(7) FIG. 1 depicts a time plot of oxygen consumption during and after a bout of strenuous exercise. Since EPOC is defined as a measurable increase in oxygen consumption following exercise, it is calculated by integrating the area underneath the curve after exercise (1) and subtracting the resting oxygen consumption (2) from this value. This method relies on the direct measurement of oxygen consumption and is the gold standard for measuring EPOC. The method of the current invention aims to circumvent this problem by providing a means for determining continuous, real-time EPOC as well as estimated blood lactate from heart rate data. The wearable PPG device of the current invention provides a means for collecting the heart rate data that is necessary to determine these exercise parameters.

(8) FIG. 2 depicts a basic embodiment of the invention where 3 is the wearable PPG device containing the necessary sensor and processor means to measure an absorbance signal and determine heart rate. The wearable device optionally contains a display (4) and is capable of transmitting data to a mobile device (5) and or directly to an internet based platform (6). The data can be stored and further processed on a server (7) for future retrieval and to be viewed on a computing platform exemplified by the personal computer (8), the mobile phone (5) and or wearable device (3). It should be appreciated that the EPOC and estimated blood lactate levels determined using the current invention can be linked to a biomathematical model (9) of human physiology (in a preferred embodiment this biomathematical model is cloud based but can also be run on a local processor) to access hormonal changes, body composition changes or other physiological fluctuations or transient physiological behavior. The above-mentioned biological models can be coupled to the supply-demand differential equation that is used to determine EPOC. In an embodiment of the current invention, PPG and accelerometer signals are input into a biomathematical model linked to the demand block of the supply-demand EPOC equation and this can provide additional information about the exact physiological load/work intensity or real-time VO.sub.2 demand of the subject. Incorporated herein in its entirety is the provisional patent application 62/068,882 which describes how real-time physiological load is determined from PPG and accelerometer data. This method assumes a mapping between measured activity and physiological energy demand. It is able to predict what the steady-state oxygen consumption is given a measure of activity level in conjunction with heart rate data. Similarly in another embodiment of the current invention, where one keeps in mind that EPOC is determined by integrating over time the difference between the supposed steady state oxygen consumption rate for a given physiological state (nearly always considered as rest after an exercise session in the literature) and the measured or inferred time varying oxygen consumption rate, it is possible to include biomathematical models to augment our estimate of either said steady state rate or said time varying rate to improve the accuracy of the EPOC calculation. Here the provisional patent application 62/068,882 is again a good example, showing how the steady state oxygen consumption rate can be estimated using easily accessible physiological signals.

(9) FIG. 3 depicts a flow diagram of an exemplary embodiment of the current invention. In the first step, the heart rate is determined (10), using the measured R-R intervals, frequency domain technique such as Fourier spectrum analysis or other means, and the relationship between the HR.sub.reserve(HR.sub.max−HR.sub.rest) and VO.sub.2reserve (VO.sub.2max−VO.sub.2rest) is computed. From this relationship, it is possible to determine the current oxygen consumption (VO.sub.2) (11) and therefore the Percentage VO.sub.2max (12) that the subject is currently performing at.

(10) The change in EPOC over time (13) is determined by a supply in reactions that increases EPOC and a demand in reactions that decreases EPOC. These reactions are conveniently incorporated into a supply (ƒ.sub.supply) and demand (ƒ.sub.demand) reaction block (equation 1). Percentage VO.sub.2max (V), whether directly measured or inferred from heart rate, is used to parameterize the supply block (ƒ.sub.supply) and V is also used, along with EPOC, to parameterize the demand block (ƒ.sub.demand). A non-abstracted version of equation 1 is presented in equation 2 where ƒ.sub.supply=a*e.sup.b*V and ƒ.sub.demand=EPOC*c*e.sup.d*(1-V). From the ƒ.sub.supply equation it is evident that, as V increases the ƒ.sub.supply reaction also increases. The parameters a and b (14) in the ƒ.sub.supply equation are empirically determined and e is the base of the natural logarithm. Also, from the ƒ.sub.demand equation it is evident that, as V increases the ƒ.sub.demand reaction decreases. In addition, the EPOC term in the ƒ.sub.demand equation simply indicates that, as EPOC increases, the ƒ.sub.demand reaction increases causing the change of EPOC (equation 2) to slow down. The parameters c and d (14) in the ƒ.sub.demand equation are empirically determined and e is the base of the natural logarithm. Equation 2, including both the ƒ.sub.supply and ƒ.sub.demand blocks, ensures that as an individual trains at a higher V the positive rate of change in EPOC also increases until a point of saturation is achieved. V can also denote percentage VO.sub.2reserve instead of percentage VO.sub.2max, but then the parameters a, b, c and d will be different when determined empirically.

(11) $\begin{array}{cc}\frac{\mathrm{dEPOC}}{\mathrm{dt}}=f_{\mathrm{supply}}\left(V\right)-f_{\mathrm{demand}}\left(V,\mathrm{EPOC}\right)& \left(1\right)\\ \frac{\mathrm{dEPOC}}{\mathrm{dt}}=a*e^{b*V}-c*e^{d*\left(1-V\right)}*\mathrm{EPOC}& \left(2\right)\end{array}$

(12) Practically, EPOC is initialized at zero (equation 3). Subsequently EPOC at time t+1 is determined by adding the ƒ.sub.supply−ƒ.sub.demand value to EPOC at time t (15) (equation 4). Equation 5 shows a non-abstracted version of equation 4. The parameters a, b, c and d are the same as previously described.
EPOC=0  (3)
EPOC.sub.(t+1)=EPOC(t)+ƒ.sub.supply−ƒ.sub.demand  (4)
EPOC.sub.(t+1)=EPOC(t)+a*e.sup.b*V−c*e.sup.d*(1-V)*EPOC(t)  (5)

(13) Even though there is no clear causal association between lactate metabolism and elevated oxygen uptake, post-exercise oxygen can be used to estimate blood lactate (16). lactate.sub.max (17) is the maximal blood lactate achievable (approximately 25 mmol/l). klactate (18) is empirically derived and dvar (19) is a parameter that ensures that, at EPOC=0, blood lactate is initialized at a non zero value (resting blood lactate value).

(14) $\begin{array}{cc}\mathrm{Estimated}\mathrm{blood}\mathrm{lactate}=\frac{{\mathrm{lactate}}_{\max }*\left(\mathrm{dvar}+\mathrm{EPOC}\right)}{\mathrm{klactate}+\mathrm{EPOC}}& \left(6\right)\end{array}$

(15) FIG. 4A depicts an exemplary embodiment of a plot of EPOC (L) (20) over time (seconds) generated using heart rate data from a wearable PPG sensor and the method of the current invention. The data was collected from a subject who was performing a VO.sub.2max test and therefore the EPOC value rises to approximately 10 L after 20 minutes (1200 seconds).

(16) FIG. 4B depicts an exemplary embodiment of a plot comparing measured (21) and estimated (22) blood lactate over time using the method of the current invention. Blood lactate is measured in mmol/L.