Method and apparatus for determining a smoothed data point within a stream of data points

Abstract

A method and an apparatus for determining at least one smoothed data point (t.sub.k, s.sub.k) within a stream of data points {t.sub.i, s.sub.i} with 1≤i≤z, k<z is disclosed. Herein, the stream of data points {t.sub.i, s.sub.i} is consecutively acquired in a manner that a data point (t.sub.i, s.sub.i) is acquired after an acquisition of a preceding data point (t.sub.i−1, s.sub.i−1), wherein each data point (t.sub.i, s.sub.i) comprises a valid value or an invalid value or a missing value for the signal s.sub.i at a time t.sub.i. Herein, the signal s.sub.i at the time t.sub.i comprises physical, chemical, biological, environmental, and/or technical data acquired by means of a technical set-up. According to the method, a set of data points is provided, wherein for each smoothed data point (t.sub.k, s.sub.k) a smoothing set is created. For each smoothed data point (t.sub.k, s.sub.k), trailing data resulting from large gaps are removed until it is verified whether the smoothing set comprises a minimal number of data points. Thereafter, for each smoothed data point (t.sub.k, s.sub.k) an initial slope set is calculated, on which at least one exponential smoothing is applied, in which cause an at least once modified slope set is determined. By integrating the at least once modified slope set, a value for the smoothed data point (t.sub.k, s.sub.k) is determined and returned. The method provides a good degree of smoothing without introducing any lag time and with minimal distortions, and is capable of reporting derivatives for the set of smoothed data points at the same time. The method is particularly suited in real-time or nearly real-time measurements which may comprise large gaps within the stream of data points.

Claims

1. A method for glucose monitoring and treatment of a patient using a glucose monitoring apparatus, the method comprising: capturing a stream of data points by a glucose monitor sensor of the glucose monitoring apparatus, wherein the stream of data points is based on a signal related to a glucose concentration of a body fluid of the patient; receiving, by a processor of the glucose monitoring apparatus, a set of data points selected from the stream of data points; generating, by the processor, a smoothing set for each data point of the set of data points to be smoothed; verifying, by the processor, whether a first condition has been fulfilled for each data point of the set of data points to be smoothed, wherein the first condition requires that in each pair of adjacent first and second data points of the smoothing set, a difference in measurement time between the adjacent first and second data points does not exceed a predefined gap length threshold; removing, by the processor, each second data point that does not fulfill the first condition; verifying, by the processor, whether a second condition has been fulfilled for each data point of the set of data points to be smoothed, wherein the second condition requires that at least a threshold number of data points remain after removal of each second data point that does not fulfill the first condition; calculating, by the processor, a slope set corresponding to the smoothing set for each data point to be smoothed in response to determining that the second condition has been fulfilled; applying, by the processor, at least one exponential smoothing to the slope set to generate an at least once modified slope set for each data point to be smoothed; determining, by the processor, a corresponding smoothed value for each data point to be smoothed by integrating the at least once modified slope set for each data point to be smoothed; and treating the patient based on the corresponding smoothed value for each data point to be smoothed.

2. The method of claim 1, wherein the signal comprises a measured amplitude of at least one of a voltage or current related to the glucose concentration of the body fluid.

3. The method of claim 1, wherein applying the at least one exponential smoothing to the slope set comprises performing a first forward exponential smoothing to the slope set based on a first weight.

4. The method of claim 3, wherein applying the at least one exponential smoothing to the slope set further comprises performing a reverse exponential smoothing to the slope set based on a second weight in response to performing the first forward exponential smoothing.

5. The method of claim 4, wherein applying the at least one exponential smoothing to the slope set further comprises performing a second forward exponential smoothing to the slope set based on a third weight in response to performing the reverse exponential smoothing.

6. The method of claim 1, wherein receiving the set of data points selected from the stream of data points comprises receiving the set of data points in real time relative to capturing the stream of data points by the glucose monitor sensor.

7. The method of claim 1, wherein receiving the set of data points selected from the stream of data points comprises wirelessly receiving at least one of the signal or the stream of data points from the glucose monitoring sensor.

8. The method of claim 1, wherein the glucose monitoring sensor comprises an optical sensor.

9. The method of claim 1, wherein the body fluid comprises an interstitial fluid of the patient.

10. A glucose monitoring apparatus, comprising: a glucose monitoring sensor configured to capture a stream of data points, wherein the stream of data points is based on a signal related to a glucose concentration of a body fluid of the patient; a processor; and a memory comprising a plurality of instructions stored thereon that, in response to execution by the processor, causes the processor to: receive a set of data points selected from the stream of data points; generate a smoothing set for each data point of the set of data points to be smoothed; verify whether a first condition has been fulfilled for each data point of the set of data points to be smoothed, wherein the first condition requires that in each pair of adjacent first and second data points of the smoothing set, a difference in measurement time between the adjacent first and second data points does not exceed a predefined gap length threshold; remove each second data point that does not fulfill the first condition; verify whether a second condition has been fulfilled for each data point of the set of data points to be smoothed, wherein the second condition requires that at least a threshold number of data points remain after removal of each second data point that does not fulfill the first condition; calculate a slope set corresponding to the smoothing set for each data point to be smoothed in response to determining that the second condition has been fulfilled; apply at least one exponential smoothing to the slope set to generate an at least once modified slope set for each data point to be smoothed; and determine a corresponding smoothed value for each data point to be smoothed by integrating the at least once modified slope set for each data point to be smoothed, wherein the corresponding smoothed value is associated with treatment of the patient.

11. The glucose monitoring apparatus of claim 10, further comprising: a first part including the glucose monitoring sensor; and a second part including the processor and physically separated from the first part.

12. The glucose monitoring apparatus of claim 11, wherein processor is configured to wirelessly receive at least one of the signal or the stream of data points from the glucose monitoring sensor.

13. The glucose monitoring apparatus of claim 10, wherein the glucose monitoring sensor comprises a fluorescence sensor.

14. The glucose monitoring apparatus of claim 10, wherein the body fluid comprises an interstitial fluid of the patient.

15. The glucose monitoring apparatus of claim 10, wherein the signal comprises a measured amplitude of at least one of a voltage or current related to the glucose concentration of the body fluid.

16. The glucose monitoring apparatus of claim 10, wherein to apply the at least one exponential smoothing to the slope set comprises to perform a first forward exponential smoothing to the slope set based on a first weight.

17. The glucose monitoring apparatus of claim 16, wherein to apply the at least one exponential smoothing to the slope set further comprises to: perform a reverse exponential smoothing to the slope set based on a second weight in response to the first forward exponential smoothing; and perform a second forward exponential smoothing to the slope set based on a third weight in response to the reverse exponential smoothing.

18. One or more non-transitory machine-readable storage media comprising a plurality of instructions stored thereon that, in response to execution by a processor, causes the processor to: instruct a glucose monitoring sensor to capture a stream of data points, wherein the stream of data points is based on a signal related to a glucose concentration of a body fluid of a patient; receive a set of data points selected from the stream of data points; generate a smoothing set for each data point of the set of data points to be smoothed; verify whether a first condition has been fulfilled for each data point of the set of data points to be smoothed, wherein the first condition requires that in each pair of adjacent first and second data points of the smoothing set, a difference in measurement time between the adjacent first and second data points does not exceed a predefined gap length threshold; remove each second data point that does not fulfill the first condition; verify whether a second condition has been fulfilled for each data point of the set of data points to be smoothed, wherein the second condition requires that at least a threshold number of data points remain after removal of each second data point that does not fulfill the first condition; calculate a slope set corresponding to the smoothing set for each data point to be smoothed in response to determining that the second condition has been fulfilled; apply at least one exponential smoothing to the slope set to generate an at least once modified slope set for each data point to be smoothed; and determine a corresponding smoothed value for each data point to be smoothed by integrating the at least once modified slope set for each data point to be smoothed, wherein the corresponding smoothed value is associated with treatment of the patient.

19. The one or more non-transitory machine-readable storage media of claim 18, wherein the signal comprises a measured amplitude of at least one of a voltage or current related to the glucose concentration of the body fluid.

20. The one or more non-transitory machine-readable storage media of claim 18, wherein to apply the at least one exponential smoothing to the slope set comprises to: perform a first forward exponential smoothing to the slope set based on a first weight; perform a reverse exponential smoothing to the slope set based on a second weight in response to the first forward exponential smoothing; and perform a second forward exponential smoothing to the slope set based on a third weight in response to the reverse exponential smoothing.

Description

SHORT DESCRIPTION OF THE FIGURES

(1) Further optional features and embodiments of the invention will be disclosed in more detail in the subsequent description of preferred embodiments, preferably in conjunction with the dependent claims. Therein, the respective optional features may be realized in an isolated fashion as well as in any arbitrary feasible combination, as the skilled person will realize. The scope of the invention is not restricted by the preferred embodiments. The embodiments are schematically depicted in the Figures. Therein, identical reference numbers in these Figures refer to identical or functionally comparable elements.

(2) In the Figures:

(3) FIG. 1 presents a schematic overview over a preferred embodiment according to the method for determining at least one smoothed data point within a stream of data points;

(4) FIGS. 2A-B show a comparison for a stream of data points with a gap of 25 data points (FIG. 2A), and a gap of 42 data points (FIG. 2B), respectively, as presented in a first set of original raw data points, in a second and a third set of data points which are smoothed according to methods known from the state of the art, and in a fourth set of data points which are smoothed according to the present method; and

(5) FIGS. 3A-B schematically depict two different embodiments (FIGS. 3A and 3B) of an apparatus for determining at least one smoothed data point within a stream of data points.

DETAILED DESCRIPTION OF THE EMBODIMENTS

(6) FIG. 1 presents a schematic overview over a preferred embodiment according to the method for determining at least one smoothed data point (t.sub.k, s.sub.k) within a stream of data points {t.sub.i, s.sub.i} 110 with 1≤i≤z, k<z, wherein i, z, and k are integers. Herein, a signal s.sub.i at a time t.sub.i 112 comprises physical, chemical, biological, environmental, and/or technical data acquired by means of a technical set-up. Within this regard, the stream of data points 110 may be consecutively acquired over the time 112 in a manner that a previous data point may be recorded at an earlier time 114 whereas the latest data point 116 may be reported near the actual reporting time 112. By going back in time from the latest data point 116 by a number of points equal to Smoothing Window 118, a smoothing set 120 may be created. Hereby, an offset 119, which describes the difference between the latest data point 116 and the actual reporting time 112, occurs. In a subsequent verifying step 122, data points which comprise an invalid value or a missing value may be removed from the smoothing set 120. The method as presented in FIG. 1 may comprise an additional condition 124 which may examine whether any data still exist in the offset 119 after having removed a number of data points from the smoothing set 120 during the verifying step 122. If the additional condition 124 is not fulfilled, no output will be available from the recorded stream of data points. In this case, a waiting step 126 may be introduced, where the further performance of the method may pause until a recording of the next data point may occur. As soon as the next data point may be available, the smoothing set 120 may be moved in a sliding step 128 to the right into a position where the latest data point 116 is located. From the latest data point 116 it may then be feasible to restart the method with creating a new smoothing set 120 from the accordingly adjusted Smoothing Window 118.

(7) On the other hand, if data exist in the offset 119 according to the additional condition 124, it may then be verified whether a first condition 130, which may examine whether there are large gaps within the smoothing set 120, may be fulfilled or not. If the first condition 130 is fulfilled, trailing data may be removed from the smoothing set 120. Subsequently, it may be examined whether a second condition 132, which may verify whether the smoothing set may be long enough for a further performing of the method according to the invention, may be fulfilled. If the second condition 132 may be not fulfilled, the same consequence as described above when no data did exist in the offset 118 may occur. Consequently a waiting step 126 may be performed in this case until the next data point may be available, on which event the sliding step 128 may be performed as described above.

(8) On the other hand, when the smoothing set may be examined by verifying the second condition 132 to be long enough, a first calculating step 134 may be performed, wherein the parameter orig mean within the smoothing set 120 is determined. Subsequently, in a second calculating step 136 an initial slope set may be calculated for the data points in the smoothing set 120, on which a first forward smoothing step 138 may be applied, followed by a reverse smoothing step 140, and, subsequently, by a second forward smoothing step 142. During the smoothing steps 138, 140, 142 the slope set may such be modified three times, wherein the finally modified slope set may be employed as an input for an integrating step 144, in which course a value for the smoothed data point is determined and returned in a determining and returning step 146.

(9) Having finished such a single performance with the latest data point 116 as input, the method may terminate. Alternatively, the method may continue with a subsequent pass as soon as the next data point may be available and the smoothing set may be moved to the right according to the sliding step 128 in order to cover the latest data point 116.

(10) In the following a number of specific embodiments will be described which may be selected due to a specific requirement with regard to the time series data.

(11) A first embodiment which could be designated as a “one-pass real-time smoothing”, therefore, employs the steps as presented in FIG. 1 and the respective description together with parameters which are selected from the range and/or values as given in Table 1.

(12) A second embodiment, which could be designated as a “two-pass real-time smoothing with data reduction” may be selected in a case where a better smoothing is required while reporting in real-time or nearly real-time is still needed. In this case, the method as presented schematically in FIG. 1 may be applied twice in the following manner. First, the method as presented in FIG. 1 may be applied in a first pass to the original data set with parameters taken from Table 1. Thereafter, only every p-th data point in the data set resulting from the determining and returning step 146 may be retained while discarding the rest of the data points, wherein a typical value for p may be selected to be equal to 3. Thereby, a reduced data set may be obtained. Then, the method as depicted in FIG. 1 may be applied in a second pass to the reduced data set, particularly with the same parameters as used in the first pass. Alternatively, it may be possible to employ differing parameters, either selected from Table 1 or not, for the second pass compared with the first pass.

(13) As a variation of the second embodiment, p data sets may be created from the original data set, wherein the first of these data sets may start with the data points 1, 1+p, 1+2p, . . . whereas the second data set may start with 2, 2+p, 2+2p, . . . etc. Thereafter, the method as presented in FIG. 1 is applied to each of the p data sets, by which p smoothed data sets may be obtained. Subsequently, the p smoothed data sets may be merged either without further processing, or, preferably, after applying calculating means of corresponding items within the p subsets. Hereby, the calculating means may be selected from arithmetic means, medians or other such calculations, which may be applied to the respective data points either in a direct manner, resulting in a reduced number of data points compared to the input data set, or in a sliding manner, resulting in the same number of data points compared to the input data set. In addition, data points may be eliminated according to any criterion before calculating means.

(14) In a third embodiment, which may be designated as a “real-time smoothing on a preprocessed reduced data set”, the method as shown in FIG. 1 may be applied to a reduced data set. The reduced data set may be prepared from the original data set by retaining only every p-th data point or by retaining items at such data points which are recorded at times t.sub.0, t.sub.0+r.Math.Δt, t.sub.0+2r.Math.Δt, . . . with 0<r, r being an integer. In case such a selected item turns out to be an invalid value or a missing value, an adjacent item, in particular wherein the adjacent item is at a distance of ±Δt or ±2.Math.Δt from the respective data point, may be selected. Hereby, a number of attempts for searching a valid data point backward and/or forward may be chosen appropriately as long as any point may not be used twice. Thereafter, the method which is depicted in FIG. 1 may be applied to the reduced data set with parameters selected from Table 1.

(15) A similar variation as applied to the second embodiment may mutatis mutandis be also applied to the third embodiment. In this manner, it may also be feasible within the third embodiment to create p data sets which are used as an input for the method according to FIG. 1, wherein the resulting smoothed data sets may be merged in one of the manners as described above.

(16) Whereas the first embodiment may provide a good smoothing on short time scales, it has been found that the method according to the second and/or the third embodiment may be particular useful for smoothing noise on longer times scales. Whereas the second embodiment may often provide a better smoothing compared to the method according to the third embodiment, the second embodiment may computationally be more demanding and requires more data points in the future. Consequently, the method according to the second embodiment may not return a smoothed data point as early as a data point which may have been smoothed by a method according to the third embodiment. The above specified variations to the second embodiment and/or to the third embodiment, however, may demand more computational time and effort and, therefore, may be only suitable in a case where an additional smoothing and/or a tight spacing of the data points over the time may be required.

(17) The variations of the second and third embodiment may particularly be advantageous when an output in form of a triple comprising the slope, (t.sub.k, s.sub.k, s.sub.k′) is desired. Hereby, the calculating means for merging the subset are particularly adapted to result in a smooth value for the slope s.sub.k′.

(18) As a practical example, the method according to the present invention has been applied on the data points which were acquired during a clinical study which comprised 20 sensors in a cohort of ten patients and up to six streams of data points per sensor. As a result, it could be proved that by an application of the method according to the present invention data are recorded that show less distortion and approximately equal noise compared to data acquired with a sliding average as used before. In addition, the present method allowed to calculate a slope of the signal and, thus, to provide the data in a manner that a numerical correction for deviations which are caused by glucose dynamics could be applied. Over the whole cohort, the methods according to the second embodiment and to the third embodiment have been compared with a nearly identical result. An important parameter adapted to compare such kinds of results is the “mean absolute relative deviation” (MARD) which describes deviations from a reference value being expressed in a percent value, whereby the absolute value is taken and the mean is calculated over one set of data, for example one data stream of the sensor. As an example, it has been found that in a typical experiment the MARD value decreases from a mean over the whole cohort from 14.6% to 13.6% by the application of the method according to the present invention. With streams of data points which particularly comprise a lot of noise, the improvement was often found to be much better.

(19) As an example, a reduction of the MARD value from 35% to 25% by the application of the method according to the invention could be observed in a particularly noisy data set. In addition to this statistical value which disregards any dynamics in the glucose values, less bias could be observed, particularly within dynamic regions.

(20) The method according to the present invention is particularly suited to deal with large gaps which may occur in the stream of data points. FIGS. 2A and 2B show two examples in which there are large gaps in the data stream. In FIG. 2A, a gap of 25 data points occurs, whereas in FIG. 2B even 42 data points exhibit a missing value. In both FIGS. 2A and 2B, the original raw data 148 as obtained from the sensor which may be located within the technical set-up are presented together with the smoothed data points, which are smoothed according to the state of the art either with a symmetric moving average 150 over 30 data points or with the so-called “reverse smoothing” method 152 according to Roark, as well as smoothed data points 154 returned by the method according to the present invention. A comparison between the sets of the smoothed data 150, 152 smoothed according to the state of the art and the set of smoothed data 154 smoothed according to the present invention shows that the method proposed here is far more capable of dealing with large gaps within the stream of data points than the “reverse smoothing” method 152, and comparable to the symmetric moving average 150 which requires 15 data points in the future. This feature is of particular importance in the case of real-time or nearly real-time acquisition and smoothing of data points.

(21) FIGS. 3A and 3B schematically display two embodiments of an apparatus 156 which is adapted to determining at least one smoothed data point within a stream of data points.

(22) According to the embodiment shown in FIG. 3A, the apparatus 156 comprises an instruction device 158 for instructing a sensor 160 to record a series of signals s.sub.i in a time t.sub.i and to deliver a stream of data points {t.sub.i, s.sub.i} with 1≤i≤z to a receiving and storing device 162 which is also comprised within the apparatus 156. The apparatus 156 further comprises a calculating device 164 which receives the stream of data points by means of a first connecting device 166 from the receiving and storing device 162, wherein the calculating device 164 is configured to determining the at least one smoothed data point (t.sub.k, s.sub.k) with k<z within the stream of data points, wherein the at least one smoothed data point (t.sub.k, s.sub.k) may be provided by an output 167 for any further purpose. Hereby, the instruction device 158 may comprise a sending device 168 which is configured for forwarding instructions wire-bound and/or wireless to the sensor 160, whereas the receiving and storing device 162 may comprise a receiving device 170 which is configured for receiving the stream of data points {t.sub.i, s.sub.i} wire-bound and/or wireless from the sensor 160. In this specific example as depicted in FIG. 3A, the sensor 160 does not form a constituent part of the apparatus 156. However, other embodiments may be feasible, in particular, wherein the sensor 160 may, nevertheless, constitute an integral part of the apparatus 156.

(23) FIG. 3B shows a particularly preferred embodiment, wherein the apparatus 156 may be mechanically and/or physically separated into a first part 172 and into a second part 174. Hereby, the instruction device 158 may together with the sensor 160 be located within the first part 172 of the apparatus 156, wherein the first part 172 of the apparatus 156 may, by way of example, be worn on or near the human body, where the sensor 160 may be applied. For this purpose, the instruction device 158 may comprise a wire-bound sending device 166 configured to forward instructions to the sensor 160, wherein the sensor 160 may comprise a wire-bound transfer device 176 configured for transferring data to the instruction device 158. This preferred arrangement may particularly allow to realize a preferred function which comprises that a data point (t.sub.i, s.sub.i) may be acquired prior to the end of a specific time interval Δt=(t.sub.i−t.sub.i−1), in particular in a case wherein the preceding data point (t.sub.i−1, s.sub.i−1) may comprise a value which is either invalid or missing. However, other types of connections between the instruction device 158 and the sensor 160 may also be possible.

(24) In addition, both the receiving and storing device 162 as well as the calculating device 164 may be located within the second part 174 of the apparatus 156 and may be coupled together, for example as a part of an ASIC, and, by way of example, may be carried by the user or may be left under supervision of a nursing staff. Hereby, it is particularly preferred when the calculating device 164 receives the stream of data points by {t.sub.i, s.sub.i} means of a first connecting device 166 from the receiving and storing device 162 and may, additionally, be configured for forwarding intermediate values to the receiving and storing device 162 by means of a second connecting device 178. Also in this embodiment, the calculating device 164 may be configured for providing the at least one smoothed data point (t.sub.k, s.sub.k) for any purpose via the output 167. In this preferred embodiment, the receiving and storing device 162 may comprise a wireless receiving device 170 which is configured for receiving the stream of data points from the sensor 160. However, other types of connections between the receiving and storing device 162 and the calculating device 164 may also be possible. In addition, the receiving and storing device 162 may also be realized as at least two separate entities which might communicate with each other by various possible ways.

LIST OF REFERENCE NUMBERS

(25) 110 stream of data points

(26) 112 recording time

(27) 114 earlier data point

(28) 116 latest data point

(29) 118 smoothing window

(30) 119 offset

(31) 120 smoothing set

(32) 122 verifying step

(33) 124 additional condition

(34) 126 waiting step

(35) 128 sliding step

(36) 130 first condition

(37) 132 second condition

(38) 134 first calculating step

(39) 136 second calculating step

(40) 138 first forward smoothing step

(41) 140 reverse smoothing step

(42) 142 second forward smoothing step

(43) 144 integrating step

(44) 146 determining and returning step

(45) 148 set of original raw data

(46) 150 symmetric moving average over 30 points (state of the art)

(47) 152 set of smoothed data according to Roark (state of the art)

(48) 154 set of smoothed data according to the present invention

(49) 156 apparatus

(50) 158 instruction device

(51) 160 sensor

(52) 162 receiving and storing device

(53) 164 calculating device

(54) 166 first connecting device

(55) 167 output

(56) 168 sending device

(57) 170 receiving device

(58) 172 first part of the apparatus

(59) 174 second part of the apparatus

(60) 176 transfer device

(61) 178 second connecting device