Keywords

1 Introduction

Recent studies confirm the efficacy of transcranial magnetic stimulation (TMS) as a noninvasive treatment of medication-resistant depression [1, 2]. Four different devices, the Neuronetics Neurostar Stimulator, Brainsway H-Coil system, Magstim Magnetic Stimulator, and MagVenture Stimulator, have been cleared by the U.S. Food and Drug Administration (FDA) for the treatment of medication-resistant depression [3, 4].

Even though TMS coil holders, and even robots, have been developed that might make the application of TMS more spatially precise and efficient, to date, TMS is often applied by an operator who manually positions and retains the TMS coil over the subject’s head. A potential safety concern is thus generated when the operator is a woman and is pregnant. There are no studies to date that assess the safety of TMS for a fetus. In the case of a pregnant woman as a TMS operator, we must consider two possibilities:

  • Standard operation with the TMS coil held at distances of approximately 1–2 ft from the belly

  • Accidental TMS coil discharge when the coil is in direct contact with the belly or in its immediate vicinity

In addition to the scenario of a pregnant woman as a TMS operator, the possibility of a pregnant woman as a TMS patient is also important to consider. TMS can cause a generalized tonic seizure, which can pose a significant risk for the integrity of a pregnancy. Therefore, in most instances, pregnancy will be an exclusion criterion for TMS. However, a considerable percentage of women experience symptoms of depression during pregnancy and develop clinical depression requiring medical intervention. TMS has been proposed as a method to treat maternal depression while avoiding fetal exposure to drugs [5, 6]. So while the risk-benefit profile is argued to be better for TMS than for medications, one must consider that TMS may cause fetal exposure to high induced currents.

In estimating acceptable levels of induced currents, we refer to guidelines from the International Commission on Non-Ionizing Radiation Protection (ICNIRP) [7, 8]. The 2010 ICNIRP basic restrictions for occupational exposure to time-varying electric and magnetic fields for frequencies in the band 1 Hz–100 kHz [8] recommend that the exposure should be limited to electric fields in the head and body of less than 800 mV/m in order to avoid peripheral and central myelinated nerve stimulation. ICNIRP also recommends that the restrictions on electric or magnetic fields including transient or very short-term peak fields (which are encountered during TMS) be regarded as instantaneous values which should not be time averaged.

We assume that the estimate of 0.8 V/m maximum peak field should also apply to the fetal brain, body, and trunk.

2 Methods and Materials

2.1 Existing Computational Models of a Pregnant Woman

Induction currents in the entire human body (or bodies) of a pregnant subject caused by a TMS coil can be established in every particular case via numerical electromagnetic modeling. One of the primary investigated concerns has been a significant electric current density, which may develop in the highly conducting amniotic fluid surrounding the fetus and subject to an external time-varying magnetic field [9, 10]. Table 3.1 lists computational models of a pregnant woman and/or a fetus currently available for electromagnetic and radiological simulations.

Table 3.1 Computational pregnant-woman models (after ~2004)
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These models (except for Refs. [10, 11], which are highlighted in the table) are based on insertion of a fetus into an existing nonpregnant female model. Meanwhile, the models developed from scans of pregnant females include the abdominal region only [10, 11].

All models in Table 3.1 are voxel models, except for Ref. [11] which used B-splines or NURBS, while some parts of the body are adapted from the Visible Human Project [12, 13]. Figure 3.1 shows a NURBS model from Ref. [11], while Fig. 3.2 shows the voxel model family from Ref. [14].

Fig. 3.1
figure 1

NURBS model of a pregnant woman [11]

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Fig. 3.2
figure 2

Voxel model of a pregnant woman [16]

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2.2 Construction of FEM (CAD) Full-Body Pregnant Woman Model and Model Topology

The voxel models listed in Table 3.1 are perfectly fine for radiation dosimetry studies [10, 11, 18] and for high-frequency and RF simulation studies of specific absorption rates [14,15,16, 18] based on the finite-difference time-domain (FDTD) approach. However, they are not suitable for the finite element method (FEM), which is generally employed by the TMS community [23,24,25,26,27,28,29,30,31,32,33]. This method more accurately captures complicated coil geometry(s) and curved boundaries between tissues. The NURBS surfaces [11] also have limited value for an FEM solver, which internally operates with geometry primitives: triangular facets and tetrahedra. A conversion from NURBS surfaces to triangular surfaces may require (very) significant additional meshing time.

To enable FEM analysis, a full-body CAD model of a pregnant female in the form of triangular surface meshes has been developed. As an initial dataset, we have chosen the detailed voxel model of a pregnant female by Nagaoka [14, 17, 18]; see second row of Table 3.1. We received the voxel model after signing a licensing agreement with the National Institute of Information and Communications Technology, Japan. This model is based on a 22-year-old pregnant Japanese female (26th week or second trimester) [17]. The original pregnant female voxel model was developed from MRI data collected on a nonpregnant Japanese woman who was 160 cm tall and weighed 53 kg. Further, abdominal MR images of a 26-week pregnant woman were segmented and inserted into this full-body model.

We converted this voxel model into an FEM CAD model using isosurface extraction in ITK-SNAP [35] and MATLAB. Mesh decimation, healing, and smoothing were performed using custom MATLAB scripts and ANSYS SpaceClaim. Standard mesh intersection approaches [36,37,38,39,40,41] typically result in a large number of triangles close to intersection chains and loops. Furthermore, they leave coincident faces, which might create compatibility problems. Resulting object intersections (which are usually “shallow” intersections) were resolved by locally moving intersecting surfaces in their respective normal directions with a step size of 0.2 mm or so until the intersection was no longer present [42, 43].

A well-known problem with FEM models is object matching in a contact region. Usually, the contact region is not explicitly defined in an imported CAD model and has to be discovered separately by testing for face-to-face overlaps and matching CAD faces/edges [44]. This circumstance may lead to problems for certain CAD kernels such as ACIS. To prevent CAD import errors, a thin gap was introduced between all tissue objects and was filled with “average body properties” of an outer enclosing shell. In some sense, this gap represents membranes separating different tissues. If the gap is reasonably small, it provides a close approximation to reality for different physical processes.

In order to construct the fetus model representing a pregnant female during the first and third trimester, we used the base data for the second trimester and the deformation approach described in Refs. [14, 18].

Figure 3.3 shows three variations of the CAD model constructed for the present study. The corresponding tissue mesh inventory is summarized in Supplement I. To our knowledge, this is the only detailed FEM-compatible model of a pregnant female currently available. The current model contains approximately 100 individual parts. Its distinct feature is a continuous CSF shell around the gray matter for both the mother and the fetus. Creation and testing required about 12 man months and continues as a work in progress. Figure 3.4 illustrates the corresponding fetal volume (second trimester) on a larger scale.

Fig. 3.3
figure 3

CAD models of a pregnant woman during the first, second, and third trimesters

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Fig. 3.4
figure 4

Detailed view of the fetus for the second trimester model – posterior view with pelvic bones and other nearby tissues removed

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Other biomechanical CAD models of pregnant women having different degrees of approximation have also been constructed [45,46,47,48]. However, these models do not include detailed geometry of the fetus suitable for EM simulation [47,48,49,50]. Figure 3.4 demonstrates the corresponding fetal volume (second trimester) on a larger scale.

2.3 Tissue Properties

Most tissues were assigned material properties (conductivity and dielectric constant) following the Gabriel & Gabriel database [49], which is further replicated in the IT’IS database [50]. Fetal properties follow Refs. [11, 51] and are outlined in Table 3.2. The conductivity and permittivity of fetal brain are comparable to that of the fetus and also behave similarly. Hence, the fetal brain is assigned scaled fetus material properties; the scaling factor is obtained from the available dataset. The material property values assigned to all tissues are also provided in the supplement.

Table 3.2 Material properties used in mother/fetus models [11, 51]
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3 Study Design

3.1 TMS Coil

Similar to Ref. [26], the base coil is a figure-eight straight coil with a loop radius of 35 mm. However, instead of a stranded conductor, a solid conductor (copper) with a diameter of 8 mm was used.

3.2 Pulse Form and Duration

TMS pulse forms vary widely in shape and duration [52,53,54,55]. Table 3.3 summarizes the data for four common FDA-approved TMS machines.

Table 3.3 Pulse widths and SMT values for different TMS setups
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In order to take the majority of cases into consideration, we have chosen a simple biphasic harmonic coil pulse current:

$$ I(t)={I}_0\sin \left(2\pi t/\tau \right),\kern0.5em \frac{dI}{dt}=\frac{2\pi }{\tau }{I}_0\cos \left(2\pi t/\tau \right), $$
(3.1)
$$ 0\le t\le \tau, I(t)=0\kern0.5em \mathrm{otherwise} $$

The derivative of the coil current, I, is proportional to the induced electric field/induced electric current in the body. In order to include the majority of cases from Table 3.3, the total pulse duration or length τ was evaluated for two limiting values:

$$ \tau =1\ \mathrm{ms},\kern1em \tau =0.1\ \mathrm{ms} $$
(3.2)

Please note that the equivalent frequency of the biphasic harmonic pulse given by (3.1) is

$$ f=1/\tau $$
(3.3)

Other more elaborate pulse forms have also been studied [62].

3.3 Coil Current

For every pulse duration and coil position, the coil current amplitude I0 in (3.1) has been found from the condition of one standard motor threshold (SMT) unit [61, 62]. One SMT means that the electric field at a point 2 cm from the surface of the head beneath the coil center reaches the motor threshold value of approximately 130 V/m [61, 62]. Motor threshold, a measure of the TMS intensity necessary to evoke a peripheral motor response, is variable across individuals but is also remarkably constant in a given individual [63]. For example, the peak coil current for a 0.1-ms-long pulse was found to be approximately 9000 A·turns magnetomotive force (mmf) at 1 SMT unit.

3.4 Coil Positions

Two coil positions for a pregnant patient have been considered (see Fig. 3.5). In the first case (Fig. 3.5a), the straight coil is located 10 mm above the top of the head. In the second case (Fig. 3.5b), the straight coil is translated and then tilted by 60 degrees. The first case might represent a standard TMS coil placement for studies aimed at evaluating central motor conduction, though a circular TMS coil would be generally used in such instances. The second case aims to approximate the position of the TMS for the treatment of depression.

Fig. 3.5
figure 5

Two coil positions used for the pregnant patient study

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A coil positioning map for the pregnant operator is shown in Fig. 3.6 for the second trimester. The closest distance from the coil center to the body is 115 mm. We consider three representative polarizations of the major current dipole of the coil:

  1. A.

    In the coronal plane (z-polarization in Fig. 3.6, Config. A, labeled as A1-A6)

  2. B.

    In the sagittal plane (y-polarization in Fig. 3.6, Config. B, labeled as B1-B6)

  3. C.

    In the transverse plane (x-polarization in Fig. 3.6, Config. C, labeled as C1-C4)

Fig. 3.6
figure 6

Coil positioning map for a pregnant operator (second trimester) study. Some tissues are hidden for clarity

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For every polarization type, four to six representative coil locations have been tested in the sagittal plane as shown in Fig. 3.6. The operator could achieve any of these positions by moving their right arm along with the coil holder. This results in a total of 16 test cases. For each test case, the eddy current density and the corresponding electric field everywhere in the body were computed. Each test case is conducted for the first, second, and third trimesters. For the first trimester, the closest distance from the coil center to the body is 45 mm (B) or 80 mm (C), 115 mm (B) and (C) for the second, and for the third – 40 mm (B) and 80 mm (C). The remaining topology is the same.

3.5 Accidental Coil Discharge

Two extreme cases have also been considered, which are not shown in Fig. 3.6. These are when the coil is moved in the xy-plane until it is as close to the body as possible. These cases will be labeled as B7, B8 and C5, C6, respectively.

3.6 Frequency-Domain Computations

All simulations were performed in the frequency domain using ANSYS Maxwell 3D FEM software (v. 16). ANSYS Maxwell 3D is a commercial FEM software package with adaptive mesh refinement and has been extensively used for eddy current computations, similar to the earlier studies [24,25,26]. The software takes into account both conduction and displacement currents (as well as free and polarization charges), and solves the full-wave Maxwell equation for the magnetic field, H, in the frequency domain

$$ \nabla \times \frac{1}{\sigma + j\omega \varepsilon}\times \mathbf{H}=- j\omega \mu \mathbf{H} $$
(3.4)

where σ is the local medium conductivity, and ε and μ are the local permittivity and permeability, respectively. The major difference from the full-wave case is that the phase is assumed to be constant over the volume of interest. Although Maxwell 3D also has a transient FEM solver, this solver does not take into account the displacement currents and was therefore not used.

All simulations made use of the automated adaptive meshing technology available in Maxwell to iteratively refine the mesh. Five adaptive meshing passes were performed during the calculation, with the final meshes approaching about 2 M tetrahedra. Details of the adaptive mesh refinement procedure have been discussed previously [60].

3.7 Time-Domain Computations

Frequency-domain results (coil excitation with a sinusoidal waveform) for fields and currents have been collected for multiple frequencies (a logarithmic frequency sweep) over the band from 300 Hz to 3 MHz in order to generate the required pulse forms via the fast Fourier transform (FFT) and inverse FFT (IFFT) as described in Ref. [60]. The corresponding method has been described in the same reference; it is time-consuming but accurate. The time-domain solution is required for any pulse form including the harmonic pulses given by (3.1) since they are distorted quite differently from the harmonic wave of the same frequency. This solution is also important for other (nonharmonic) pulse forms [60].

3.8 Finding Maximum Peak Current Density/Electric Field Strength in Individual Tissues

A uniform 5 × 5 × 5 mm grid of observation points was introduced within a rectangular box, which covers the abdominal area only. This resulted in approximately 150,000 observation points within the body, where the induced current and the electric field are evaluated. For every such point, the pulse form has been restored via IFFT. Then, interpolation of peak pulse values onto a finer 2 × 2 × 2 mm grid was performed, followed by averaging over each small tissue volume as recommended in Ref. [8]. Finally, the absolute maximum peak current/field has been evaluated for every all tissues.

4 Results: Pregnant Patient

4.1 Qualitative Behavior of Induced Currents in the Body of a Pregnant Patient at Different Frequencies (Pulse Durations)

Figure 3.7 shows eddy current amplitude distribution in a coronal plane of a pregnant patient for three representative frequencies: 3 kHz, 30 kHz, and 300 kHz. The coil current amplitude is 10,000 A (10,000 A·turns mmf). Note that the color scale has been multiplied by the factor of 10 for every subsequent figure.

Fig. 3.7
figure 7

Eddy current amplitude distribution in a coronal plane for three representative frequencies: 3 kHz, 30 kHz, and 300 kHz (second trimester model). The coil current amplitude is 10,000 A (10,000 A·turns mmf). Note that the color scale was increased by a factor of 10 and 100 for the middle and right-hand figures, respectively

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We observe that the peak current in the fetal area does not exceed 0.1 mA/m2, 1 mA/m2, and 40 mA/m2. Comparing Fig. 3.7a, b, the induced current initially appears to behave as a linear function of frequency. However, the behavior becomes nonlinear after 30 kHz or so as seen in Fig. 3.7c.

We also observe that the bulk of the induced current at any frequency is primarily excited in the amniotic fluid, but not in the fetus. This is to be expected due the very high conductivity of the amniotic fluid.

4.2 Quantitative Results for Maximum Peak Electric Field at One SMT Unit

In the subsequent study, the excitation is always given by a biphasic pulse from Eqs. (3.1)–(3.3) and the TMS intensity is always equal to one SMT unit. Figure 3.8 presents the results for the maximum peak electric field (maximum magnitude of the electric field vector, E(t)) for the two coil configurations in Fig. 3.5, respectively, and for every involved tissue. The first, second, and third trimester models were used in this study.

Fig. 3.8
figure 8

Maximum peak electric field values at two different pulse durations, two different coil positions, and three different stages of pregnancy computed separately for each fetal tissue

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4.3 Comparison with the Recommended Safe Value of Electric Field

According to the safety requirements discussed in the Introduction, the peak electric field throughout the fetal volume (including fetus, placenta, uterus, and amniotic fluid) shall not exceed 800 mV/m. This condition is certainly met for all cases given in Fig. 3.8, even using a reduction factor of 10. One obvious reason is that the magnetic field from the coil decays very rapidly far from the head, being approximately proportional to the inverse third power of the distance [64].

4.4 Observations from the Quantitative Solution

The following observations follow from the analysis of the results given in Fig. 3.8:

  • Values of the peak electric field obtained using the condition of one STM unit weakly depend on the pulse duration. This is in contrast to the results shown in Fig. 3.7, where the dependence on frequency is paramount. The reason is the normalization condition of one SMT unit, which means, for example, that the amplitude of the coil current is significantly increased for the 1.0 ms pulse.

  • The largest fields are observed in the placenta/uterus.

  • The smallest fields are observed in the fetal brain.

  • Peak values for two different coil orientations are quite similar.

  • The third trimester is characterized by somewhat larger values of the maximum peak electrical field as compared to the first and second trimesters.

These observations suggest that the results given in Fig. 3.8 are rather general and should be valid for a wide variety of coil orientations and pulse durations.

4.5 Comparison with Upper Analytical Estimate for Electric Fields/Eddy Currents

Using a simplified upper analytical estimate for eddy current/induced electric field in the human body [60], the local electric field anywhere within the body is expressed directly through a time-varying lumped coil current, I0f(t), in the following form

$$ E=-\frac{\partial {A}^{\mathrm{inc}}}{\partial t},{A}^{\mathrm{inc}}\left(r,t\right)=\frac{\mu_0{I}_0f(t)}{4\pi }{\oint}_C\frac{dl}{\left|r-{r}^{\prime }(l)\right|} $$
(3.5)

This estimate does not depend on the specific human model under study. We first apply eq. (3.5) to the coil setup from Fig. 3.5a, assuming an observation point located beneath the coil center and at a distance of 62 mm from the coil (representing the distance from the coil center to the top of the uterus for the present model). The resulting upper electric field estimate is obtained as 90 mV/m at any pulse duration (when normalized to one SMT unit). Neither of the maximum peak values in Fig. 3.8 for the coil from Fig. 3.5a exceeds this value. For the coil from Fig. 3.5b, the same or a more elaborate estimate (with spatial averaging to undo a loci effect) [60] can be applied. Again, neither of the maximum peak values in Fig. 3.8 for the coil from Fig. 3.5b exceeds the value of 90 mV/m. Hence, the upper analytical estimate given by (3.5) is justified for all considered cases.

4.6 Using the Analytical Estimate for Predicting Maximum Fields for Different Patients

To provide results which may be expected for different patients, we apply the upper analytical estimate of Eq. (3.5) to different distances from the coil center to the top (or a closest point in the general case) of the uterus. The corresponding data rounded to within ±3 mV/m is summarized in Table 3.4. Although the present results are given for one specific coil type, similar estimates may be expected for other coil geometries according to the study performed in Ref. [60].

Table 3.4 Estimates for the maximum peak field in the fetal volume at one SMT unit
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5 Results: Pregnant Operator and Accidental Coil Discharge

5.1 Quantitative Results for Maximum Peak Electric Field at One SMT Unit

All coil configurations shown in Fig. 3.6 have been studied for three stages of pregnancy and for different pulse durations. Figure 3.9 presents typical data for the second trimester and for the biphasic pulse of 0.1 ms duration. The following observations can be made from these and other relevant computations:

  • For coil positions in close proximity to the belly (A-1, A-2, C-1), the peak electric field in the fetal volume may exceed the safe limit of 800 mV.

  • When the distance from the coil center to the nearest point of the uterus is less than 60 cm, the maximum peak values in excess of 100 mV/m may be observed (this number is adopted from Table 3.4).

  • When the distance from the coil center to the nearest point of the uterus is greater than 60 cm, the upper estimate from Table 3.4 can be applied.

Fig. 3.9
figure 9

Maximum peak electric field values for the second trimester for all coil configurations/positions depicted in Fig. 3.6

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Coil polarization B in Fig. 3.6 creates the smallest values of the peak electric field. This result is to be expected since the equivalent dipole of the figure-eight coil is essentially perpendicular to the abdominal surface.

5.2 Accidental Coil Discharge

In the two extreme cases (polarization B and C in Fig. 3.6), the coil is placed as close to the body as possible by moving it in the xy-plane. The corresponding cases for polarization B and C in Fig. 3.6 have been labeled as B7, B8 and C5, C6, respectively. The corresponding maximum peak field values for the entire fetal volume are shown in Fig. 3.10. For these cases, the suggested limit of 800 mV/m may be exceeded by a factor of ten or higher. Similar results were obtained for polarization A for similar extreme coil placements.

Fig. 3.10
figure 10

Maximum peak electric field values for all trimesters and for all coil positions listed in Fig. 3.6

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6 Conclusion

At present, safe limits of fetal exposure to TMS electric and magnetic fields are an open subject. This study aimed to perform both numerical and analytical analyses of this important issue.

As a limit of the maximum peak electric field observed in the fetal volume, we have chosen the value of 800 mV/m, which allows us to avoid peripheral and central myelinated nerve stimulation [8].

Our numerical and analytical estimates for biphasic TMS pulses of different durations provide similar safety estimates. They reveal that:

  1. 1.

    For the TMS intensity of one SMT unit and when the closest distance between the center of the coil and the uterus is greater than or equal to 60 cm (2 ft.), the maximum peak electric field in the fetal volume (including fetus, placenta, uterus, amniotic fluid) is expected to be less than or equal to 100 mV/m. This value is significantly lower than the recommended safe limit of 800 mV/m.

  2. 2.

    The estimate given above was shown for any stage of pregnancy, for two realistic pulse durations, and for pregnant woman either as a patient or an operator.

  3. 3.

    This estimate appears to scale linearly with TMS intensity. For example, at the TMS intensity of 1.5 SMT unit, the peak field in the fetal volume is less than or equal to 100 × 1.5 = 150 mV/m when the closest distance between the coil center and the uterus is still 60 cm or greater.

  4. 4.

    This estimate is scaled approximately proportional to the inverse third power of the distance. For example, at the TMS intensity of one SMT unit, the peak field in the fetal volume is less than 100 × (6/5)3 ~ 170 mV/m when the closest distance between the coil center and the uterus is 50 cm or greater.

  5. 5.

    The following approximate equation for the maximum peak electric field E in the fetal volume is suggested

$$ E\le 100{\left(\frac{60}{d}\right)}^3I\ \left[\mathrm{mV}/\mathrm{m}\right] $$
(3.6)

where d is the closest distance between the coil center and the uterus in cm and I is the TMS intensity in SMT units. We expect (3.6) to hold at the distances d gretater than 30 cm.

  1. 6.

    FDA-cleared TMS devices employ a TMS coil holder. A pregnant operator can (and should) maintain a larger – and thus safer – distance when using a coil holder during TMS treatment. However, the possibility of accidental TMS coil discharge close to the belly has to be considered. In this case, the suggested limit of 800 mV/m may be exceeded by a factor of ten or greater.

  2. 7.

    Given the unknown biological consequences of a large number of pulses in a typical treatment sequence, the decision of whether to use TMS for treatment of depression (the only currently approved indication) should be based on a risk-benefit analysis. In considering the risk-benefit balance, it is important to contemplate the fetal risks posed by pharmacologic treatments for depression in pregnant patients [65, 66]. For more experimental and less evidence-supported indications, a prudent course of action would be to avoid the use of TMS in pregnant women. In any case, appropriate informed consent is critical.

The content of this chapter is solely the responsibility of the authors and does not necessarily represent the official views of Harvard Catalyst, Harvard University, and its affiliated academic health care centers, the National Institutes of Health, or the Sidney R. Baer Jr. Foundation.