Deriving tissue physical densities based on Dixon magnetic resonance images and tissue composition prior knowledge for voxel-based internal dosimetry

Abstract

Background

Magnetic resonance (MR) images have been applied in diagnostic and therapeutic nuclear medicine to improve the visualization and characterization of soft tissues and tumors. However, the physical density (ρ) and elemental composition of human tissues required for dosimetric calculation cannot be directly converted from MR images, obstructing MR-based personalized internal dosimetry. In this study, we proposed a method to derive physical densities from Dixon MR images for voxel-based internal dose calculation.

Methods

The proposed method defined human tissues as composed of four basic tissues. The physical densities of the human tissues were calculated using the standard tissue composition of the basic tissues and the volume fraction maps calculated from Dixon images. The derived ρ map was applied to calculate the whole-body internal dosimetry using a multiple voxel S-value (MSV) approach. The accuracy of the proposed method in deriving ρ and calculating the internal dose of ¹⁸F-FDG PET imaging was evaluated by comparing with those obtained from computed tomography (CT) images of the same patient and was compared with those obtained using generative adversarial networks (GANs).

Results

The proposed method was superior to the GANs in deriving ρ from Dixon MR images and the following internal dose calculation. On average of a validation set, the mean absolute percent errors (MAPEs) of the whole-body ρ derivation and internal dose calculation using the proposed method were 14.28 ± 11.11% and 3.31 ± 0.69%, respectively. The MAPEs were respectively reduced to 5.97 ± 2.51 and 2.75 ± 0.69% after excluding the intestinal gas with different locations in the Dixon MR and CT images.

Conclusions

The proposed method could be applied for accurate and efficient personalized internal dosimetry evaluation in MR-integrated nuclear medicine clinical applications.

Introduction

Personalized internal dosimetry plays a pivotal role in precision nuclear medicine. Accurate internal dosimetry helps assess radiation risk to patients during nuclear imaging diagnostic procedures and evaluate the efficacy of nuclear medicine treatments and their potential radiation toxicity [1—3]. Personalized internal dose calculation can be performed using the direct Monte Carlo (MC) method and the multiple voxel S-value (MSV) approach [4, 6] but necessitates individual computed tomography (CT) images to obtain the essential physical density (ρ) and elemental composition of tissues. However, limited tissue contrast of CT images obstructed the diagnosis and characterization of tissues. By contrast, magnetic resonance (MR) images can present anatomical, metabolic, and functional information with various types of image contrasts, such as diffusion-weighted imaging [5] and Dixon imaging [7], to enhance the identification of tumors. In recent years, MR images have been gradually integrated into various clinical nuclear medicine applications to elevate the quality of nuclear medicine image diagnoses and optimize the planning for radionuclide therapy. Positron emission tomography (PET)/MR has been applied clinically for tumor detection and characterization [8]. However, unlike the HU values in CT images, MR signals lack direct relationships for converting the signal into the ρ and elemental composition required for internal dose calculation. Therefore, personalized internal dose calculation cannot be directly executed through MR images.

Numerous methods have been proposed for deriving physical tissue parameters or synthesizing CT images from MR images. These methods can be categorized as atlas-based methods, deep learning-based methods, and segmentation-based methods [9]. Atlas-based methods generate pseudo-CT images by aligning images from an atlas or conducting patch-wise comparisons [10, 11]. Nonetheless, the accuracy of atlas-based methods relies on the available atlases and the anatomical structures depicted in the atlases. The synthesis results of unique anatomical features or lesions in individuals may not be accurate and present limited features [12]. Currently, atlas-based methods are mainly used for the attenuation correction of PET/MR imaging [10, 12]. Generative artificial intelligence has proven highly effective in medical image translation. After unsupervised learning, generative adversarial networks (GANs), such as cycle-consistent GAN (cGAN) and unsupervised image-to-image translation networks (UNIT), enable the accurate synthesis of CT images from MR images [13–19]. However, a substantial amount of image data is required to train CNNs to ensure high accuracy and robustness. Therefore, the clinical application of deep learning-based methods remains limited at present. Furthermore, no study has yet explored deep learning-based chest CT image synthesis. Segmentation-based methods primarily involve segmenting MR images acquired using specific pulsed sequences. A common approach in current clinical practice is to segment Dixon images into distinct regions representing air, lung, fat, and muscle, then assign specific physical tissue parameters or HU values to each region to synthesize CT-like images [20]. However, weak bone and lung signals in Dixon images lead to inaccurate derivation of physical tissue parameters. Several studies have confirmed that these inaccuracies result in considerable errors in internal dosimetry calculation and attenuation correction of nuclear medicine images [21]. To enhance bone and lung signals for physical tissue parameter derivation and HU synthesis, MR imaging with shortened echo time has been widely applied to overcome the short-lived signal of bones and lungs. Modified Dixon quantification parameters of fat fraction and T₂* values were used to establish conversion relationships with volumetric bone mineral densities for bone quality assessment [22]. Furthermore, ultrashort-echo-time (UTE) and zero-echo-time (ZTE) MR imaging techniques have been successfully employed for bone and lung imaging. HU or attenuation maps of bones and lungs can be obtained by assigning pre-defined values to extracted bone regions [23] or by converting from UTE or ZTE images using pre-determined conversion relationships [24–28]. Nevertheless, assigning fixed values for heterogeneous bones and lungs leads to errors. Determining the conversion relationships requires paired MR and CT images of the same patient acquired from the scanners specific for the conversion. The imaging requirement for UTE and ZTE also hinders the clinical application of these methods. In current clinical practice, UTE and ZTE are primarily utilized for the attenuation correction of head PET images, but effective methods for other body parts are still lacking. Segmentation-based methods for accurately synthesizing bone and lung remain unsolved, especially using only Dixon images. Moreover, current segmentation-based methods are primarily applied and validated in the attenuation correction of nuclear medicine images, with very limited research conducted on MR-based internal dosimetry.

In this study, we propose a method to derive ρ maps from Dixon MR images for voxel-based internal dosimetry. The proposed method has the advantage of using only Dixon images and accurate ρ derivation of heterogeneous bones and lungs without establishing conversion relationships. The proposed method categorizes human tissues into three tissue types based on standard tissue composition and were considered to be composed of corresponding basic tissues. Volume fraction maps derived from the Dixon images and the standard tissue composition of the basic tissues were applied to calculate the ρ map. The ρ map was used to calculate internal dose using the MSV method with 23 voxel S-values (VSVs) established based on the standard tissue composition. The accuracy of the proposed method in deriving ρ and calculating internal dose was evaluated using the Dixon images and ¹⁸F-fluorodeoxyglucose (¹⁸F-FDG) PET/CT images of the same patients and were compared with GANs. The accuracy in different types of tissues was also assessed.

Materials and methods

Study subjects and imaging

This retrospective study has been approved by the local institutional review board, and the need for written informed consent was waived (No. 2023-02-003AC). Whole-body PET/CT images (Discovery MI DR, GE HealthCare) and whole-body Dixon MR images (GE SIGNA, GE HealthCare) acquired on the same day from 29 patients were retrospectively collected. Whole-body images ranging from the top of the lungs to the bottom of the pelvis were used in this study. The CT scans were performed with a helical pitch of 0.984, a tube voltage of 120 kVp, an auto exposure-controlled tube current ranging from 30 to 130 mA, and a slice thickness of 3.75 mm. The 3 T MR scans were conducted to generate Dixon images using a body coil with a repetition time of 4 ms, an echo time of 1.7 ms, and a slice thickness of 5.2 mm. The whole-body MR scans involved 5–6 bed positions. The whole-body internal dose calculation of ¹⁸F-FDG PET imaging was performed using PET images obtained from the PET/CT scanner. The PET scans were started 60 min after ¹⁸F-FDG FDG injection. The PET scans were performed with a bed position of 15 cm and a bed overlap of 23.4%. The scanning time for each bed position was 2 min. The whole-body scans encompassed 8–10 bed positions. The PET images were reconstructed using a TOF-OSEM with two iterations, 24 subsets, and a 5.0-mm Gaussian post-filter.

Deriving tissue physical densities from Dixon images

In this study, human tissues were categorized into three types: soft tissue, bone, and air-containing tissue. Each type of tissue was defined as consisting of different basic tissues. According to the water and fat volume fraction maps generated from Dixon images, high-water and high-fat volume fraction regions coincided with the muscle and fat regions, respectively. By summing the water and fat volume fraction maps, nearly all soft-tissue regions exhibited a 100% volume fraction in the summation map. These findings were consistent with the standard tissue composition that human tissues are primarily composed of water and fat, and the ρ and elemental composition of most soft tissues with high water content closely resemble that of muscle [29, 30]. Therefore, the water volume fraction map was used to represent the distribution of muscle in this study. Human bones primarily comprise osseous tissue and bone marrow [30, 31]. The cortical bone and trabeculae, composed of osseous tissue, contribute minimally to the signals in Dixon images. The composition of the bone marrow is similar to a mixture of fat and muscle (Table 1). Therefore, bones were regarded as a composition of three basic tissues of muscle, fat, and cortical bone in varying proportions. Soft tissues that contain air are the lungs and digestive tract. In the Dixon images, air does not contribute to signals, but both lung parenchyma and the intestinal wall contribute to the signal intensity. The composition of lung parenchyma and the intestinal wall closely resembles that of muscle (Table 1) [29, 30]. Therefore, air-containing tissues were considered to be composed of two basic tissues of muscle and air in varying proportions. The entire human body was considered to comprise three tissue types, each composed of different basic tissue sets with different proportions. The volume fractions for bone and air were derived by subtracting the fractions of muscle and fat from 100%. Therefore, physical densities can be derived by the following equation:

$${\rho }_T=\sum _{i=1}^N{\rho }_i·v_i$$ 1

where v_i denotes the volume fraction of a basic tissue i for a tissue T. ρ_T and ρ_i represent the physical densities of the tissue T and basic tissue i, respectively. The calculation procedures of the proposed method for deriving ρ maps from Dixon images are presented in Fig. 1. Multiplicative intrinsic component optimization (MICO) was initially adopted for the bias correction of Dixon images [32]. Masks for high-signal regions in the water and fat images generated in the MICO calculation were applied to calculate the mean signal intensities of water and fat. The water and fat volume fraction maps were obtained by normalizing the bias-corrected water and fat images with the mean signal intensities. Regions with a sum of water and fat volume fractions less than 100% were considered bone and air-containing regions. In these regions, the air-containing region (lungs and intestinal gas) was segmented using the TotalSegmentator [33] extension within the 3D Slicer software [34]. The remaining regions were defined as the bone regions. Finally, ρ maps were derived from the volume fraction maps of each region using their corresponding basic tissue sets and the physical densities of the basic tissues.

Table 1.

Standard elemental compositions and physical densities of tissues applied in the proposed method

Element	H	C	N	O	Ca	P	Others	ρ (g/cm3)
Tissues	Weight fraction (%)
Fat	11.4	59.8	0.7	27.8	0	0	0.3	0.95
Small intestine wall	10.6	11.5	2.2	75.1	0	0.1	0.5	1.03
Lung parenchyma	10.3	10.1	2.9	75.5	0	0.2	1	1.05
Muscle	10.2	14.3	3.4	71	0	0.2	0.9	1.05
Red marrow	10.5	41.4	3.4	43.9	0	0.1	0.7	1.03
Yellow marrow	11.5	64.4	0.7	23.1	0	0	0.3	0.98
Cortical bone	3.4	15.5	4.2	43.5	22.5	10.3	0.6	1.92

Fig. 1.

Calculation procedures of the proposed method. First, Dixon water and fat images were corrected for bias field using the MICO and normalized as the volume fraction maps of the basic tissues of muscle and fat. The TotalSegmentator was then applied to segment bone and air regions from the summation map of the muscle and fat volume fraction maps, and the volume fractions of the basic tissues of cortical bone and air were calculated within these regions. Finally, a ρ map was derived by summing the volume fraction-weighted standard densities of the basic tissues

Deriving tissue physical densities from CT images

Tissue physical densities derived from CT images were used as reference standards. The derivation of ρ from CT images was conducted using conversion relationships pre-determined for the CT scanner [35, 36]. A stoichiometric calibration was performed using a parametrical physical model with a tissue-equivalent phantom (RMI-467, GAMMEX) to obtain spectrum characteristic parameters of the scanner. Subsequently, the HU values of 2 lung tissues, 45 soft tissues, and 29 bones were estimated using the model with their standard compositions and spectrum characteristic parameters [37]. The estimated HU values for fat and connective tissues were used as breakpoints to classify all tissues into three categories [35]. HU–ρ conversion relationships were determined for the air-containing tissues, soft tissues, and bones through piecewise linear fittings of their estimated HU values and known physical densities. The CT images can be converted into ρ maps using the relationships.

Voxel-based internal dosimetry based on basic tissues

To calculate internal doses using the MSV approach, VSVs for multiple tissues were established based on the basic tissue concept proposed in this study. For bones, 10 VSVs were established with weight fractions of cortical bone varying from 10 to 100%, and the remaining weight fraction was allocated to the bone marrow. Bone marrow was assumed to be a mixture of red and yellow marrow with each of 50% weight fractions due to their similar electron densities and linear attenuation coefficients. For air-containing tissues, 10 VSVs were established with weight fractions of muscle ranging from 10 to 90%, and the remaining weight fraction was designated as air. For soft tissues, VSVs for fat, water, and muscle were established. A total of 23 VSVs were established in this study. The physical densities of water, connective tissue, and the four basic tissues were obtained from the standard tissue composition (Table 1). The ρ and elemental composition for establishing the VSVs of bones and air-containing tissues through MC simulations were calculated as follows:

$$w_T^e=\sum _{i=1}^N{w}_i^e·v_i^{}·{\rho }_i$$ 2

where $w_T^e$ and $w_i^e$ denote the weight fractions of the element e in the tissue T and basis tissue i, respectively. Table 2 lists the compositional elemental weight fractions and physical densities of the 20 VSVs.

Table 2.

Compositional elemental weight fractions and physical densities of the VSVs of 10 air-containing tissues and 10 bones established in this study. The weight fractions of the basic tissues of the VSVs are listed

Tissue type	Weight fraction of basic tissue (%)		Elemental weight fraction (%)								ρ (g/cm3)
	Muscle	Air	H	C	N	O	Ca	P	Ar	Others
Air-containing tissue	0	100	0.00	0.00	75.50	23.20	0.00	0.00	1.30	0.00	0.001293
	10	90	1.02	1.40	68.25	28.03	0.00	0.03	1.17	0.10	0.11
	20	80	2.04	2.81	61.00	32.85	0.00	0.06	1.04	0.20	0.21
	30	70	3.06	4.21	53.75	37.68	0.00	0.09	0.91	0.30	0.32
	40	60	4.08	5.61	46.50	42.51	0.00	0.12	0.78	0.40	0.42
	50	50	5.10	7.02	39.25	47.33	0.00	0.15	0.65	0.50	0.53
	60	40	6.12	8.42	32.00	52.16	0.00	0.18	0.52	0.60	0.64
	70	30	7.14	9.82	24.75	56.99	0.00	0.21	0.39	0.70	0.74
	80	20	8.16	11.23	17.50	61.81	0.00	0.24	0.26	0.80	0.85
	90	10	9.18	12.63	10.25	66.64	0.00	0.27	0.13	0.90	0.95
	Cortical bone	Bone marrow
Bone	10	90	10.24	49.16	2.27	34.50	2.25	1.08	0.00	0.51	1.10
	20	80	9.48	45.42	2.48	35.50	4.50	2.10	0.00	0.52	1.19
	30	70	8.72	41.68	2.70	36.50	6.75	3.13	0.00	0.53	1.28
	40	60	7.96	37.94	2.91	37.50	9.00	4.15	0.00	0.54	1.37
	50	50	7.20	34.20	3.13	38.50	11.25	5.18	0.00	0.55	1.46
	60	40	6.44	30.46	3.34	39.50	13.50	6.20	0.00	0.56	1.55
	70	30	5.68	26.72	3.56	40.50	15.75	7.23	0.00	0.57	1.65
	80	20	4.92	22.98	3.77	41.50	18.00	8.25	0.00	0.58	1.74
	90	10	4.16	19.24	3.99	42.50	20.25	9.28	0.00	0.59	1.83
	100	0	3.40	15.50	4.20	43.50	22.50	10.30	0.00	0.60	1.92

For calculating the internal dose from ¹⁸F-FDG PET imaging, the MCNP (version 6, Los Alamos National Laboratory, USA) was employed for particle transportation to generate VSVs of ¹⁸F radionuclides in the 23 compositions. The VSVs were constructed with a voxel size of 3 × 3 × 3 mm³ and a matrix size of 65 × 65 × 65 mm³, resulting in a total size of 195 × 195 × 195 mm³ to encompass the mean free path of annihilation photons. The ¹⁸F radionuclide was assumed to be uniformly distributed in the central voxels of the VSVs. The simulations for β⁺ particles and annihilation photons emitted by ¹⁸F decays were performed separately. The energy spectrum of the β⁺ particles was obtained from the RAdiation Dose Assessment Resource (RADAR) [38]. The dose deposition results of the MCNP simulations were recorded using a mesh tally. The number of tracked events for each VSV simulation was five million. After obtaining the VSVs, the ρ maps obtained from the Dixon and CT images were employed to calculate the internal doses of the PET imaging using the MSV approach. The doses contributed from β⁺ particles and annihilation photons were separately calculated and then summed to generate an internal dose rate (D, mGy/s) map.

Competing methods

The accuracy of the proposed method in calculating physical densities from Dixon MR images was compared with the widely studied GANs of the cGAN and UNIT [13, 16]. The cGAN and UNIT were trained to synthesize ρ maps from Dixon water or fat images using the paired Dixon images and ρ maps converted from the CT images. The cGAN includes two generators with an encoder-decoder architecture and two patch-level discriminators with an encoder module for Dixon-to-ρ and ρ-to-Dixon translations. The UNIT consists of a generator with encoder-decoder architecture and two patch-level discriminators. The residual blocks of the generator are partially shared between Dixon and ρ image domains. A total of 8537 paired Dixon images and ρ maps were prepared from the image data of the 29 patients. 75% (22 patients, 6495 images) were used for training, and 25% (7 patients, 2042 images) were used to validate the cGAN and UNIT. The hyperparameters for the cGAN and UNIT were adjusted based on the validation results. For the cGAN, a learning rate of 2 × 10^–4 and the weight for the cycle-consistency loss of 10 were used. For the UNIT, a learning rate of 1 × 10^–4 was used, and the weights for self-reconstruction loss, cycle-consistency loss, and adversarial loss were 10, 10, and 1, respectively. Both the cGAN and UNIT were trained for 100 epochs.

Evaluation

Ρ and D calculated using the CT images were employed as the reference standard to assess the accuracy of those calculated from the Dixon images using the GANs and proposed method. Due to the variations in patient posture and position during CT and Dixon imaging, nonrigid deformable registration was performed to align the ρ maps derived from the Dixon images with those derived from the CT images using an Advantage Workstation (AW) server (version 3.2, GE Healthcare). Percent error maps and mean absolute percentage errors (MAPE) between the ρ and D maps obtained from the Dixon and CT images were calculated. Moreover, MAPEs were computed for the soft-tissue, bone, lung, and whole-body regions with and without excluding the intestinal gas. The MAPE calculation was as follows:

$$MAPE\left(\%\right)=\frac{1}{N}\sum _{i=1}^N\frac{\left|f_{\mathit{Dixon}}\left(i\right)-f_{\mathit{CT}}\left(i\right)\right|}{f_{\mathit{CT}}\left(i\right)}\times 100\%$$ 3

where N is the number of voxels. f_Dixon and f_CT are the maps of ρ or D calculated from the Dixon and CT images, respectively. Additionally, joint histogram and linear regression analysis for different tissue regions were conducted to evaluate the agreement between the ρ maps obtained from the Dixon image and the reference ρ maps derived from the CT images.

Results

Figure 2 shows the ρ maps derived from the Dixon images of a representative validation case using the proposed method and GANs and corresponding percent error maps calculated by comparing the density maps with the reference map derived from the CT image (ρ_CT). The GANs and proposed method successfully derived the ρ of most soft-tissue regions with MAPEs lower than 5% compared with the ρ_CT map. However, the UNIT with a fat image input (ρ_UNIT(Fat)) failed to derive the physical densities of bone and lung regions with MAPEs of 12.17% and 273.44%, respectively. The UNIT with a water image input (ρ_UNIT(Water)) and the cGANs (ρ_cGAN(Water) and ρ_cGAN(fat)) derived more accurate results with MAPEs lower than 12% and 97% for bone and lung regions, respectively. Nevertheless, the GANs were unstable in deriving physical densities from the Dixon images with regional inaccuracies of fallacious anatomy. On average of the whole body, the MAPEs of the ρ_cGAN(Water), ρ_cGAN(fat), ρ_UNIT(Water), and ρ_UNIT(Fat) were 44.21%, 59.8%, 58.87%, and 79.28%. It can be noticed the differing positions of intestinal gas in the Dixon and CT images resulted in significant errors. After excluding the intestinal gas, the MAPE of the ρ_cGAN(Water), ρ_cGAN(fat), ρ_UNIT(Water), and ρ_UNIT(Fat) were reduce to 7.92%, 8.27%, 10.86%, and 22.36%, respectively. By comparison, the proposed method accurately derived ρ maps (ρ_Dixon) anatomically matched with the Dixon images. The MAPEs for the bone and lung regions of the proposed method were 6.73% and 27.6%, respectively. The MAPEs of the whole-body region without and with excluding the intestinal gas were 36.13% and 4.17%, respectively.

Fig. 2.

Physical density maps (ρ) derived from the CT and Dixon MR images of a representative validation case. The percent error maps between the maps derived from the Dixon MR images and the reference map derived from the CT image are also shown. Display windows of the CT image, Dixon MR image, ρ maps, and percent error maps are [-1000 1000] HU, [0 1000], [0 2] g/cm³, and [0 1], respectively

Figure 3 shows the D maps calculated using the MSV method with the density maps presented in Fig. 2 and corresponding percent error maps calculated by comparing the D maps with the reference map (D_CT) calculated using the ρ_CT map. The applied ρ map directly influenced the accuracy of the calculated D map. The MAPEs of the soft-tissue regions were lower than 2% for the GANs and proposed method. However, the MAPEs of the bone and lung regions were higher than 5% and 22% for the GANs, respectively. On average for the whole body, the MAPEs of the D_cGAN(Water), D_cGAN(fat), D_UNIT(Water), and D_UNIT(Fat) were 11.19%, 7.27%, 6.29%, and 5.92%, and were reduced to 4.04%, 3.57%, 3.34%, and 4.82% after excluding the intestinal gas, respectively. The impact of the incorrect ρ derivation for lungs and bones on the dose calculation was minor due to the radioactivities mainly concentrated in soft tissues. By contrast, the D_Dixon calculated using the ρ_Dixon map was close to the D_CT calculated using the ρ_CT map. The MAPEs for the bone, lung, and whole-body regions without and with excluding the intestinal gas were 3.23%, 11.82%, 2.53%, and 1.77%, respectively.

Fig. 3.

Internal dose rate maps (D) calculated from the ¹⁸F-FDG PET image of the representative validation case using the MSV method and the ρ maps shown in Fig. 2. The percent error maps between the D maps calculated using the ρ maps derived from the Dixon MR images and the reference D map (D_CT) calculated using the ρ_CT maps are also shown. Display windows of the PET image, D maps, and percent error maps are [0 0.19] Bq/ml, [0 0.088] mGy/s, and [0 1], respectively

Tables 3 and 4 list the mean and standard deviation of the MAPEs of the ρ and D maps of the validation set, respectively. Among the GANs, the cGAN with a water image input and the UNIT with a water image input presented the most accurate results in the ρ derivation and D calculation, respectively. Although having lower MAPE for the soft-tissue, bone, and whole-body regions, the cGANs mis-derived the ρ of lungs as soft tissues, resulting in higher dose errors. In comparison, the UNIT with a water image input derived the ρ of lungs accurately and ensured the accuracy of the following dose calculation. However, the ρ derivation and D calculation of the GANs for the lung region were inaccurate with mean MAPEs higher than 50% and 20%, respectively. By contrast, the proposed method presented the most accurate density and dose calculation results. The mean MAPEs of the ρ and D for the soft tissue, bone, and whole-body regions, excluding the intestinal gas, were lower than 10%. Relatively large errors appeared in the lung region with a mean MAPE of 33.22% for the ρ and a mean MAPE of 15.14% for the D. Since the proposed method was training-free, the mean and standard deviation of the MAPEs of the ρ and D were also calculated from the training set to further evaluate the proposed method and are listed in Table 5. For all regions, the MAPEs of the training set were close to those calculated from the validation set. The mean MAPEs of the ρ and D for the soft-tissue, bone, and whole-body regions, excluding the intestinal gas, were lower than 9%, and the mean MAPEs for the lung region were 36.98% and 13.79%, respectively.

Table 3.

Mean and standard deviation values of the MAPEs between the ρ maps derived from the Dixon MR and CT images of the validation set

Region	Whole body	Whole body w/o gas	Soft tissue	Bone	Lung
Proposed method	14.28% ± 11.11%	5.97% ± 2.51%	2.51% ± 0.34%	9.20% ± 1.30%	33.22% ± 25.04%
cGAN(Water)	18.40% ± 13.45%	8.58% ± 2.57%	3.93% ± 0.62%	10.37% ± 1.15%	50.85% ± 25.59%
cGAN(Fat)	25.03% ± 16.74%	11.56% ± 5.37%	4.36% ± 0.38%	11.49% ± 1.25%	79.30% ± 53.53%
UNIT(Water)	22.87% ± 16.65%	10.84% ± 4.98%	4.15% ± 0.56%	11.33% ± 1.92%	71.71% ± 54.61%
UNIT(Fat)	43.38% ± 23.01%	30.19% ± 11.46%	4.25% ± 0.49%	12.39% ± 2.41%	286.99% ± 90.98%

Table 4.

Mean and standard deviation values of the MAPEs between the D maps calculated using the ρ maps derived from the Dixon MR and CT images of the validation set

Region	Whole body	Whole body w/o gas	Soft tissue	Bone	Lung
Proposed method	3.31 ± 0.69%	2.75% ± 0.69%	1.12% ± 0.16%	4.78% ± 0.81%	15.14% ± 3.38%
cGAN(Water)	10.18 ± 3.47%	4.73% ± 1.04%	1.63% ± 0.26%	7.03% ± 1.82%	33.32% ± 43.51%
cGAN(Fat)	13.45 ± 11.16%	7.29% ± 3.59%	1.83% ± 0.21%	8.31% ± 2.51%	59.85% ± 65.36%
UNIT(Water)	6.74% ± 1.46%	4.00% ± 0.86%	1.72% ± 0.27%	7.33% ± 2.13%	22.72% ± 5.08%
UNIT(Fat)	7.51% ± 1.52%	6.06% ± 1.35%	1.91% ± 0.28%	6.98% ± 1.46%	43.51% ± 6.04%

Table 5.

Mean and standard deviation values of the MAPEs computed by comparing the ρ and D maps calculated from the training set Dixon MR images using the proposed method with those calculated from the training set CT images

Region	Whole body	Whole body w/o gas	Soft tissue	Bone	Lung
Density	17.35 ± 11.55%	5.18 ± 2.56%	2.18 ± 0.39%	8.34 ± 1.34%	36.98 ± 25.45%
Dose rate	2.57 ± 0.7%	2.04 ± 0.54%	0.92 ± 0.18%	4.36 ± 0.85%	13.79 ± 3.16%

Figure 4 presents the joint histograms and R² values from the linear regression analysis between the ρ maps derived from the Dixon images and the reference ρ maps obtained from the CT images across all validation cases. In all tissue regions, the ρ values synthesized by the GANs showed significant deviation from the diagonal isodensity line, resulting in R² values lower than 0.5. In contrast, the ρ values derived through the proposed method closely aligned with the diagonal isodensity line, achieving R² values higher than 0.6. For the whole-body region, excluding intestinal gas, the proposed method presented the highest R² value of 0.87, compared to the R² values of 0.73, 0.68, 0.68, and 0.19 of the GANs.

Fig. 4.

Joint histograms between the ρ maps derived from the Dixon images using the proposed method, cGAN, and UNIT and the reference ρ maps obtained from the CT images across all validation cases. R² values computed by linear regression analysis for soft-tissue, bone, lung, and whole-body regions, excluding the intestinal gas, are addressed. The black diagonal line in the joint histogram is an isodensity line

Discussion

Tissue physical densities are essential for precise internal dosimetry calculation. However, deriving physical densities using only Dixon images remains challenging for heterogeneous bones and lungs. Current deep-learning and atlas-based methods for deriving or converting MR images into CT images or ρ maps usually need time-consuming model training or image registration with large image datasets. In most segmentation-based methods that rely on Dixon images alone, different categories of tissues were assigned attenuation values directly, which may result in considerable errors, particularly in heterogeneous tissues such as bone and air-containing tissues. Nevertheless, accurate derivation of bone and lung tissue densities was rarely discussed. For accurate Dixon MR-based internal dosimetry, this study proposed a method that adopted the standard tissue composition for deriving the ρ of human tissues from Dixon images and establishing multi-tissue VSVs. In the proposed method, human tissues classified into soft tissue, bone, and air-containing tissue were regarded as mixtures of basic tissues, including muscle, fat, cortical bone, and air. Physical densities of human tissues were calculated using the standard composition of the basic tissues with the volume fractions derived from Dixon images. For the D calculation using the MSV method with the derived ρ map, 23 VSVs were established based on the basic tissue concept of the proposed method. The compositional elemental weight fractions and physical densities of the established VSVs were close to those originally proposed in the MSV method. The major difference between them was the elemental composition of the established VSVs with ρ ranged from 0.11 to 0.85 g/cm³ was considered as a mixture of air and lung parenchyma, but the original VSVs with ρ ranged from 0.1 to 0.8 g/cm³ have the same elemental composition. The established VSVs were more consistent with the partial volume effect in an image voxel. Applying the established VSVs for calculating the internal dose of the lungs might be more accurate and requires further examination.

The accuracy of the proposed method was evaluated by comparing it with the CT-based method and the cGAN and UNIT. For the GANs, the accuracy of the ρ derivation using fat images as input (ρ_cGAN(fat) and ρ_UNIT(fat)) was lower than that using water images (ρ_cGAN(water) and ρ_UNIT(water)), especially for the lungs. This could be due to the low signal intensity of lungs and soft tissues in fat images presenting distinct HU values in CT images. This inconsistency leads to low correspondence between fat and CT images, resulting in large errors in the ρ derivation of the lungs. By contrast, the lungs and soft tissues can be simply differentiated in water images, thereby improving the ρ derivation accuracy. In addition, the cGAN was superior to the UNIT in the ρ derivation and presented the highest accuracy with water image input. However, the ρ derivation results of all GANs suffered from regional inaccuracies of mis-derivation of tissue types. The accuracy in the ρ derivation of soft tissues and bones was comparable between water and fat images and between cGAN and UNIT. The errors in the ρ derivation were directly exhibited in the D calculation results. Nevertheless, small ρ errors have a minor impact on the D calculation since the difference between the VSVs with similar ρ was negligible. Overall, the MAPEs of the D calculation were lower than that of the ρ derivation. In addition, the radioactivity accumulated in the lungs was low, so the error in the D of the lungs was lowered further. The errors of D calculation mainly appeared in the regions with the mis-derivation of tissue types of the GANs. Since the 2D image to 2D image conversion architecture of the GANs was maintained, this study did not attempt to input both water and fat images for ρ derivation. This approach may improve the accuracy of ρ maps derivation from Dixon images using the GANs and requires further research.

Compared with the GANs, the proposed method was more accurate in the ρ derivation of various tissue types, resulting in lower D calculation errors. The proposed method presented similar accuracy in the training and validation sets, indicating its robustness. However, relatively large errors appeared in the bone, lung, and intestinal gas regions. These errors were mainly attributed to the accuracy of the image segmentation and tissue volume fraction derivation, which depended on the quality of the applied Dixon images. In the proposed method, regions where the sum of water and fat fractions was less than 100% were identified as bone or air-containing tissues. The TotalSegmentator was applied to segment and differentiate between various tissue regions for density derivation using corresponding basic tissue sets. The segmentation results at tissue boundaries of bones and lungs might exhibit deviations or discontinuities due to the partial volume effect resulting from the relatively limited resolution of the Dixon images compared with the CT images. Applying focal Dixon images with a higher spatial resolution for the ρ derivation using the proposed method could be expected to better differentiate tissue boundaries and reduce the segmentation deviation. Atlas-based or deep learning-based segmentation methods for segmenting low-signal bones and lungs from Dixon images could be developed to improve the accuracy of the ρ derivation and dose calculation of the proposed method. Moreover, in contrast to rapid CT scans, a relatively longer time required for MR imaging led to noticeable respiratory motion artifacts. The artifacts caused the MR signals of vessels, bronchus, and lung parenchyma to be averaged, resulting in overestimating the ρ. Respiratory-gated MR imaging could be applied to improve the accuracy of the density and internal dose calculated using the proposed method by reducing respiratory motion artifacts. The position difference of intestinal gas between the CT and MR scans contributed error, even though the scans were conducted on the same day. The ρ maps also demonstrated that the intestinal gas regions and contours in Dixon images were not as distinct as in CT images. The MAPEs of the ρ derivation and D calculation in whole-body regions were decreased after excluding the intestinal gas for both the proposed method and cGANs. Although the differences in the position of intestinal gas had a noticeable impact on the ρ derivation, their influence on dose calculation was minor since low radioactivity accumulated in the intestinal gas region.

In targeted radionuclide therapy with potential bone marrow toxicity, such as the Lu-177-Dotatate therapy [39], determining the volume fraction of active marrow is crucial for accurate marrow dosimetry. The dose delivered to the active marrow is a critical factor that directly affects the determination of the prescribed dose and the effectiveness of the treatment. Fixed fractions of active marrow for different ages and bone types provided in the ICRP publication 116 [40] are currently used for bone marrow dosimetry. By contrast, the volume fraction of active marrow in cancellous bones could be simply determined by subtracting the fat and cortical bone fractions [41]. The influence of active marrow volume fraction on bone marrow dosimetry will be further investigated. In addition, the proposed method can also be applied to determine the elemental composition of tissues from Dixon images. Dixon-MR-based MC simulations and attenuation correction performed using the proposed method will also be studied.

This study has a few limitations that need to be considered. First, the Dixon MR and PET/CT images were acquired using the same scanners from relatively few patients. Multi-center or multi-scanner studies with more patients imaged with different parameters are needed to assess the accuracy and robustness of the proposed method further. Second, the effectiveness of the proposed method for the ρ derivation of pathological tissues or lesions was not specifically evaluated. The accuracy of the proposed method in deriving the ρ of pathological tissues with low water and fat content needs to be further investigated. Third, the internal dose calculated in this study was the dose rate D computed using the static PET images instead of the absorbed dose computed using dynamic PET images. Since the convolution-based MSV method is dependent on activity distribution, the impact of using the ρ derived by the proposed method on the absorbed dose calculation required further evaluation using dynamic PET images.

Conclusion

In this study, we proposed a method that derives ρ maps solely from Dixon MR images for voxel internal dosimetry. The proposed method defined human tissues as composed of four basic tissues with known ρ and elemental composition. The volume fraction maps of the basic tissues were obtained by normalizing Dixon water and fat images and were used to calculate the ρ maps with the known ρ of the basic tissues. The same tissue composition definition was also used to establish the VSVs of 23 tissues. The results show that the proposed method could accurately derive the physical densities and help calculate the internal dose for homogeneous soft tissues and heterogeneous lung and bone tissues using Dixon MR images alone. In addition, the proposed method does not involve iterative computation and model training using large image datasets. In conclusion, the proposed method could be applied for personalized internal dosimetry evaluation in nuclear medicine diagnosis and treatments integrated with MR imaging.

Abbreviations

MC

Monte Carlo

MSV

Multiple voxel S-value

CT

Computed tomography

MR

Magnetic resonance

PET

Positron emission tomography

GAN

Generative adversarial network

cGAN

Cycle-consistent generative adversarial network

UNIT

Unsupervised image-to-image translation network

UTE

Ultrashort-echo-time

ZTE

Zero-echo-time

VSV

Voxel S-value

¹⁸F-FDG

¹⁸F-fluorodeoxyglucose

MICO

Multiplicative intrinsic component optimization

RADAR

Radiation dose assessment resource

MAPE

Mean absolute percentage errors

Author contributions

CT.S. contributed to the methodology, study design, curation, data preprocessing, analysis, investigation, interpretation, validation, visualization, supervision, funding acquisition, manuscript writing, and editing. KH.L. contributed to the data acquisition, data preprocessing, validation, and funding acquisition. BH.Y. and CY.L. contributed to the data acquisition, data preprocessing, and validation. TL.L. contributed to the data preprocessing and analysis. G.M. contributed to the validation. TH.W. contributed to the methodology, study design, curation, interpretation, funding acquisition, manuscript writing, and editing. All authors read and approved the final manuscript.

Funding

The project was supported by a research grant from the National Science and Technology Council of Taiwan under Grant Number 112-2314-B-039-064-MY3, 112-2314-B-A49-062-MY3, 112-2314-B-075-065, and University of Macau and University of Macau Development Foundation (MYRG-GRG2024-00061-FST-UMDF).

Availability of data and materials

The data will be made available on request from the corresponding author.

Declarations

Ethics approval and consent to participate

The local institutional review board approved the retrieval and use of patient data for this study, and the need for written informed consent was waived (No. 2023-02-003AC).

Consent for publication

All authors are consent for publication.

Competing interests

The authors declare that they have no competing interests.