Medical & Biological Engineering & Computing

, Volume 49, Issue 2, pp 213–220 | Cite as

Automatic detection of motion artifacts in the ballistocardiogram measured on a modified bathroom scale

  • Richard M. Wiard
  • Omer T. Inan
  • Brian Argyres
  • Mozziyar Etemadi
  • Gregory T. A. Kovacs
  • Laurent Giovangrandi
Original Article

Abstract

Ballistocardiography (BCG) is a non-invasive technique used to measure the ejection force of blood into the aorta which can be used to estimate cardiac output and contractility change. In this work, a noise sensor was embedded in a BCG measurement system to detect excessive motion from standing subjects. For nine healthy subjects, the cross-correlation of the motion signal to the BCG noise—estimated using a simultaneously acquired electrocardiogram and statistics of the BCG signal—was found to be 0.94 and 0.87, during periods of standing still and with induced motion artifacts, respectively. In a separate study, where 35 recordings were taken from seven subjects, a threshold-based algorithm was used to flag motion-corrupted segments of the BCG signal using only the auxiliary motion sensor. Removing these flagged segments enhanced the BCG signal-to-noise ratio (SNR) by an average of 14 dB (P < 0.001). This integrated motion-sensing technique addresses a gap in methods available to identify and remove noise in standing BCG recordings due to movement, in a practical manner that does not require user intervention or obtrusive sensing.

Keywords

Ballistocardiography Cardiac output Contractility Heart failure Cardiovascular monitoring Signal processing Noise identification 

1 Introduction

Heart failure (HF) is a growing problem in the United States, affecting over five million Americans. It is estimated that there are over five hundred thousand new cases annually [14], and HF is the single largest cause of hospitalizations for people over 65 years of age [2]. Furthermore, nearly half of all HF patients are readmitted to the hospital within 6 months of release [11]. Since many re-hospitalizations are associated with fluid overload—and subsequent decompensation—the American Heart Association (AHA) recommends daily weight monitoring to detect the onset of fluid retention and direct therapeutic interventions [2]. HF-related weight increase can often be just a few pounds, within normal bodyweight fluctuations, so HF-related complications without significant weight increase may go undiagnosed. Therefore, there is a need for home monitoring devices that utilize information besides weight gain alone. Specifically, measures of hemodynamic flow and the overall strength of the heart could be used as metrics to trend cardiac health over time at home. This may improve diagnostic accuracy for the detection of imminent HF-related complications.

Within the clinical setting, cardiac output (CO) and ejection fraction (EF) are metrics used to distinguish a healthy heart from a weakened heart. Doppler ultrasound is the non-invasive gold standard used to measure CO and EF; however, the need for a trained operator combined with the high cost of ultrasound equipment, effectively precludes its use in the home. Impedance cardiography is a more cost-effective technology to measure CO, however, this technology requires precise electrode placement and data interpretation can be confounded with other fluid volume changes in the body [12]. Another less prevalent method is ballistocardiography (BCG), the measurement of the heart-induced movements of the body in response to cardiac ejection of blood into the arterial tree [15, 16]. BCG measurements have been shown to reliably trend CO changes [6] and indices of contractility [1, 4].

Recent studies using bathroom scale BCG recording systems are showing promise as practical solutions for home monitoring of heart activity [7]. A subject simply stands on a scale to record the BCG and this technique does not require a trained technician to obtain the recording. When a subject stands on a bathroom scale, his/her weight fluctuates synchronously with the beating heart. By amplifying and filtering the AC component of the differential strain gauge output from an ordinary bathroom scale, high fidelity BCG recordings can be taken, provided that the amplifier noise is sufficiently low and the subject stands still for the recording. This approach shows great potential, however, in some instances, the BCG signal quality can suffer from changes in posture while the user is standing upright. The BCG signal bandwidth is approximately 0.5–10 Hz [13], which unfortunately coincides with several sources of interference, including: artifacts due to ambient ground vibrations, respiratory amplitude fluctuations in the signal, and body movements.

In this paper, we demonstrate a simple method to automatically detect motion artifacts in the BCG, using a secondary sensor incorporated within the scale. By detecting and rejecting segments of data corrupted by motion artifacts, this method would improve BCG signal analysis, while maintaining the user requirements of a self-contained and easy-to-use system.

2 Methods

2.1 Overview

Practical solutions to minimize interference resulting from body movements in BCG recordings have not been sufficiently addressed. The BCG can be estimated accurately for subjects standing still; however, some situations may lead to an unacceptable number of noisy segments resulting from motion. The BCG force signal level is on the order of a few Newtons in magnitude. Body movement can easily introduce noise artifacts of similar magnitude and orders greater. Large motion artifacts can be observed and removed with manual identification, however, noise on the order of the BCG signal level is less obvious to detect and ignore from the analysis. A noise signal reference to systematically identify motion while standing on a BCG scale would be highly beneficial. In a previous study for instance, exercise recovery was used as a method to study CO change [6]; this study revealed significant motion artifacts in the recordings that had to be removed manually to estimate CO change, as shown in Fig. 1. While this approach is acceptable in a research environment, it would not be practical in a home monitoring setting.
Fig. 1

Time traces from a previous study for one subject during exercise recovery. The spikes in the BCG trace (top) were caused by body movements of the subject on the scale. The percent changes in cardiac output (CO) measured by Doppler ultrasound, are also shown in the bottom plot, and are correlated to changes in root mean square (RMS) BCG power. Motion artifacts present in the RMS BCG power are indicated (arrows)

The method uses a secondary set of strain gauges and analog amplifier to measure body motion while standing on the scale. The proposed BCG noise reference signal is based on established works to quantify body movement during quiet standing. This noise reference is first verified by calculating its correlation with a separate noise estimate derived from BCG and ECG. For validation, this noise reference is used to flag segments corrupted by excessive motion noise and the signal-to-noise ratio (SNR) is quantified with and without noise flagging.

2.2 System development

2.2.1 BCG instrumentation and software for data collection

An InnerScan BC-534 scale (Tanita, Tokyo, Japan) was used as the BCG sensing platform. The load cells were wired in a Wheatstone bridge configuration and were then connected to an analog BCG amplifier. The analog circuit had an overall gain of 11,000 and a bandwidth of 0.1–24 Hz, and the bridge was excited by a ±9 V DC voltage. A laptop computer and 16-bit data acquisition card (National Instruments, USB6218, Austin, TX) sampled the output at 1 kHz. The signals were then acquired, stored, and processed using MATLAB (MATLAB® R2008b, The MathWorks, Natick, MA). For a detailed characterization of the BCG electronics and scale, the reader is referred to previous works described in [7].

2.2.2 Motion sensor setup in BCG scale

To obtain a motion signal from the scale, secondary strain gauge sensors were added to measure weight distribution changes. The motion of standing subjects has been previously researched and modeled as an inverted pendulum [5, 17], where body motion is highly correlated to anterior–posterior weight distribution changes and this methodology is thus proposed as a noise reference technique for standing BCG measurements.

The four load cells in the bathroom scale were modified to enable simultaneous BCG and motion measurements. Each load cell, comprised of a metallic strain gauge (Tanita strain gauge) affixed to a mechanical cantilever beam, was supplemented with a 350 Ω Omega metallic strain gauge (SGD-7350-LY13, Omega Engineering Inc., Stamford, CT). The Omega strain gauge was placed on the opposite side of the cantilever from the Tanita strain gauge. Thus, deflections in the beam resulted in tensile strain for the Tanita strain gauge, and compressive strain for the Omega strain gauge. In this study, secondary strain gauges were added since the Tanita strain gauges are specifically configured into a Wheatstone bridge to record the BCG. The Omega sensor was chosen based primarily on its size relative to the physical space available for mounting on the cantilever.

The motion-sensing circuit for the Omega strain gauges consisted of an instrumentation amplifier with a gain of 1,000 and a Sallen-Key low-pass filter (second order, 24 Hz cutoff). The Omega strain gauges were wired into a half-bridge arrangement to detect anterior–posterior motion, and the output was recorded simultaneously with the BCG and electrocardiogram (ECG), at a 1 kHz sampling rate. Figure 2 depicts the overall measurement setup.
Fig. 2

Block diagram depiction of the measurement setup. A bathroom scale was modified to measure the BCG and a signal representing body motion. Human balance is typically quantified by measuring the changes in the center of mass (COM) position in the anterior–posterior plane using force plates. Works by Winter et al., have correlated the true COM movement with the changing pressure signal on force plates, which demonstrate that the COM and weight shift signals track together in direction and amplitude, with virtually no lag between the two signals [5, 17]. For this experimental setup, the modified bathroom scale was configured to measure the anterior–posterior COM weight shift to represent the motion signal

2.2.3 Mechanical characterization of the scale platform

Following the addition of the Omega strain gauges, the scale was characterized to obtain the overall frequency response of the BCG recording system. The electrical bandwidth is limited by the circuitry and mechanical bandwidth is limited by the stiffness and damping of the scale. Since adding secondary strain gauges to the system had the potential to change mechanical bandwidth after strain gauge placement, verification was performed to ensure that the system was still suitable for BCG recording. A series of weights were placed on the scale and the BCG bridge voltage was recorded to verify linearity. The differential signal from the BCG bridge had a linear force-to-voltage response with sensitivity equivalent to previous studies [7]. The mechanical frequency response of the scale and strain gauges was estimated through a series of impulse response measurements, at loads ranging from 22.6 to 104.3 kg. At the highest load, the bandwidth of the scale platform was determined to be 0.1–19.5 Hz, which is sufficient to measure the BCG.

2.3 Study 1: Noise correlation (BCG noise vs. motion signal noise estimates)

2.3.1 Noise correlation study details

A study was conducted to investigate relationships between BCG noise estimate and the motion signal. The protocol was designed to capture a range of motions at and beyond what would be considered typical. Nine healthy subjects (8 males, 1 female, age: 21–52 years) participated in the study (Stanford IRB Protocol 6503). First, ECG electrodes were placed on each subject in a Lead I configuration [3] and then each subject was asked to stand still on the scale for 30 s, while recording ECG, BCG, and motion signals simultaneously. These quiet standing recordings represent the expected intended use of the BCG platform. Next, subjects were instructed to induce random motions 3–4 times during the next 30 s, pausing 7–10 s between each motion to allow the BCG signal to recover for several beats. These large perturbations represent extreme cases where a subject cannot stand still and the BCG signal integrity is lost, and therefore should not be included in BCG signal analysis.

2.3.2 Signal processing

The raw BCG, ECG, and motion signals were post-processed to extract two signals: (1) an estimate of the sample-by-sample BCG noise, vBCG[k], derived from the BCG and the ECG, and (2) an estimate of the sample-by-sample motion noise, vmot[k], derived from the motion signal.

The methods used for estimating vBCG[k] are described briefly here; for a full treatment, the reader is referred to [8]. First, the BCG and ECG signals were digitally band-pass filtered (0.5–20 Hz, and 5–45 Hz, respectively). Then, the R-waves of the ECG were automatically detected and used for segmenting an ensemble of BCG beats, using a fixed-threshold algorithm and confirmed visually. The ensemble averaged BCG was then computed from these beats and used to estimate the noise-free BCG signal. The residual signal, computed by subtracting this noise-free BCG from the recorded BCG, was then considered the BCG measurement noise, vBCG[k].

Similarly, to derive an estimate of the motion noise, vmot[k], the raw output from the strain gauge conditioning circuit was digitally processed: after low-order polynomial fitting (tenth order, 30 s frame) was used to subtract the baseline wander, the signal was low-pass filtered (10 Hz cutoff). All low-pass filters were FIR filters, with a Kaiser window.

2.3.3 Noise correlation: ECG-timing-based BCG noise estimate vs. motion noise

The two noise signals, vBCG[k] and vmot[k], were not expected to be correlated in terms of polarity, rather only in magnitude, due to the specific strain gauge wiring of the BCG and motion circuits: downward deflections on the front and back of the scale platform would both result in positive deflections in the BCG signal, while they would result in opposing polarity signals in the motion signal output. For this reason, the temporal correlation between signal powers—not sensitive to polarity—was investigated. The methods used to evaluate this correlation over all subjects are described below.

Both noise signals were down-sampled by a factor of 10, to 100 samples per second. Then, the moving average (2 s window—200 samples) BCG noise power (RMS), \( \overline{{\nu_{\text{BCG}} }} [k] \), was calculated as follows:
$$ \overline{{v_{\text{BCG}} }} \left[ k \right] = \sqrt {\frac{1}{200}\sum\limits_{n = 0}^{199} {v_{\text{BCG}} \left[ {k + n} \right]^{2} } } ,\,k = 1,\,2,\, \ldots ,\,N_{\text{samp}} - 200 $$
(1)
where Nsamp is the number of samples in the recording. The moving average motion noise power (RMS), \( \overline{{\nu_{\text{mot}} }} [k] \), was then calculated using similar methods. The maximum cross-correlation between the two moving average noise powers was then calculated, with both sequences normalized such that their zero-lag autocorrelation functions were unity. This method results in an output that is similar to a correlation coefficient: for two perfectly correlated sequences, this maximum cross-correlation would be unity, while for two uncorrelated sequences, the output would be zero. The cross-correlations were then computed for the subject rest and excessive motion datasets. The maximum cross-correlation was then obtained along with its latency between \( \overline{{\nu_{\text{BCG}} }} [k] \) and \( \overline{{\nu_{\text{mot}} }} [k] \).

2.3.4 Motion noise flagging algorithm

A motion-signal-derived noise metric was then established to flag segments of the BCG corrupted with excessive motion. The noise index was calculated as follows: first, a baseline recording was used to establish a ‘normal’ RMS level for the motion signal. This ‘normal’ level was then used to set a subject-specific threshold—twice the ‘normal’ level—above which the BCG trace was considered corrupted by noise. As a result, periods of the BCG signal during which the motion was greater than the threshold were considered ‘high’ for the noise index, and other periods were ‘low’.

While this approach—using a baseline recording to find a subject-specific threshold—is fundamentally sound, there could be a practical advantage to being able to forego this initial baseline recording altogether. This would require a non-subject-specific, fixed, threshold to be set for all recordings. For this paper, a fixed threshold was set as the average subject-specific threshold measured for all participants. Noisy beats were removed based on the noise index and the SNR improvement using both the subject-specific and the fixed threshold to flag the noise were then computed and compared for Study 2. This approach was only intended here to provide an initial assessment of the feasibility of a fixed noise-threshold flagging algorithm, and will be further investigated in future studies.

2.4 Study 2: BCG signal-to-noise improvement using the motion signal

2.4.1 BCG SNR improvement study details

After correlations were identified in the previous study, a second study was conducted to demonstrate a noise flagging algorithm to improve the BCG SNR [8], using the motion signal as a noise reference. Seven healthy subjects (3 females, 4 males, age: 25–38 years) participated in a study designed to capture typical body motions that would be encountered when using a bathroom scale. The ECG, BCG, and motion signals were acquired simultaneously for each recording. For each subject, a 1-min baseline recording was taken during which subjects were instructed to remain as still as possible, to determine a threshold. Next, five independent 30 s recordings were obtained for each subject during which they were instructed to perform motions considered “typical” when standing on a scale. Each 30 s recording contained four motions: looking down to read the scale, looking up, yawning, and talking. Between each motion segment were approximately 5–7 beats of quiescent BCG data. To test significance in this study, the paired t test was used to examine the change between the non-gated BCG SNR and the noise-gated BCG SNR—a total of five paired comparisons per subject.

2.5 Supplemental study: Noise flagging during exercise recovery

To investigate future applications for the algorithm and motion signal, an exercise recovery dataset was obtained from one subject while recording BCG, ECG, and motion signals simultaneously. The subject was first asked to stand on the BCG/motion-sensing scale for a 30 s baseline recording (at rest). Then, the subject exercised on a treadmill for 15 min. Immediately following exercise, the subject stood on the scale for 7 min while his heart rate recovered to baseline. Note that the noise flagging algorithm was applied, however, the SNR was not computed since the signal is rapidly changing in amplitude and shape. Exercise recovery studies are valuable protocols for researchers and demonstration of this noise flagging approach may improve methods to analyze such recordings.

3 Results

3.1 Study 1: Noise correlation (BCG noise vs. motion signal noise estimates)

3.1.1 Example time traces

The signals recorded for one subject, after digital band-pass filtering, are shown below in Fig. 3. In Fig. 3 (left), the subject was standing relatively still and motion artifacts were subtle in the BCG signal. Note that there is a respiratory component to the motion signal, which is expected since the body moves during inspiration and expiration. The two signals are also shown for more pronounced motion artifacts (Fig. 3, right)—here, the subject was asked to produce random excessive motions (deep knee bends) while on the scale to generate noise spikes in the BCG signal. The correlation between the motion signal and the motion noise present in the BCG is more apparent in this figure (right), since the motion artifacts are more significant.
Fig. 3

BCG and motion signals recorded from one subject during quiet standing (left time traces), and for voluntary excessive motion (right time traces). Note the change in magnitude in the amplitude scales for the BCG and motion signals between quiet standing and excessive motion

3.1.2 Noise correlation

The results from all subjects are summarized in Table 1, alongside the subject demographics for each participant. The cross-correlations ranged from 0.86 to 0.97 for the resting datasets (quiet standing), which demonstrates a strong correlation (P < 0.001) for each recording, present between the ECG-timing-based noise estimate from the BCG signal and the noise power derived from the motion signal. Each individual cross-correlation contained approximately 3,000 data points after down-sampling the 30 s recordings. Cross-correlations ranged from 0.79 to 0.96 for the data when subjects induced excessive motion—also significant (P < 0.001), but with a slightly lower mean and larger standard deviation than for quiet standing. The correlations for the second group of motions were slightly lower since some of the exaggerated movements saturated the BCG amplifier. Note that for such exaggerated movements that saturate the BCG signal, having an external noise signal is unnecessary—saturation can be detected electronically.
Table 1

Characteristics and motion artifact correlation to BCG noise for all subjects

Subject

Age (years)

Height (cm)

Weight (kg)

Heart rate (bpm)

Cross-correlation

Quiet standing

Excessive motion

1

21

195.6

97.5

50

0.86

0.93

2

52

154.5

65.8

66

0.98

0.96

3

36

185.0

68.0

88

0.95

0.82

4

26

175.0

63.5

85

0.94

0.82

5

23

165.0

56.7

91

0.96

0.94

6

27

201.0

143.0

88

0.94

0.96

7

28

182.0

87.0

68

0.97

0.86

8

32

177.8

95.3

101

0.90

0.77

9

22

160.0

57.6

105

0.96

0.73

Mean

29.7

177.3

81.6

82

0.94

0.87

SD

9.7

15.6

27.8

17.8

0.04

0.09

Another important characteristic of the motion signal as noise reference is the minimal delay between the motion-related noise in the BCG and the noise detected by the motion sensor. On average, the motion signal was found to lag the BCG noise signal by 13 ms ± 36 ms at rest, and 17 ms ± 300 ms for excessive motion (the latter varying so much due to the recovery of the BCG signal from saturation following a BCG spike). Such minimal delays provide the time resolution necessary to flag single heartbeat events, thus maximizing the selectivity of the approach. This represents a significant improvement over a previously reported technique using leg EMG as an indirect measurement of body motion (muscles contract to compensate original motion), where delays were found to be more variable and sometimes reaching multiple seconds [9].

3.2 Study 2: BCG signal-to-noise improvement using the motion noise signal

3.2.1 BCG SNR improvement

With encouraging results from the noise correlation, the second study was directed at BCG SNR improvement, using the motion signal and a noise flagging algorithm. Table 2 summarizes the average BCG SNR improvement (SNR difference from non-gated) in dB.
Table 2

Summary of BCG signal-to-noise ratio results utilizing noise flagging algorithm

Subject

Age (years)

Height (cm)

Weight (kg)

Non-gated

Subject-specific threshold improvement

Fixed threshold improvement

BCG SNR* (dB)

BCG SNR* (dB)

BCG SNR* (dB)

1

33

178.0

88.5

−25.3

16.0

22.2

2

33

167.6

63.5

−7.4

13.2

13.2

3

38

185.0

69.9

−5.3

22.9

16.8

4

27

175.2

63.6

−4.0

14.6

9.3

5

32

160.0

54.0

−14.4

3.0

3.0

6

25

172.7

65.8

−12.8

13.7

10.8

7

27

157.5

55.3

−0.4

1.3

1.4

Mean

30.7

170.9

65.8

−7.3**

14.3**

10.7**

SD

4.6

9.8

11.5

P value**

<0.001

<0.001

* Average SNR of five independent recordings per subject

** Paired t test performed against 35 pairs of data

The average SNR improvement was 14.3 dB using subject-specific noise thresholds, with high significance (P < 0.001) over the 35 recordings. For the fixed threshold, the average SNR improvement was 10.7 dB (P < 0.001) for 35 recordings. The data was examined to verify that no more than 30% of the beats were removed by the flagging process. For Subject 2 and Subject 5, the SNR improvements were identical as their individual calibration thresholds were similar to the fixed threshold. For six subjects, SNR improved in all of the five separate trials; for one subject, four of five trials. Overall, the SNR improved for 34 of 35 trials.

3.3 Supplemental study: Automatic noise flagging in exercise recovery

The exercise recovery data is depicted in Fig. 4 for one subject, along with the noise index. A resting dataset was acquired prior to exercise, then used to estimate the baseline motion noise signal. A noise threshold was determined based on the RMS criteria described in the methods section. In Fig. 4, the BCG signal during exercise recovery is clearly corrupted by motion noise at several instances. Most pronounced are the noise components due to the initial post-exercise phase—when it is most difficult to remain still—and periodically throughout the recovery due to normal postural shifting. As shown in this figure, the noise index closely tracks the instances at which the BCG spikes (e.g., Fig. 4, second arrow); however, it also flags segments of the BCG with no apparent spikes since the motion noise thresholds are exceeded (Fig. 4, first and third arrows)—the latter would not be detected using manual identification techniques.
Fig. 4

Raw BCG time trace for one subject during exercise recovery. The noise index changes state (downward arrows) based on information collected from the motion signal vmot[k]. The initial phase of recovery contained several successive noise flags which reduced in frequency after the subject improved their balance

4 Discussion

The results from the correlation and BCG SNR improvement studies demonstrate that anterior–posterior motion sensing serves as a reliable noise reference to detect noise in standing BCG measurements. For BCG SNR improvement, two calibration approaches were presented to set the threshold for noise flagging; both yielded large and statistically significant improvements in SNR. In Study 2, individualized thresholds led to more significant increase in SNR improvement where unique aspects of each subject such as height, weight, and/or motor control could factor in the flagging threshold. Both thresholds approaches led to very large BCG SNR improvements when using the motion signal to flag noise-corrupted segments, which further supports the findings in Study 1. Furthermore, the latencies from the cross-correlation demonstrated reliable detection of noise to occur within a single heartbeat. Therefore, we conclude that anterior–posterior motion sensing has the capability to determine motion artifact noise in the BCG without the need for the ECG-timing-based estimation as a trigger for ensemble averaging, which is a goal for future studies.

For the supplemental study, a transient monotonic decrease cannot be assumed for exercise recovery. In examining these signals, one could suggest that the amplitude envelope of the BCG would suffice to estimate the noise in the signal. For example, a threshold could be adaptively set, and any portions of the signal exceeding this threshold could be considered noise. While this may be true for short recordings taken at rest, this is not the case in an exercise recovery recording. Homeostatic recovery may be interspersed with plateaus and even some upwards transients. Consequently, fitting a simple envelope function would not be adequate. A reference signal is therefore necessary to provide robust detection of motion artifacts. During exercise recovery, the amplitude envelope is precisely the information of interest, since it relates to the changes in BCG RMS power induced by changes in CO. In contrast to the recording shown in Fig. 3 (left), the exercise recovery signal is not in steady state (Fig. 4): the cardiovascular system is constantly adapting after heavy exercise to recover to its baseline resting state. Gross changes in BCG amplitude are not only due to motion artifacts, but they are also due to changes in stroke volume. With the methods described in this paper, increased RMS power at the motion sensor simply indicates increased noise in the BCG trace—these segments can then be ignored from the analysis of the signal.

In future implementations regarding hardware and software, it is conceivable to minimize the circuitry and sensors required for these measurements and to improve the analog recovery time of the BCG electronics. For example, a circuit could be implemented using the same four strain gauges to switch between BCG bridge arrangement, and anterior–posterior motion sensing—thereby eliminating extra strain gauges. The noise index algorithm may also be optimized further to improve the SNR of the BCG.

BCG in home monitoring applications may be beneficial for trending clinical hemodynamic parameters (e.g. CO and contractility change), which may supplement other cardiovascular home monitoring methods [10]. The practicality of this embedded motion-sensing approach enables automatic noise flagging algorithms to be realized without the ECG reference, with application to steady and transient BCG recordings. This method improves the robustness and practicality of BCG measurements for home monitoring applications without burden to the user.

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Copyright information

© International Federation for Medical and Biological Engineering 2010

Authors and Affiliations

  • Richard M. Wiard
    • 1
  • Omer T. Inan
    • 2
  • Brian Argyres
    • 3
  • Mozziyar Etemadi
    • 4
  • Gregory T. A. Kovacs
    • 2
    • 5
  • Laurent Giovangrandi
    • 2
  1. 1.Department of BioengineeringStanford UniversityStanfordUSA
  2. 2.Department of Electrical EngineeringStanford UniversityStanfordUSA
  3. 3.Department of Mechanical EngineeringStanford UniversityStanfordUSA
  4. 4.Division of Pediatric SurgeryUniversity of California, San FranciscoSan FranciscoUSA
  5. 5.Department of MedicineStanford UniversityStanfordUSA

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