New Semi-quantification Approach for Dopamine Transporter Scan: Quantification of 2 Accumulation by Examining the Approximate Image 3

Semi-quantitative analysis is used to evaluate the degree of tracer binding to the striatum in 33 dopamine transporter (DaT) single-photon emission computed tomography (SPECT). In DaT 34 SPECT, it is difficult to evaluate the accurate tracer accumulation due to the partial volume 35 effect (PVE). In this study, we propose a novel semi-quantitative approach for measuring the 36 amount of accumulation by examining the approximate image. Using the striatal phantom, 37 we verified the validity of a newly proposed method that can accurately evaluate the tracer 38 accumulations in the caudate and putamen, separately. approximated The proposed method was able to compute the accurate accumulation amounts in the 62 caudate and putamen, considering the PVE.

The striatal phantom DaT1308 (NMP Business Support Co., Ltd., Hyogo, Japan) was used. We 133 filled 123 I solution into the right caudate and left caudate regions of the striatal phantom at a 134 scheduled radioactivity concentration ratio of 1.80:1.00, and water into the right and left 135 putamen regions, and the whole brain region which considered as background (BG). A 136 phantom created by this condition of radioactivity concentration ratio was defined as 137 "Phantom1." Then, we filled 123 I solution into the right caudate, right putamen, left caudate, 138 left putamen, and BG regions of the striatal phantom at a scheduled radioactivity 139 concentration ratio of 9.00:9.00:5.00:4.00:1.00. A phantom created by this condition was 140 defined as "Phantom2." We measured the actual count densities of the 123 I solution filled into 141 "Phantom1" and "Phantom2" by an auto-well counter (ARC-7001, Hitachi Aloka Medical, Ltd., 142 Tokyo, Japan) and computed the actual count density ratio. The data of the created 143 "Phantom1" and "Phantom2" are shown in Table 1. 144 145

2-3. Calculation process by the proposed method 146
The definitions of the terms used in the calculation process of the proposed method are 147 shown in Table 2. Moreover, an overview of the calculation process of the proposed method 148 is shown in Fig. 1. accumulation amounts assigned to each region. Since five values (i.e., 0, 0.5, 1.0, 1.5, 2.0) were 167 assigned to the five regions (the left and right caudate/putamen and BG regions), five to the 168 fifth power (3125) images with no blur (we defined these images as "assigned images") were 169 generated. Three-dimensional (3D) Gaussian filter equivalent to SPECT spatial resolution in 170 clinical conditions (FWHM: x = 11.52 mm, y = 11.89 mm, z = 11.71 mm) was applied to 3125 171 "assigned images." Therefore, the SPECT-like spatial resolution images (we defined these 172 images as "blurred images") generated the same number as the "assigned image." 173 174 2-3-3. Process No. 3 of the proposed method: Generating the "difference image" (Fig. 4) 175 We defined the image, obtained by the actual SPECT imaging, and normalized it with the 176 maximum value, as the "real image." The voxel-by-voxel differences between the "blurred 177 image" generated in Process No. 2 and the "real image" were calculated. Thereby, the 178 subtracted images between the "real image" and the "blurred image" (we defined these 179 subtracted images as the "difference image") generated the same number as the "blurred 180

5) 185
The "difference image" with the minimum summed value was extracted from 3125 "difference 186 images" obtained by Process No. 3. In other words, the "difference image" was extracted 187 when the "blurred image" was approximated most to the "real image." We defined the 188 assumed accumulation amounts, assigned to the "blurred image" used when the extracted 189 "difference image" was created, as the accumulation amounts in the left and right 190 caudate/putamen and the BG regions. The accumulation amounts in the left and right caudate/putamen, and BG regions obtained 195 by Process No. 4 were obtained from the approximately assumed accumulation amounts, 0, 196 0.5, 1.0, 1.5, and 2.0 (the range of the assumed accumulation amounts was 0-2.0, and the 197 interval of the assumed accumulation amounts was 0.5). Therefore, the assumed 198 accumulation amounts were updated in detail to examine the "blurred image" that 199 approximated more to the "real image." In this update, the range and interval of the assumed 200 accumulation amounts assigned in the second step were updated to half of the range and 201 interval of the assumed accumulation amounts assigned in the first step of Process No. 2. For 202 example, it hypothesizes that the "blurred image" is approximated most to the "real image" 203 when 1.0 as the assumed accumulation amount is assigned to a certain region. Among the 204 assumed accumulation amounts (0, 0.5, 1.0, 1.5, 2.0) assigned in the first step, the values 205 before and after the 1.0, which is the value when the "blurred image" is approximated most 206 to the "real image" are determined as the range of the assumed accumulation amounts 207 assigned in the second step. In other words, the range of the assumed accumulation amounts 208 assigned in the second step is 0.5 to 1.5. Moreover, although the interval of the assumed 209 accumulation amounts 0, 0.5, 1.0, 1.5, and 2.0 is 0.5 in the first step, the interval is 0.25 in the 210 second step, which is half of the interval in the first step. Therefore, in the second step, the 211 five values 0.50, 0.75, 1.00, 1.25, and 1.50, as the assumed accumulation amounts are 212 reassigned to the same region. We performed an exception process in case the "blurred 213 image" was approximated most to the "real image," when the assumed accumulation amount 214 was zero, since the process in the proposed method was performed so that the assumed 215 accumulation amount was not negative. In case the "blurred image" is approximated most to 216 the "real image" when the assumed accumulation amount is 0, the range of the assumed 217 accumulation amount assigned in the second step is not the value before and after 0, which 218 is assigned in the first step, and as an exception, only the value after the 0 is used. In other 219 words, the range of the assumed accumulation amounts assigned in the second step will be 220 from 0 to 0.50 in this update. However, the interval of the assumed accumulation amounts is 221 0.25, as with the usual process. Therefore, three values, 0, 0.25, 0.50, as the assumed 222 accumulation amounts are assigned again in the second step in case the "blurred image" is 223 most approximated to the "real image" when the assumed accumulation amount is 0. This After Process No. 2-No. 5 was performed 10 times, the final "blurred image," which used for 231 generating the "difference image" indicated the minimum summed value, was extracted. In 232 other words, the "blurred image," which was approximated most to the "real image" in all 233 generated "blurred images," was extracted. We subsequently defined this final extracted 234 "blurred image" as the "generated image." This obtained "generated image" was undone 235 before a 3D Gaussian filter was applied, i.e., the "assigned image" corresponded to the 236 "generated image," was extracted. This "assigned image" obtained by this process was the 237 ideal image with no blur reflecting the accumulation amounts in the left and right 238 caudate/putamen and BG regions, and we defined this image as the "ideal assigned image." 239 We finally determined the assumed accumulation amounts, assigned to the left and right 240 caudate/putamen and the BG regions when the "ideal assigned image" was created, as the 241 accumulation amounts for each region. The final accumulation amount obtained by the 242 proposed method was determined as SPECT count density by the proposed method . We computed the 243 SBR and caudate-putamen ratio (CPR) following the formula using SPECT count density by the 244

2-4. Comparison method 249
To represent the validity of the proposed method, as a comparison with the proposed method, 250 we computed the SPECT count density using the comparison method. In the comparison 251 method, the SPECT count density was calculated using the VOIs for the left and right 252 caudate/putamen and BG regions, which were applied from the CT images to the SPECT 253 images in Process No. 1. Since Process No. 2 and the subsequent in proposed methods were 254 not performed in the comparison method, PVE correction (PVC) was not performed in the 255 SPECT count density calculated by the comparison method, which was different from the 256 proposed method. Therefore, we defined the SPECT count density calculated by the 257 comparison method as SPECT count density without PVC . 258 259

2-5. Evaluation method 260
We measured the actual count density (count/s･g) of the 123 I solution filled into the striatal 261 phantom by an auto-well counter. The correlation between the actual count density and the 262 SPECT count density by the proposed method was evaluated using the Pearson's correlation coefficient. 263 In addition, the correlation coefficient between the actual count density and the SPECT count 264 density without PVC was also calculated. The difference between these two correlation coefficients 265 was tested using the Meng-Rosenthal-Rubin method [9]. 266 In "Phantom2," we defined SBR and CPR, calculated by the actual count density of 267 123 I solution filled into the striatal phantom, as each theoretical value. The absolute errors 268 between the SBR calculated by the proposed method and the theoretical value were 269 calculated using the following formula (the absolute errors for CPR were also calculated): 270

Results 273
The comparison between the "real image" acquired by the actual SPECT imaging and the 274 "generated image" obtained by the proposed method is represented in Fig. 8. The images 275 shown in Fig. 8 were in the same display condition, and the counts and contrasts of the 276 caudate, putamen and the BG in the "generated image" were visually similar to them in the 277 "real image." 278 The correlation coefficient between the actual count density filled into the phantom 279 and the SPECT count density by the proposed method was 0.997 (p < 0.001), which showed a strong 280 positive correlation (Fig. 9a). In addition, the correlation coefficient between the actual count 281 density and the SPECT count density without PVC was 0.973 (p < 0.001), which also showed a 282 strong correlation (Fig. 9b). Upon significant difference testing between the two correlation 283 coefficients, the correlation of the proposed method was significantly higher than that of the 284 comparison method (p < 0.001). 285 In "Phantom2," the errors between the SBR calculated by the proposed method and 286 the theoretical SBR, calculated by the actual count density of 123 I solution filled into the 287 phantom are shown in Table 3 The SBR calculated by the proposed method was 288 overestimated in the left and right caudate/putamen regions, that is, all the regions. In 289 addition, the absolute errors between the CPR calculated by the proposed method and the 290 theoretical CPR were approximately 0.1, and the CPRs calculated by the proposed method 291 approached the theoretical CPRs (Table 4). 292 293

Discussion 294
From a pathological viewpoint in PD, it is desirable to evaluate the accumulation amounts in 295 the caudate and putamen through DaT SPECT. However, it is difficult to separate the caudate 296 and putamen owing to the low spatial resolution of the SPECT device. It is also difficult to 297 accurately evaluate the accumulation amounts due to PVE. Therefore, this study aimed to 298 verify whether the newly proposed method could accurately evaluate the accumulation 299 amounts in the caudate and putamen, with reduced PVE. 300 As shown in Fig. 8, the counts and contrasts of the caudate, the putamen, and the 301 BG in the "generated image" were visually similar to those in the "real image" for the same 302 display condition. In addition, the SPECT count density by the proposed method strongly correlated 303 with the actual count density of the 123 I solution filled into the phantom (Fig. 9a). This finding 304 of the correlation between true values and measured values was comparable to other 305 previously reported study [10]. Similarly, there was a strong correlation between the actual 306 count density and the SPECT count density without PVC calculated by the comparison method (Fig.  307 9b). However, the correlation coefficient of the proposed method was significantly higher 308 than that of the comparison method (p < 0.001). The SPECT count density by the proposed method 309 was an obtained value that considered the influence of PVE. As a result, it approached an 310 accurate accumulation amount, and thus, a stronger correlation in the proposed method was 311 considered. However, the SBRs calculated by the proposed method were overestimated in all 312 the regions (Table 3). This overestimation is considered since the contrast between the 313 striatum and the BG was overemphasized due to over-correction produced by SC, AC, and 314 PVC. It has been reported that the SC and the AC improve the quantitative evaluation 315 compared to no corrections [11][12][13][14]. In addition to the SC and AC, PVC also has been reported 316 to be valuable in quantitative evaluation [13,14]. Although the SBR calculated by the 317 proposed method is overestimated by the over-correction, it is considered since the SBRs 318 calculated by the proposed method did not indicate the absolute theoretical SBRs calculated 319 by the actual count density of 123 I solution filled into the phantom. However, since the SPECT 320 count density by the proposed method strongly correlated with the actual count density of 123 I solution 321 filled into the phantom, it seems that the SBRs calculated by the proposed method represent 322 not the absolute theoretical SBR, but the relative theoretical SBR on SPECT image. In support 323 of this, the CPRs obtained by the proposed method were extremely close to the absolute 324 theoretical CPR calculated by the actual count density of the 123 I solution filled in the phantom 325 (Table 4). In the proposed method, the SPECT count densities of the caudate and the putamen 326 were increased by the corrections; however, the caudate was divided by the putamen in the 327 CPR, which indicates that the influence of the corrections was canceled. Therefore, the CPRs 328 calculated by the proposed method were nearing the absolute CPRs calculated by the actual 329 count density of the 123 I solution filled into the phantom. In PD, the accumulation begins to 330 decrease from the putamen [6]. Hence, for evaluating the accurate CPR, the proposed method 331 can detect the accumulation reduction in the putamen with high sensitivity, which is expected 332 to be beneficial in clinical practice. 333 In the present study, when examining the "blurred image" approximated to the "real 334 image," the process where the assumed accumulation amounts were updated in detail to 335 examine the "blurred image" approximated more to the "real image," was performed. This 336 update process was performed 10 times. The variability rate of SBR with the number of 337 processes was calculated using the following formula: 338 Variability rate (%)= SBR n+1 -SBR n SBR n ×100 (4) 339 SBR n represents the SBR in the nth process. The variability rate of CPR was also calculated 340 using Eq. (4). The variability rate of SBR and CPR with the number of processes is shown in 341 Fig.10. We considered SBR and CPR to converge when the number of processes was over 342 seven since the variability rates of both SBR and CPR were less than 5%. Therefore, 10 times, 343 which was the number of processes used in the present study, was sufficient to converge. 344 In the present study, we only examined the use of a phantom. Therefore Southampton method tend to be overestimated especially in older age [22,23]. Therefore, it 367 is important to include the individual patient morphology. The difficulty in evaluating the 368 caudate and putamen, separately owing to the low spatial resolution of the SPECT images 369 makes the border between the caudate and putamen vague. Even when the caudate and 370 putamen can be separated by the combined use of the morphological images, the counts 371 leaking from the caudate and putamen (spill-out) enter each other's region (spill-in), making 372 the accumulation amounts in each region ambiguous. Moreover, the counts leaking from the 373 regions other than the caudate and putamen also enter the caudate and putamen regions 374 (spill-in). Therefore, it is extremely difficult to calculate the accurate accumulation amounts in 375 the caudate and putamen using SPECT images obtained by imaging. The BasGan method 376 [10] can compute the accumulation of the caudate and putamen separately with 377 consideration of PVE. The PVC method used in this method has been previously reported [24]. 378 This PVC method only uses the information included in the VOIs. The calculation process of 379 the proposed method uses reverse direction approach, which is different from the calculation 380 process that is normally used. In the proposed method, based on the anatomical position 381 information by a morphological image and the spatial resolution information of the SPECT 382 device, the calculation process involves examining the assumed accumulation amounts in 383 each region of the brain to approach the SPECT image obtained by actual imaging, and uses 384 this assumed accumulation amount to calculate the SBR. Therefore, different from the PVC 385 method using in BasGan method, the proposed method uses the all information of SPECT 386 images obtained by actual imaging for performing PVC. Therefore, since the proposed 387 method examines the realistic accumulation using the all information of SPECT images 388 obtained by actual imaging, leading to consideration of the counts leaked from the caudate 389 and putamen (spill-out), and the counts entered into the caudate and putamen from regions 390 other than the caudate and putamen (spill-in). Thus, it is expected that the proposed method 391 can evaluate the accumulation amounts in the caudate and putamen more accurately. 392 This study has some limitations. The primary limitation of this study is that it 393 examined only the phantom data in this study. In the present study, the image, which was 394 approximated most to the SPECT image obtained by imaging, was examined by generating 395 tens of thousands of SPECT-like images. As a result, the process took a few hours, which is 396 not suitable for clinical practice. Moreover, the accumulation amounts in the VOI were 397 assumed to be uniform in the proposed method. The voxel-by-voxel process allows the 398 consideration of the non-uniformity of the accumulation amounts. However, since an 399 enormous amount of processing is required, it was not performed in the present study. By 400 using an optimization method that minimizes the difference between the SPECT image 401 obtained by imaging and the generated SPECT-like image, the process takes lesser time, and 402 it is possible to apply the proposed method in clinical practice. In the present study, the 403 reason for not using the optimization method was that it was expected that the differences 404 in the optimization method or the parameter would lead to different results. Hence, an 405 exhaustive method was implemented to examine the usefulness of the proposed method in 406 a pure state without any influence other than the calculation process. If the process takes 407 lesser time by using the optimization method in the future, it is expected possible to perform 408 the voxel-by-voxel process and calculate the accumulation amounts in the detailed regions 409 of the brain. We consider that in the future this leads in the computation of more accurate 410 accumulation in detailed regions of the brain, considering the non-uniformity. the assumed accumulation amounts are assigned into each region, and the images with no 553 blur, called the "assigned image," were generated. A three-dimensional Gaussian filter 554 equivalent to SPECT spatial resolution in clinical condition was applied to the "assigned 555 image," and the single-photon emission computed tomography (SPECT)-like images, called 556 the "blurred image," was generated. The voxel-by-voxel differences between the actual image 557 obtained by imaging ("real image") and "blurred image" were calculated, and the "difference 558 image" was generated. The "difference image" with the minimum summed values was 559 extracted, and the assumed accumulation amounts, assigned into the "blurred image" used 560 when generating the extracted "difference image," were determined as the accumulation 561 amounts in the left and right caudate/putamen and BG regions. The assumed accumulation 562 amounts assigned to each region were updated in detail, and Process No. (=3125) images with no blur (these images are called the "assigned image") were generated. 584 A three-dimensional Gaussian filter equivalent to single-photon emission computed 585 tomography (SPECT) spatial resolution in clinical condition was applied to the "assigned 586 image." Thus, 3125 SPECT-like spatial resolution images (these images were called the 587 "blurred image") were generated. The accumulation amounts obtained from Process No. 4 were calculated from the roughly 607 assumed accumulation amounts. Therefore, the assumed accumulation amounts were 608 updated in more detail to examine the image that was more approximated to the "real image." 609 For example, it hypothesizes that the "blurred image" was most approximated to the "real 610 image" when the assumed accumulation amount in a certain region was 1.0. Then, among 611 the assumed accumulation amounts (0, 0.5, 1.0, 1.5, and 2.0) assigned in the first step, the 612 values before and after the 1.0, which is the value when the "blurred image" was most 613 approximated to the "real image," are determined as the range of the assumed accumulation 614 binding ratio (SBR). When the number of processing times was low, SBRs were greatly variable. 657 However, SBRs were converged as the processing was repeated. When the number of 658 processing times was more than seven, the variability rates of the SBR were less than 5%.  Table 1 Phantom data 673 The scheduled ratios show the radioactivity ratios of the 123 I solution scheduled before 674 creating the phantom. The actual count densities show that the 123 I count density actually 675 filled in the phantom was measured by an auto-well counter. The actual ratios show the ratio 676 calculated using the actual count density. In "Phantom1", 123 I solution was only filled in the 677 left and right caudate, and the other regions (the left and right putamen, and background 678 [BG] regions) were filled with water. In "Phantom2", the 123