Int J CARS (2009) 4:45–52 DOI 10.1007/s11548-008-0268-8

ORIGINAL ARTICLE

Localization and registration accuracy in image guided neurosurgery: a clinical study Reuben R. Shamir · Leo Joskowicz · Sergey Spektor · Yigal Shoshan

Received: 9 January 2008 / Accepted: 23 September 2008 / Published online: 28 October 2008 © CARS 2008

Abstract Purpose To measure and compare the clinical localization and registration errors in image-guided neurosurgery, with the purpose of revising current assumptions. Materials and methods Twelve patients who underwent brain surgeries with a navigation system were randomly selected. A neurosurgeon localized and correlated the landmarks on preoperative MRI images and on the intraoperative physical anatomy with a tracked pointer. In the laboratory, we generated 612 scenarios in which one landmark pair was defined as the target and the remaining ones were used to compute the registration transformation. Four errors were measured: (1) fiducial localization error (FLE); (2) target registration error (TRE); (3) fiducial registration error (FRE); (4) Fitzpatrick’s target registration error estimation (F-TRE). We compared the different errors and computed their correlation. Results The image and physical FLE ranges were 0.5–2.0 and 1.6–3.0 mm, respectively. The measured TRE, FRE and F-TRE were 4.1 ± 1.6, 3.9 ± 1.2, and 3.7 ± 2.2 mm, respectively. Low correlations of 0.19 and 0.37 were observed between the FRE and TRE and between the F-TRE and the TRE, respectively. The differences of the FRE and F-TRE from the TRE were 1.3 ± 1.0 mm (max = 5.5 mm) and 1.3 ± 1.2 mm (max = 7.3 mm), respectively.

R. R. Shamir (B) · L. Joskowicz School of Engineering and Computer Science, The Hebrew University of Jerusalem, Givat Ram Campus, 91904 Jerusalem, Israel e-mail: [email protected]; [email protected] S. Spektor · Y. Shoshan Department of Neurosurgery, School of Medicine, Hadassah University Hospital, Jerusalem, Israel

Conclusion Contrary to common belief, the FLE presents significant variations. Moreover, both the FRE and the F-TRE are poor indicators of the TRE in image-to-patient registration. Keywords Neurosurgery · Image-guided navigation · Localization error · Registration error Introduction Image-guided surgery (IGS) has become one of the methods of choice in a wide variety of neurosurgical procedures, including tumor biopsy, tumor resection, minimal access craniotomies, catheter placement, treatment of hydrocephalus, and deep brain stimulation, among many others [1]. IGS provides real-time, visual information of the intraoperative location of surgical tools with respect to preoperative CT/MRI images on which skull entry points and targets inside the brain have been defined. Since the surgeon relies on this information to manipulate the tools and perform surgical gestures, the localization accuracy with respect to the preoperative images is of utmost importance. Inaccurate localization can be misleading at best and may result in undesired complications. A key step in IGS is the accurate intraoperative alignment, commonly termed registration, between preoperative CT/MRI images and the intraoperative physical anatomy. Landmark-based registration consists of correlating fiducials and/or anatomical landmarks present in both the preoperative image and intraoperatively on the patient’s anatomy. Patients are preoperatively imaged with a few fiducial markers affixed to their skin or bone, which are then localized in the images together with additional anatomical landmarks. Intraoperatively, the surgeon touches the markers and the anatomical landmarks with a tracked pointer and pairs them

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to those defined in the preoperative CT/MRI image. The transformation that aligns the point pairs is then computed, and the CT/MRI image is registered to the intraoperative coordinate system. Landmark-based registration is the method of choice in many commercial IGS systems. The spatial intraoperative localization accuracy of the IGS system depends on four factors: (1) the accuracy of the landmarks and target localization on preoperative CT/MRI images; (2) the accuracy of the landmarks localization on the intraoperative physical anatomy; (3) the accuracy of the computed rigid registration transformation; (4) the accuracy of the real-time tracking system. The first two can be measured directly, while the tracking system accuracy can be obtained from the manufacturer or measured directly. Determining the accuracy of the registration requires further investigation. The most important and clinically relevant measure is the target registration error (TRE). The TRE is defined as the distance between the image and physical targets locations after registration. In practice, the targets are located inside the brain; so, the TRE can not be directly measured. Instead, the root mean square (RMS) distance between the fiducial and the anatomical landmarks in both datasets after registration, also known as the fiducial registration error (FRE), is often provided to the surgeon as an estimate of the localization error. The differences between the FRE and the TRE were addressed in previous studies, and new methods were developed to obtain a better TRE estimation [2–11]. These methods usually incorporate fiducial localization error (FLE). The FLE is defined as the distance between the actual (unknown) landmark location and the landmark location selected by the surgeon. Maurer et al. [2] propose a simulation-based TRE estimator that incorporates FLE values previously measured on skull-mounted fiducials and on their image locations. Fitzpatrick et al. [3,4] present an analytic expression to compute a first-order approximation of the TRE [3] and of its distribution [4]. The method assumes identical, independent, and isotropic FLE distribution. Since the actual FLE is usually unknown, Fitzpatrick et al. propose to correlate it to the FRE and use it in place of the FLE to compute the TRE estimation [3]. Ma and Ellis [5] describe an analytic TRE estimation method for landmark-based and surface-based registration. They have shown that when the registration is landmarkbased, their method is equivalent to Fitzpatrick’s method. Moghari and Abolmaesumi [6,7] propose an analytic method to compute a second-order approximation of the TRE with an unscented Kalman filter algorithm, based on the same FLE assumptions in [3]. Wiles and Peters [8] develop a statistical TRE model that models the situation where the landmarks are obtained with respect to a reference frame, a common situation in actual IGS. More recent works present TRE estimation models that handle anisotropic FLE distribution [9,10].

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Of the published TRE estimation studies, only two have compared the computed TRE values to those measured in a clinical setup [2,11]. Maurer et al. [2] compared estimated TRE distribution to the measured one. The TRE estimation is computed on different artificial targets from four landmarks located on a 100 mm radius sphere. The measured TRE is then computed on a predefined skull-mounted marker, which was not used for the registration computation. The study concludes that the TRE estimation method significantly underestimates the measured TRE. West et al. [11] also compare the estimated and the actual TRE values in a clinical setup. In their experiment, several fiducial markers are implanted prior to imaging on the patients’ skull. Then, both MRI and CT images are acquired for each patient. The fiducial centers are then automatically extracted and paired on both the MRI and the CT images. One pair of fiducials is defined as the target and the rest are used for registration. The rigid registration transformation is computed, and the actual TRE values are measured and compared with Fitzpatrick’s TRE (F-TRE) estimated values. Their results indicate that the F-TRE is a good predictor of the measured TRE. Their work validates F-TRE for image to image registration with skull-mounted fiducial markers, but includes no skin markers or anatomical landmarks, which are the ones commonly used in image to patient registration, as they are less invasive. In this paper, we measure and compare in a clinical setup on 12 patients the localization and registration errors in image-guided neurosurgery. Specifically, our study aims at answering three key questions: (1) Does the FLE distribution is indeed identical as assumed in all TRE estimation methods? (2) What is the deviation of the FRE from the TRE in practice? (3) How well does the F-TRE predict the actual TRE in image to patient registration? Among the TRE estimation methods presented before, we chose Fitzpatrick’s method [3,4] for two reasons: (1) it is the only clinically validated method; (2) other methods may require the FLE distribution, which is usually unavailable.

Materials and methods We first define formally the FLE, FRE, F-TRE, and TRE. Then, we describe the experimental setup to measure and compare these values in a clinical setup. Mathematical definitions Landmarks } and L INTRAOP= Let L PREOP= {l1PREOP , l2PREOP , . . . , l PREOP N INTRAOP INTRAOP INTRAOP , l2 , . . . , lN } be two sets of N corre{l1 lated landmarks, where liPREOP and liINTRAOP are the corre-

Int J CARS (2009) 4:45–52

lated landmark location coordinate vectors in the preoperative and intraoperative datasets, respectively. Preoperative landmarks can be from MRI/CT images, while intraoperative landmarks are chosen on the physical anatomy. Each set of landmarks is defined with respect to their local coordinate system. Fiducial localization error

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Fitzpatrick’s TRE estimation Since the TRE cannot be directly measured for targets inside the brain, several methods were developed to estimate it. Fitzpatrick et al. [3] introduce the following formula to estimate the TRE:

3  FLE2  1  dk2 PREOP = 1+ F-TRE t N 3 f k2 k=1

Since landmark locations cannot be determined precisely, we associate a localization error to each, denoted FLE(liPREOP ) and FLE(liINTRAOP ), to model the location’s uncertainty. This error is commonly called the FLE in the literature, and it is defined as the distance between the actual and the selected landmark locations. Since the actual landmark location is unknown, the FLE is estimated by averaging the measured distances between repeated selections of the same landmark. Fiducial registration error INTRAOP defines the optimal relaThe rigid transformation TPREOP tion between three position and three orientation parameters that best match the preoperative landmarks with the intraoperative ones. It is computed to minimize the RMS distance between the landmark sets. INTRAOP = arg min(RMS(L PREOP , L INTRAOP , T )) TPREOP T

where T is a rigid transformation and the RMS is defined as:    N   T · l PREOP − l INTRAOP 2 i i  RMS ≡ N i=1

The FRE is computed as the RMS distance between correlated landmarks after registration:  2  N  INTRAOP PREOP  T · li − liINTRAOP  PREOP  FRE ≡ N i=1

Target registration error Let t PREOP and t INTRAOP be the correlated target locations on the preoperative and the intraoperative datasets, respectively. Target coordinates are with respect to their local coordinate system. Usually, t INTRAOP is inside the anatomy; so, INTRAOP · its actual location is unknown and is estimated as TPREOP PREOP . The TRE is defined as the distance between the actual t and the estimated target locations:     INTRAOP PREOP ·t − t INTRAOP  TRE ≡ TPREOP

where t PREOP is a single target location, f k is the RMS distance of the landmarks from the principal axis k (in x, y, z coordinates), dk is the distance of the target the land from marks configurations principal axis k, and FLE2 is the expected value landmark FLE squared values.  of the Since FLE2 is usually unknown, Fitzpatrick et al. use the following FRE-based estimate:

 N FRE2 i 2 FLE = i=1 N −2 where     INTRAOP PREOP FREi = TPREOP · li − liINTRAOP  Clinical experiment Twelve patients who underwent brain biopsy with a commercial IGS navigation system were randomly selected and imaged with MRI. Each MRI image consists of 512 × 512 × 160 voxels, with a voxel size of 0.47 × 0.47 × 1.0 mm3 . An expert neurosurgeon defined three skin-applied fiducials and four to nine anatomical landmarks on the patient’s image. Then, in the operating room, after the patient was positioned for surgery, the neurosurgeon located and correlated these landmarks with the physical landmarks locations by touching them with a tracked pointer on a StealthStation (Medtronic, CO, USA) as shown in Fig. 1. Each landmark was selected for three to six times on both the preoperative image and on the intraoperative physical anatomy. Because of computer communication problems in the operating room, the intraoperative data was recorded with the StealthLink software for 10 out of the 12 patients. Then, in the laboratory, we analyzed the landmark localization errors (FLE), the registration errors (the actual TRE, the FRE, and the F-TRE), and computed the FLE to TRE and F-TRE to TRE correlations. Fiducial localization error The FLE was computed as the distance between the different repetitive selections of the same landmark, both on the MRI and on the physical anatomy. In particular, we analyzed the FLE distribution and examined its suitability with existing TRE estimation methods. Furthermore, we compared the

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Int J CARS (2009) 4:45–52

Fig. 1 a Preoperative localization of landmarks on MRI images; b intraoperative localization of the same landmarks on the physical anatomy with a tracked pointer; c simultaneous recording of intraoperative landmark localization data from the Medtronics’ StealthStation on a standard laptop

FLE between the expert and the novice neurosurgeons in the physical landmarks localization. Target registration error One fiducial pair was selected as the target and four different landmarks configurations, with zero to two fiducials and four to nine anatomical landmarks selected from the remaining landmarks pairs. The target fiducials simulate lesion targets near the cortical surface. The four landmark configurations were selected as follows (Fig. 2): (1) the anatomical landmarks; (2) the anatomical landmarks and one fiducial; (3) the anatomical landmarks and the other fiducial; (4) the anatomical landmarks and both fiducials. Then, the registration transformation was computed with Horn closed form method [12]. From the four different landmarks configurations and the three to six repetitive selections of the same landmarks (both fiducials and anatomical) we obtained 612 different landmarks pairings on 10 out of the 12 patients. The actual TRE, FRE, and F-TRE values were computed on each of the 612 scenarios with the formulas presented before. We analyzed the

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Fig. 2 The fiducials (crossed circles) and anatomical landmarks (blank circles): lateral (a) and frontal (b) views. One fiducial pair is selected as the target and four different landmark configurations were defined for each patient as follows: (1) the anatomical landmarks; (2) the anatomical landmarks and fiducial A; (3) the anatomical landmarks and fiducial B; (4) the anatomical landmarks and both A and B. Below each anatomical landmark is the average image and physical FLE

TRE distribution, its variability among both neurosurgeons, and the TRE range for each patient.

Fiducial registration error The computed FRE values were analyzed individually and compared with the TRE. The differences between the FRE and the TRE of each observation were computed, and the correlations between FRE and TRE were plotted and quantified with Kendall’s τ estimator [13]. The absolute value |τ | indicates the pairwise value correlation. It varies from 0 (no correlation) to 1 (full correlation).

Int J CARS (2009) 4:45–52

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Fitzpatrick’s estimation of the target registration error The F-TRE was computed with the formula described before. The differences between the F-TRE and the TRE of each observation were computed, and the correlation between F-TRE and TRE was plotted and quantified with Kendall’s τ estimator. The landmark selection on the images was performed on a standard laptop with ITK-SNAP [14] and the physical landmarks were gathered from the StealthStation (Medtronic, USA) navigation system with the StealthLink software. The data analysis was performed with MATLAB (MathWorks, USA) running on a standard PC.

cal cruz (RHC), and 1.6–3.0 mm in the physical domain, between the fiducial marker and the RHC. Of note, landmarks with similar FLE values in one domain do not necessarily have similar values in the other domain. The left helical cruz (LHC) and the nose bridge (NB) landmarks, for example, have similar image localization errors of 1.2 ± 1.1 and 1.2±1.0 mm, respectively, but their physical localization errors are significantly different: 2.8 ± 1.6 and 1.9 ± 1.1 mm, respectively. The expert and novice neurosurgeon’s average FLE values on the physical landmarks were 1.6 ± 1.5 and 2.2 ± 1.3 mm, respectively. Target registration error

Results The FLE, TRE, FRE, and F-TRE errors were measured, and the FRE to TRE and F-TRE to TRE correlation values were computed. Fiducial localization error The observed landmark localization error distribution parameters are summarized in Table 1. The total number of observations was n = 39 and n = 45 for each landmark selected on the 12 head images and located on the ten patients heads, respectively. For each landmark type, the mean and STD of the localization errors are presented for both the image and the physical domains. Figure 2 shows the location of the left anatomical landmarks along with their mean FLE. The variation of landmark localization error distribution is readily observed. The range of the mean FLE in the image domain is 0.5– 2.0 mm, between the right tragus (RT) and the right heli-

The observed average and STD of the actual TRE on the ten patients (612 observations) is 4.1 ± 1.6 mm, the 95% confidence interval is 6.7 mm, and the maximum targeting error is 9.3 mm. The differences of the actual TRE values observed for the same target are up to 4 mm. To compare the performance of the novice and expert neurosurgeons, we used a total of 432 observations on five of the patients. The expert and novice neurosurgeon’s average TRE values on the physical landmarks were 4.0 ± 1.5 mm (max = 7.7 mm), and 4.3±1.5 mm (max = 8.7 mm), respectively. Fiducial registration error

Landmark

LT

LHC

LLC

LMC

NB

MRI FLE

0.6 (0.5)

1.2 (1.1)

1.3 (0.9)

1.1 (0.9)

1.2 (1.0)

Physical FLE

1.9 (1.0)

2.8 (1.6)

2.7 (1.7)

2.1 (1.3)

1.9 (1.1)

Landmark

RT

RHC

RLC

RMC

Fiducial

The observed average and STD of the FRE on ten patients and 612 observations is 3.9 ± 1.2 mm, the 95% confidence interval is 6.1 mm, and the maximum error is 7.6 mm. The computed FRE to TRE Kendall’s τ correlation average and STD is 0.19 ± 0.16, which indicates a low relation between the two measurements. Figure 3 shows the correlation plots for one typical case, where the low correlation is readily observed. The average and STD of the observed absolute differences between TRE and FRE values on ten patients and 612 observations is 1.3 ± 1.0 mm. In about 20% of the observations, the absolute difference was larger than 2 mm, which we consider clinically significant, the 95% confidence interval was 3.3 mm, and the maximum absolute difference was 5.5 mm. Figure 4 shows the histogram of the observed differences between TRE and FRE values.

MRI FLE

0.5 (0.6)

2.0 (2.0)

0.9 (0.7)

0.9 (1.0)

0.8 (0.6)

Fitzpatrick’s estimation of the target registration error

Physical FLE

2.0 (1.4)

3.0 (1.6)

2.3 (1.4)

1.9 (1.1)

1.6 (0.9)

Table 1 The mean and STD of the landmarks localization errors for each landmark type (mm), on the preoperative MRI image and on the intraoperative physical anatomy

The numbers of observations are n = 39 and n = 45 for each landmark selected on the 12 head images and located on ten patients heads, respectively Landmarks key: LT left tragus, LHC left helical cruz, LLC left lateral cantus, LMC left medial cantus, NB nose bridge, RT right tragus, RHC right helical cruz, RLC right lateral cantus, RMC right medial cantus, Fiducial: skin marker

The observed average and STD of the F-TRE on ten patients and 612 observations is 3.7 ± 2.2 mm, the 95% confidence interval is 9.2 mm, and the maximum targeting error is 13.6 mm. The computed F-TRE to TRE Kendall’s τ correlation average is 0.37 ± 0.18, which indicates a low relation between the two measurements.

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Fig. 3 Comparison of FRE and TRE values (n = 72) observed for the same target. The FRE values are increasing along the X -axis, but the TRE values vary up and down, indicating a poor correlation between the two values

Fig. 4 Histogram of the differences between the TRE and the FRE values (n = 612). The average and STD of the observed absolute differences between TRE and FRE values are 1.3 ± 1.0 mm, the 95% confidence interval was 3.3 mm, and the maximum absolute difference is 5.5 mm

Figure 5 shows the correlation plots for two cases, where the low correlation is readily observed. The average and STD of the observed absolute differences between TRE and F-TRE values on ten patients and 612 observations is 1.3±1.2 mm, the 95% confidence interval is 3.4 mm, and the maximum absolute difference is 7.3 mm. In about 20% of the observations, the absolute difference was larger than 2 mm, which we consider clinically significant. Figure 6 shows a histogram of the observed differences between TRE and F-TRE values.

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Fig. 5 Two comparisons of the F-TRE and TRE values (n = 72) observed for the same target. The F-TRE values are increasing along the X -axis, but the TRE values does not follow this pattern always. In some cases, the F-TRE to TRE correlation was as low as that between the FRE and the TRE (a), while in other cases, the F-TRE demonstrated higher relation (b)

Discussion We observe that different anatomical landmarks are correlated with different landmark localization errors (FLE) on both the MRI images and the physical anatomy. The differences in the FLE values may be elucidated by the differences in the anatomical landmark shapes. The Tragus, for example, is a cone-shaped structure; so, its apex recognition was relatively accurate, with a low FLE. In contrast, the helical cruz is at the start of a tunnel behind the ear and is hard to identify; it is correlated with high FLE. The differences in the FLE indicate that TRE estimation methods that assume identical (isotropic or anisotropic) FLE

Int J CARS (2009) 4:45–52

Fig. 6 Histogram of the difference between the Fitzpatrick’s TRE estimate and the actual TRE for each observation (n = 612). The average and STD of the observed absolute differences between TRE and F-TRE values are 1.3 ± 1.2 mm, the 95% confidence interval was 3.4 mm, and the maximum absolute difference is 7.3 mm. This can be misleading and might result in larger than expected target localization errors

distributions for all landmarks may yield inaccurate estimates. Therefore, better TRE estimation methods are needed to incorporate different landmark-specific FLE distributions. The mean actual TRE is 4.1 ± 1.6 mm, and the 95% confidence interval is 6.7 mm. This result is consistent with other works on neurosurgery navigation accuracy, which report a TRE range of 2.5–4.2 mm [15–18]. The expert neurosurgeon showed better landmark localization accuracy than the novice (FLE of 1.6 ± 1.5 vs. 2.2 ± 1.3 mm). Interestingly, this difference is not reflected in the targeting errors, which were similar for both surgeons (TRE of 4.0 ± 1.5 vs. 4.3 ± 1.5 mm). The average values of the FRE and the F-TRE are close to the average TRE, and it is tempting to believe that both are good estimators for the TRE. Yet, when examining the variance of the values for each patient, significant differences were observed. Our results show that, contrary to common belief, the FRE is not always good estimate of the TRE as differences larger than 2 mm were measured on 20% of the 612 different observations. The F-TRE is somewhat better correlated with the TRE than the FRE, but the observed absolute differences of the F-TRE and the actual TRE were similar to those measured with the FRE, and therefore, the F-TRE may be inaccurate or misleading as well. The differences between the FRE and TRE may be explained, as already noted in previous works, in that the TRE depends not only on the FRE, but also on other parameters such as the target location and the landmark configuration. The poor accuracy of the F-TRE estimation method may be explained by the varying FLE distributions obtained from our measurements.

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Image-guided neurosurgery systems are a mature technology whose efficiency has been clinically demonstrated. However, they provide a FRE or other estimate based on a uniform model of landmark localization error as an indication for the TRE. The value, which is often interpreted by the surgeon as an estimate of the inaccuracy of the navigation localization, can differ by as much as 5 mm. It is not uncommon in neurosurgery to access targets deep in the brain with the size of 10–15 mm (e.g., brain biopsies, deep brain stimulation). In those cases, a target localization error of 3–5 mm might result in missing the target and/or damaging the surrounding neuronal and vascular tissues. Our results point out the need to revise the accepted assumptions and find reliable TRE estimator that is not directly based on the FRE or on the assumption of identical distribution of the landmarks localization error.

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Int J CARS (2009) 4:45–52 16. Eljamel MS (1999) Frameless stereotactic neurosurgery: two steps towards the Holy Grail of surgical navigation. Stereotact Funct Neurosurg 72(2–4):125–128. doi:10.1159/000029711 17. McCutcheon IE et al (2004) Frameless stereotactic navigation in transsphenoidal surgery: comparison with fluoroscopy. Stereotact Funct Neurosurg 82(1):43–48. doi:10.1159/000076660 18. Bjartmarz H, Rehncrona S (2007) Comparison of accuracy and precision between frame-based and frameless stereotactic navigation for deep brain stimulation electrode implantation. Stereotact Funct Neurosurg 85(5):235–242. doi:10.1159/000103262

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Complexified Gravity in Noncommutative Spaces. Ali H. Chamseddine. Center for Advanced Mathematical Sciences (CAMS) and Physics Department, American University of Beirut,. Lebanon. Received: 1 June 2000 / Accepted: 27 November 2000. Abstract: The pre

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Mar 16, 2011 - in multivariate distributions, and introduce some coefficients to measure that depen- dence. ... and C(u) = uk whenever all coordinates of u are 1 except maybe uk; and. (ii) for every a = (a1, a2,..., ...... IMS Lecture Notes-Mono-.

Molecular diagnostics in tuberculosis - Springer Link
Nov 10, 2005 - species, detection of drug resistance, and typing for epi- demiological investigation. In the laboratory diagnosis of tuberculosis, the nucleic acid ...

Ethics in agricultural research - Springer Link
improvement criteria (Madden 1986). Some see distributional problems as reason to reject utilitarianism entirely (Machan 1984; Dworkin I977). Each of these.

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sic characteristic of life, although it can be lost when their costs are higher than their ... individuals with visceral regeneration in progress [7, 25–28], indicates that the ... In the following stages, the regrowth of the intestinal tract can i

Management of Diabetes in Pregnancy - Springer Link
Dec 3, 2011 - profound effects on multiple maternal organ systems. In the fetus, morbidities ... mellitus . Metformin . Glyburide . Pregnancy; diabetes management. Clinical Trial Acronyms. ACHOIS Australian Carbohydrate Intolerance Study in. Pregnant