Detection of unreliable measurements in multi-sensor devices

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1 MeMeA 8 IEEE Iteratioal Workshop o Medical Measuremets ad Applicatios Ottawa, Otario, Caada - May 9-1, 8 Detectio of ureliable measuremets i multi-sesor devices Yedek Asfaw 1, Ady Adler yasfaw@site.uottawa.ca 1, adler@sce.carleto.ca 1 School of Iformatio Techology ad Egieerig (SITE), Uiversity Of Ottawa, Caada Systems ad Computer Egieerig (SCE), Carleto Uiversity, Ottawa, Caada Abstract Multi-sesor moitorig devices that use ski surface or implated sesors are susceptible to chages i temperature, sweat, ad movemet, such that the measured data caot be used. This paper presets a automatic approach to detect such erroeous sesors. It is based o the assumptio that valid measuremets are related by a recostructio model, while measuremets from erroeous sesors are urelated. The method estimates the data at each sesor based o the measuremets from all other sesors, ad compares it to the measuremets. The sesor-data match is tested usig ANOVA to detect the presece of a erroeous sesor. The method was tested o simulated ad experimetal data of Electrical Impedace Tomography (EIT) ad ECG data which showed cosistet idetificatio of erroeous electrodes. Keywords errors, sesors, recostructio algorithms I. INTRODUCTION Health care systems worldwide are uder pressure to deliver a better ad more efficiet service. Oe approach to help deliver such services is techology to eable home ad mobile care; several studies have show that such care improves the patiet's quality of life ad outcomes, while reducig cost [14, 15]. A key techological compoet required to eable such care is o-ivasive portable biomedical moitorig devices. Such techology eables cotiuous measuremet of parameters as heart ad lug activity, blood chemical cocetratios, ad blood pressure levels. While a growig market provides great icetive for the researchers ad compaies i the field, there are difficult challeges associated with desig of these devices. The moitorig devices typically use ski surface or implated sesors to measure the electrical ad optical properties of the body. These sesors are susceptible to chages i temperature, sweat, ad movemet with exercise ad breathig. For example, it has bee show that electrodes o the body surface give false readigs due to electroic iterferece [4], patiet movemet, or sweat ad peripheral edema [6], especially i log term moitorig applicatios [5]. For reliable moitorig of patiets, it is thus importat to detect sesor errors. Ufortuately, it appears that strategies to detect such errors are rarely published ad most strategies are largely heuristic measures to verify the goodess of data. Oe commo approach is detectio based o idetificatio of uusually large chages i the measuremets. The disadvatage is the difficulty of defiig a appropriate threshold for uusual measuremets that ca be applied across differet devices. I this work, we address this issue by proposig a algorithmic framework for detectio of ureliable measuremets ad erroeous sesors i multi-sesor devices for biomedical istrumetatio. This paper develops a approach based o explicitly modelig the sesor ad device characteristics ad usig the iterrelatioships to ascertai the goodess of measuremets. II. METHODS ALGORITHM This paper exteds the method developed i [1, ] for electrical impedace tomography (EIT) systems to calculate a measure of sesor reliability for geeral multi-sesor systems with ad without kow system model. It idetifies sesors subject to data errors or variability, ad calculates a measure of the reliability of each sesor's data. Essetially, the algorithm works by iversig the detectio criterio: rather tha lookig for errors, the approach looks for good data, defied by its cosistecy with other sesor measuremets ad prior models of sesor behavior. A. System Model We assume that the system model of a multi-sesor device may be liearized aroud a operatig poit, ad expressed as: z = Hx (1) where H is the liearized observatio of model, z is a vector represetatio of measuremets from all sesors, ad x is the vector of system model parameters. H is also kow as a Jacobea or Sesitivity matrix where it is expressed as a partial derivative of z with respect to x. z1 z1 L x 1 xm () H = M O M zm zm L x 1 xm Based o the system model, we calculate a recostructio model (iverse of the system model) expressed as: xˆ = Rz (3)

2 where R the recostructio model, ad xˆ is the estimate of the system model. The recostructio model (R) is determied by ivertig the system model equatio. If the system model fulfills Hadamard coditio [6], the R ca be determied through direct iversio. Otherwise, R ca be determied usig a regularizatio scheme, such as that of [1]. I a multi-sesor device the characteristics of the system model could either be kow or ukow, hece requirig differet approaches of determiig the observatio ad recostructio model. If the system model is kow the uderlyig priciple that defies H ad R is pre-determied. [1] shows a example of a kow system model i Electrical Impedace Tomography (EIT). EIT is a imagig techique which calculates the electrical coductivity distributio withi a medium from electrical measuremets made at a series of electrodes o the medium surface. The observatio model (equatio 4) defied through a geeralized relatioship betwee the backgroud coductivity (x) of the medium ad the measuremets at the boudary (z) ad is therefore cosidered to be kow. H ι,j z = x i j σ b =σ (4) x is the differece i coductivity of the medium: 1 x = σ σ (5) ad z is the ormalized differece i the voltage measuremets v1 i ad v i which represets the i th voltage measuremets at time t 1 ad t, respectively: z = 1 v i v (6) i Sice this system does ot fulfill the Hadamard coditio [6], R is determied through a regularizatio scheme as show i [1] to solve equatio. If the system model is ukow, H ad R ca oly be deduced by applyig geeralized techiques such as Priciple Compoet Aalysis (PCA) or Idepedet Compoet Aalysis (ICA) o the test data [9, 1]. Oe such example of a multi-sesor system with ukow system model is Electrocardiogram (ECG). The system uses multiple surface electrodes to moitor the heart activity of a patiet. The measured values from each sesor are orgaized as colum vectors i the matrix z. To eforce o-sigularity the matrix is multiplied by its traspose: D=z*z T (7) Applyig SVD to the square matrix D provides us the decompositio ito eigevectors ad eigevalues: D=UΣV T (8) where V is the eigevector ad Σ is colum matrix of the eigevalue, The top domiat eigevectors 1 3 v, v, v,..., v ( ) ca be used to simulate a observatio model (equatio 9). Therefore, the eigevectors ca be used to build the observatio model H, where each colum of H represets the eigevectors. 1 3 v1 v1 v1... v1 1 3 v v v... v (9) 1 3 H = v v v... v M M M M M 1 3 v v v... v The iverse of the system model, R, is determied through direct iversio: R=(H T H) -1 H T (1) B. Estimatio Scheme The estimatio scheme is based o the assumptio that a set of good sesors produces iterally cosistet data as discussed i [3]. Such cosistecy ca be verified by estimatig the measured data at each sesor i the set, usig oly measuremets o other sesors, ad the comparig the estimate to the actual data measured. The geeral procedure for the algorithm is outlied as follows: z Selector R (s i,s j ) z j E = z i ˆ, j j j Figure 1: Block Diagram of calculatio for estimatio error of E j. R(s i,s j) is the iverse of the system model without the cotributio from s i s j. Based o the estimate of system model parameters xˆ ad H j, the measuremet from sesor s j ca be recostructed. The differece betwee the real data ad the estimate provides us with a estimatio error. We iterate over each sesor s i i set A (cotaiig all sesors), formig a set A (all sesors ot icludig s i ). I a kow system model, the cosistecy of the data withi A is tested by removig s j ad estimatig its result based o data from all other remaiig sesors. The sum of the estimatio error (T i ) from all possible s j withi A gives a idicatio of the status of s i. Whe a erroeous sesor is removed, the data that remais will be i agreemet with the model. If the erroeous sesor is a part of the A set, the estimatio error for all sesors withi that specific A set will be high as the erroeous data would ot be i agreemet with the model. I devices with ukow system models, the system parameters, H ad R, are estimated for all possible set of sesors by excludig oe sesor at a time. I the presece of a erroeous sesor, the oise itroduced ito the system will domiate all other data comig from all other sesors. Hece, the eigevectors are good descriptors of the domiat data from the erroeous sesors. Cosequetially, a model that excludes the erroeous sesors has a high estimatio error xˆ z H j ẑ j ẑ j

3 ad a model that excludes the o-erroeous sesors results i a low estimatio error. Therefore, the cosistecy test is the sum of estimatio error (T i ) for sesor s i withi all possible A. This approach stems from the fact that H ad R are maily descriptors of the data ad more specifically the domiat oisy data. Therefore, the data fits the model oly whe the erroeous sesor is part of A. I either case, H j represets the rows of the sesitivity matrix H which correspod to measuremets o s j. xˆ is the calculated from xˆ =R(s i,s j )z, which excludes data from sesors s i ad s j. The estimate of z is determied usig equatio 1 ad the estimatio error (E i,j ) is determied for all possible sesor pairs s i ad s j. We have show that E i,j ca be efficietly calculated i kow system models by precomputig parameters which are idepedet of data [3]. C. Decisio Parameter If all values of sum of estimatio error (T i ) are low, the data set cotais all good sesors; otherwise it cotais at least oe erroeous sesor. T i values are tested agaist each other to detect if ay are sigificatly less tha the others. This is tested usig Aalysis of Variace (ANOVA) betwee E i of all sesors i set A. For kow system model, E i represets a list of estimatio errors from set A whe sesor s i is removed. For ukow system model, E i represets a list of estimatio errors for s i calculated from all sets A. Usig the statistical termiology, E i are referred to as Treatmets [8]. ANOVA is used to determie the statistical similarity betwee the E i s by testig the equality of N Treatmet meas (µ 1,µ,µ 3,,µ N ) [8]. The treatmet effect (τ i ) represets differece of a idividual measuremet from the overall mea (µ). The ull hypothesis (H ) i this case is that o sesors are erroeous, ad thus the treatmet effect (τ i ) is equal to zero for all s i i A. H : τ 1 = τ = τ 3 = = τ N = H 1 : τ i for at least oe i Uder the ull hypothesis, each Treatmet cosists of µ with a radom error compoet, with observatios take from the ormal distributio of µ with overall variace (σ ). I this case, the estimatio error values of A for each cadidate sesor (s i ) are similar to oe aother. The hypothesis is tested by comparig two idepedet estimates of the populatio variace: 1. Variace betwee µ i ad µ: (µ i -µ). Variace withi Treatmets: (E i -µ i ) The first variace determies the differece betwee Treatmets ad the secod variace determies the error withi each Treatmet. From the above two variaces, we calculate sum of squares of Treatmets variaces: SS T N = i = 1 µ i (11) ( µ ) ad sum of squares of error variace: N N SS E = ( E i, j µ i ) (1) i = 1 j = 1, j i By dividig SS T ad SS E by their respective degrees of freedom (N- ad ((N-1)N)-1), the mea square Treatmet (MS T ) ad mea square error (MS E ) are calculated. MS E is a ubiased estimate of the σ regardless of statistical differece betwee Treatmets. O the other had, MS T is a ubiased estimate of the variace oly if H is true. The ratio f =MS T / MS E has a F-distributio with degree of freedom N- ad (N-1)N-1. Hypothesis H is rejected if f > f α, N-, (N-1)N-1 [8]. Thus, usig ANOVA, we test if a data set has erroeous sesors, at sigificace level α=.5. However, we do ot kow the locatio ad umber of erroeous sesors. To accomplish this task, we use Fisher s Least Sigificat differece (LSD). LSD compares all pairs of meas with the t-statistic. The pairs of meas are cosidered sigificatly differet if µ i -µ j > LSD where, MS LSD = t E (13) α/,(n 1)N-1 A erroeous sesor will have mea that is sigificatly differet from others (p<.5). O the other had, a good sesor will be statistically similar to all other o-erroeous sesors. III. METHODS-EXPERIMENTAL The proposed algorithmic framework is to be applied for detectio of ureliable measuremets ad erroeous sesors i multi-sesor devices for biomedical istrumetatio. The Biomedical systems of EIT ad ECG are used as examples. A. EIT Data EIT data are acquired by successively applyig a low amplitude low frequecy curret across each pair of electrodes while measurig the voltage differeces produced o all the other pairs of electrodes. The measuremet system used for these experimets has 16 electrodes. I adjacet curret drive patter, two adjacet electrodes are used for curret ijectio ad the remaiig electrodes are used to make voltage measuremets. Overall, there are N (N-3) measuremets available whe all electrodes give good data. However, whe there is oe erroeous electrode, the total umber of measuremets available is reduced to (N-3) (N-4). Typically, with sixtee electrodes the remaiig good data are sufficiet to recostruct a reasoable image [].

4 B. ECG Data The system uses multiple surface electrodes to moitor the heart activity of a patiet. Cosiderig that these electrodes are moitorig the same medium, we would expect a relatioship betwee the source (heart muscles) ad sesors. A setup of the 1 lead ECG with 9 electrodes is used to acquire the data. There are 1 measuremets: V I, V II ad V III, av R, av L, av F, V 1, V, V 3, V 4, V 5 ad V 6. V I, V II ad V III ad av R, av L, av F are based o measuremets from Φ L, Φ R, ad Φ F. The remaiig 6 measuremets are from electrodes attached aroud the torso o the Trasverse plae. V ad av F measure activity alog the Sagittal plae. V I, V II ad V III, av R, av L, av F measure heart activity alog Frotal plae[11]. This shows that the electrodes measure the heart activity alog a specific plae ad the measuremets are iter-related to use the estimatio scheme. C. Simulated oise The oise i EIT ad ECG data is cosidered to be ostatioary sice the mea ad variace of the oise vary over time. However, the detectio is performed over a time differece t which is geerally treated statioary Gaussia. Therefore, simulated erroeous data is geerated usig represetative o-erroeous data ad additive Gaussia oise. The low level sigal of the differece measuremet is usually domiated by oise. Therefore, the sigal power is measured ad the additive oise data has relative magitude for each data poit. A simulated erroeous data is assumed to have oe faulty sesor ad Gaussia oise is added to data that is related to the faulty sesor. IV. RESULTS A. Electrical Impedace Tomography(EIT) EIT Data were acquired from a previous study i which mechaically vetilated mogrel dogs were moitored with sixtee EIT electrodes spaced evely aroud the shaved thorax [, 13]. A represetative set EIT data of vetilated dogs was used for data with o error (Figure A), ad simulated erroeous data from electrode 5 was geerated (Figure B). Applyig the Fisher F-Test based decisio parameter, we ca look up the critical value at 95% with degree of freedom N- ad (N-1)N-1. For this experimet the critical value correspods to f.5, 14, 39 =1.67. I Figure A the ratio f is equal to 1.47, which is less tha f.5, 14, 39 =1.67; ad H caot be reject at p<.5, ad we coclude there are o erroeous electrodes. I Figure B, the electrode with errors has sigificatly lower T i (p<.5). The ull hypothesis is rejected as the ratio f =.71 is sigificatly higher tha f.5, 14, 39. To determie the sesitivity of the method, white Gaussia oise was added to the data of a particular electrode from a represetative clea data. Data were calculated for SNR values from -5dB to 5dB, where simulatios are repeated 1 times to calculate the error distributio. The resultig F ratio vs. SNR graph idicates the method ca reliably detect a erroeous electrode whe the SNR is below approximately 5dB (see Figure 3). Figure : Top: (A) Recostructed coductivity distributio of a dog thorax with o electrode error. (B) Recostructed coductivity distributio of dog thorax with simulated erroeous electrode data of SNR=-1dB to electrode 5. Electrodes are umbered i the clockwise directio startig at 1 o clock positio. Dark colors are regios of low coductivity. Bottom: (A) T vs. electrode graph shows cosistecy i the absece of o erroeous electrode. (B) T vs. electrode graph shows T for electrode 5 is much lower tha the rest of the T values, suggestig that electrode 5 is erroeous F T.8.4 A Figure 3: F statistic (± Std Dev) vs. SNR: Represetative good data were used to aalyze the sesitivity of the method. White Gaussia oise was added to electrode 5 (SNR: -5dB to 5dB). The experimet was repeated to determie the margi of error. The threshold for detectio is at a SNR of 5dB SNR B

5 B. Electrocardiogram (ECG) The ECG data were from the olie database of [11]. We categorize the data ito two classes: o-erroeous ad erroeous data due to sythetic oise. The first data category is used to establish how well the scheme ca estimate data based o the forward ad iverse model. The secod data category is used to observe the sesitivity of the data to oise. Vrms estimate V 1 origial V 1 Before applyig our sesor error detectio scheme for ECG, we eed to establish the umber of idepedet sources that cotribute to the ECG sigal ad determie its dimesioality. Oe way to establish dimesioality is by decomposig the data ito its eigevector ad eigevalue. The most domiat vectors are represeted with large eigevalues. The eigevalue aalysis shows that the maximum umber of sources preset for a ECG data is seve. As cofirmatio, [1] showed that ECG is geerated due to electrical activity of seve differet tissues of the heart that make up the typical QRS amplitude. Hece, the QRS amplitude is the liear sum of the actio potetial of the seve sources. The seve sigals are geerated i differet times by differet tissues ad do ot cotribute iformatio regardig other sources which makes them statistical idepedet. It is also clear to see that the sigals are o- Gaussia. A 1-Lead system measures activity over three measuremet plaes: V ad av F measure activity over the Sagittal plae (X-Z plae), av R, av L, I, II, av F ad III measure activity over the Frotal plae (Z-Y plae), ad V 1 to V 6 measure activity over the Trasverse plae (X-Y plae). The possibility of estimatig the measuremet of a specific electrode from the other electrodes becomes difficult as oly a fractio of the 1 leads are observig the data from the similar plae. Moreover, the data for Sagittal plae ad Frotal plae is costructed out of 6 Leads determied from 3 electrodes (measuremet poits) [1]. Ay two Leads cotai exactly the same iformatio as the remaiig four. Therefore, this characteristic violates the assumptio that the data from each lead is a idepedet measure of ECG sigal used to estimate error from a sigle electrode. I additio, the three measuremet poits are situated further away from the heart (limb, shoulder ad akle) makig ECG sigal weaker ad susceptible to oise from EEG sigal ad other sources. For the above reasos the estimatio scheme was oly applied to electrodes alog the Trasverse plae o the chest. Figure 4, shows the origial data from electrode 4 ad its estimate based o the trasverse plae. This figure demostrates that data from the Trasverse plae, based o H ad R, created through SVD is sufficiet as a estimate Time(sec) Figure 4: Origial data (dotted lie) ad estimate (solid lie) of origial data: H ad R estimated based o data of the trasverse plae. The data is from electrode 4 (V 1) Sythetic erroeous ECG data is geerated by addig white Gaussia oise to a specific sesor data. This data is used to validate the detectio scheme itroduced i the previous sectio. Figure 5 shows a ECG data corrupted with White Gaussia oise of db SNR o data from electrode 4. Whe the detectio scheme is applied, it is clear to see that the estimatio error of all electrodes except electrode 4 is high. The corrupted data from electrode 4 is cotributig to a model that caot properly estimate the other electrodes. However, the f-value for the ECG data with o erroeous electrode is greater tha f α, N-, (N-1)N-1 Vrms time(sec) Figure 5: (a) Corrupted ECG data from electrode 4 with db oise The detectio threshold of the method o Trasverse plae is determied by addig White Gaussia oise from -5 to 5 db ad plottig the F statistics vs. SNR. Lookig at the resultig graph i Figure 6, we ca clearly see a jump i the f-value after db of SNR. The ull hypothesis is rejected if the f-value is less tha f.1,4,9 = 4.1. Based o the above critical f-value, we ca coclude that the system is sesitive to oise levels of db for data o the trasverse plae.

6 F electrodes oly. Moreover, the fact that several of the Leads acquired the data from differet plaes complicated the modelig. Nevertheless, the data acquired from the 6 electrodes measurig ECG sigal o the trasverse plae was successfully used demostrate the algorithm. Automatic detectio of sesor errors i multi-sesor system has several possible applicatios. I offlie processig, such a techique could idetify ad correct for such errors. More usefully, if implemeted i multi-sesor moitorig equipmet, it would be possible to alert staff who could the atted to the problem. However, for such olie applicatios, the algorithm is still slow (5s) for real-time data aalysis, but would permit erroeous sesor detectio i the backgroud REFERENCE SNR Figure 6: F vs. SNR: F statistic (± Std Dev) vs. SNR: Represetative good data were used to aalyze the sesitivity of the method. White Gaussia oise was added to electrode 4 (SNR: -5dB to 5dB). The experimet was repeated to determie the margi of error. The threshold for detectio is at a SNR of db. V. CONCLUSION I this paper, we have preseted a method to automatically detect erroeous sesors i multi-sesor system, such as EIT ad ECG. The method is based o the model that a erroeous sesor produces measuremets icosistet with those from other good sesors. Multi-sesor systems were divided ito two categories: kow ad ukow system models. A kow system model has a uderlyig relatioship betwee the measuremet ad the medium that is idepedet of the data. Whereas a ukow system model, does ot have a obvious uderlyig relatioship ad ca oly be deduced based o the available data. Based o these two system model defiitios, a estimatio scheme was developed to hadle both scearios. Results show that the method is able to correctly detect the presece of oise ad idetify the locatio of erroeous sesors i represetative EIT ad ECG data. The decisio criterio is based o ANOVA ad shows that detectio of oe or more erroeous sesor is feasible above a specific SNR level. White Gaussia oise was added to a specific electrode, as i Figure ad 5, ad the algorithm was tested based o the appropriate estimatio scheme. The aalysis showed erroeous electrode i EIT ca be detected at oise level of 5dB with p<.5, see Figure 3. The result for ECG based o data from the trasverse plae showed that detectio of erroeous electrodes is possible above db with p<.1, see Figure 6. Our attempt to icorporate data from all 1-Leads failed due to lack of data idepedece as 6 of the Leads are determied from 3 [1] A Adler ad R Guardo, Electrical Impedace Tomography: Regularised imagig ad Cotrast Detectio, IEEE Tras. Medical Imag. Vol. 15, No., pp , April 1996 [] A Adler, R Amyot, R Guardo, J H T Bates, Y Berthiaume, Moitorig chages i lug air ad liquid volumes with electrical impedace tomography, J. Appl. Physiol., Vol. 83, No. 5, pp , Nov 1997 [3] Y Asfaw ad A Adler, Automatic detectio of erroeous electrodes i Electrical Impedace Tomography, Physiol. Meas., I press [4] F Al-Hatib, Patiet-istrumet coectio errors i bioelectrical impedace measuremet, Physiol. Meas., Vol. 19, No., pp , May 1998 [5] A Lozao, J Rosell ad R Pallás-Arey, Errors i prologed electrical impedace measuremets due to electrode repositioig ad postural chages, Physiol. Meas., Vol. 16, No., pp , May 1995 [6] S Meeso, B Blott, ad A Killigback, EIT data oise evaluatio i the cliical eviromet, Physiol. Meas., Vol. 17(suppl.), No. 4A, pp. A33-A38, November 1996 [7] R Aster, B Borchers, ad C Thurber, Parameter Estimatio ad Iverse Problems, Academic Press, 4 [8] DC Motgomery ad GC Ruger, Applied Statistics ad Probability for Egieers Chapter 13: Desig ad aalysis of sigle factor experimets: The aalysis of variace, 3 rd ed, Joh Wiley & sos ic, [9] CJ James ad CW Hesse, Idepedet compoet aalysis for biomedical sigals, Physiol. Meas., Vol. 6, No. 1, pp. R15-R39, February 5 [1] Shles J., A Tutorial o Pricipal Compoet Aalysis, December 5 [11] M Oeff, The PTB Diagostic ECG Database, [1] JG Webster, Medical Istrumetatio, Joh Wiley & Sos, 3 rd ed, 1998 [13] Guardo, R., Boulay, C., Murray, B., ad Bertrad, M., A experimetal study i electrical impedace tomography usig backprojectio recostructio, IEEE Tras. o Biomedical Egieerig. Vol. 38, Issue 7, pp , July [14] Haigh K., ad Yaco H., Automatio as Caregiver: A survey Of Issues ad Techologies, AAAI Techical Report WS--, pp , [15] Bai J., Zhag Y., She D., We L., Dig C., Cui Z., Tia F., Yu B., Dai B., Zhag J., A portable ECG ad blood pressure telemoitorig system,ieee Eg. I Medicie ad Biology Magazie, Vol. 18, Issue 4, pp. 63-7, July 1999 [16] Malmivuo J. ad Plosey R., Bioelectromagetism: Priciples ad Applicatios of Bioelectric ad Biomagetic Fields,Oxford Uiversity Press, 1995