As an emerging non-invasive neuromodulation tool, the low-intensity 23 transcranial focused ultrasound (tFUS) delivers highly controllable 24 mechanical energy from transducers, penetrating the skull with relatively low 25 tissue attenuation and modulates the targeted brain circuits with high spatial 26 selectivity. tFUS is featured with a vast parametric space, and by tuning its 27 parameters, the ultrasound wave can be steered and be used to produce 28 excitatory or inhibitory neural effects. Such neuromodulatory effects of tFUS 29 for effective brain stimulation have been evidenced on a wide range of animal 30 models (Dallapiazza et al., 2018; Daniels et al., 2018; Folloni et al., 2019b;  31 Lee et al., 2016c; Mohammadjavadi et al., 2019; Tufail et al., 2011; Verhagen 32 et al., 2019; Yang et al., 2018; Yoon et al., 2019; Yu et al., 2016) and, recently, 33 demonstrated in humans (Lee et al., 2016a; Lee et al., 2015; Lee et al., 34 2016b; Lee et al., 2017; Legon et al., 2018a; Legon et al., 2018b; Legon et 35 al., 2014) . For instances, the low-intensity diagnostic ultrasound energy has 36 been shown to suppress the pain, improve the subjects' mood and global 37 affect (Hameroff et al., 2013) . A recent study on using ultrasonic thalamic 38 stimulation assisted a patient to recover consciousness after severe brain 39 injury (Monti et al., 2016) . 40 Among accumulating experimental demonstrations on healthy humans, a 41 pioneer study using low-frequency and low-intensity tFUS was able to 42 achieve robust neuromodulation effects at the primary somatosensory cortex 43 (S1), evidenced through the ultrasound-modulated sensory-evoked brain 44 activity recorded at electroencephalogram (EEG) sensors and the 45 enhancement of sensory discrimination abilities (Legon et al., 2014) . Another 46 pilot study on tFUS modulating the S1 circuits reported direct evoked limb 47 sensations and the ultrasound stimulation event-related potentials (ERPs) 48 specifically at C3 and P3 EEG electrodes (Lee et al., 2015) . Later, the 49 acoustic stimulation was ipsilaterally targeted at S1 and S2 (i.e. the 50 secondary somatosensory cortex) simultaneously by multiple transducers.
Extensive tactile sensations were elicited and reported by the human 52 subjects (Lee et al., 2016a) . 53 The visual cortex is also a well-studied brain target for tFUS research. On 54 human, researchers administered sonication to the primary visual cortex 55 (V1). From the concurrent blood-oxygenation-level-dependent (BOLD) 56 functional magnetic resonance imaging (fMRI), researchers observed 57 ultrasound-elicited brain activations at the targeted V1 as well as the related 58 visual and cognitive brain network. Sonication-mediated ERPs and 59 phosphene perception were also reported (Lee et al., 2016b) . Very recently, 60 the ultrasound-induced illusory visual percepts were further investigated by 61 applying repeated transcranial diagnostic ultrasound at visual cortical region 62 identified by transcranial magnetic stimulation (TMS) eliciting phosphene 63 (Schimek et al., 2020) .
The motor cortex has been one of the popular sonication targets on animal 65 models for eliciting direct brain activation by tFUS, demonstrated by more 66 direct motor response readout (Kim et al., 2014; King et al., 2013; Mehic et 67 al., 2014; Tufail et al., 2010; Ye et al., 2016; Yuan et al., 2020) and/or 68 measurements from the corresponding muscle activities using 69 electromyogram (EMG) (King et al., 2013; King et al., 2014; Qiu et al., 2017; 70 Yoon et al., 2019) . In spite of this, the demonstrations of tFUS modulation on 71 human motor cortex are somehow limited. One of the recent efforts was to 72 employ a 7-Tesla BOLD fMRI for observation of tFUS modulation in the 73 targeted finger representation areas in terms of neurovascular signal change 74 while the subjects performed a simultaneous cued finger tapping task. The 75 activation volume of the thumb motor representation area was significantly 76 increased by the tFUS neuromodulation (Ai et al., 2018) . Another effort was 77 to further test how the ultrasound effects the motor cortical excitability and 78 behavior output by developing a novel hybrid brain stimulation device for 79 concurrent transcranial ultrasound and magnetic stimulation (Legon et al., 80 2018b). The tFUS neural inhibitory effects were inspected and quantified 81 through the amplitude reduction of single-pulse motor-evoked potentials and 82 the attenuation of intracortical facilitation. Interestingly, the tFUS significantly 83 shortened the reaction time on a stimulus response task (Legon et al., 84 2018b).
However, our current understanding on how tFUS can influence the human 86 voluntary motor processing in the brain is still lacking. In this study, we test 87 the ultrasound neuromodulatory effects on movement-related cortical 88 potential (MRCP) which occurs during the preparation for and execution of 89 movement with clinical significance on rehabilitation in patients (Niazi et al., 90 2012; Shakeel et al., 2015; Spring et al., 2016; Xu et al., 2014) , scientific 91 research on studying motor skill learning (Wright et al., 2011) , and enhancing 92 the brain-computer interface (BCI) (Dremstrup et al., 2013; Liu et al., 2020) .
Beyond the EEG delineation at the sensor level, in this study, we employ 94 scalp EEG based electrophysiological source imaging (ESI) (He and Ding, 95 2013; He et al., 2018; Yu et al., 2016) Furthermore, by virtue of computer modeling and simulations (Plaksin et al., 100 2016), the ultrasound pulse repetition frequency (UPRF) has been deemed 101 as one of the critical ultrasound parameters to achieve excitatory/inhibitory 102 neural effects. In a recent study, the acoustic radiation force produced by the 103 UPRF has been inferred as the most crucial source of behavioral responses 104 (Kubanek et al., 2018) . Most recently, the UPRF was also found as a critical 105 parameter in balancing the excitatory/inhibitory neuronal activities (Yu et al., 106 2019). In this study, we further assess the role of UPRF in modulating the 107 human MRCP. were later used to identfy the brain target through FreeSurfer cortical 121 reconstruction (Dale et al., 1999; Desikan et al., 2006) for guidance of the 122 low-intensity focused ultrasound focus.
During the tFUS-EEG session, the subject was seated inside a sound and 124 electromagnetic shielding room (IAC Acoustics, USA) and was instructed to impedance of all electrodes was kept below 10 kΩ during the EEG capping.
Positions of electrodes were digitized over each subjects' scalp using an 136 optical-based EEG PinPiont system (Localite GmbH, Germany). The 137 ultrasound transducer was held and mounted on top of the EEG cap using a 138 3D-printed helmet. An optical-based brain navigation system (Localite GmbH, 139 Germany) was utilized with the input of the structural MRI data and an optical Figure 1 ). This trigger signal was further stretched to 179 5 msec long by TriggerBox (Brain Products GmbH, Germany) for 180 synchronization with EEG recordings. Once triggered, the first function 181 generator was used to create the UPRF and determine the number of pulses.
The second function generator was triggered by the output of the first one in 183 burst mode and generated ultrasound fundamental frequency (UFF) of the 184 sinusoidal waveforms and determined the number of cycles per pulse (CPP).
As illustrated in Figure 2A , this study used a UFF of 0.5 MHz, CPP number 186 of 100. Each sonication lasted for 500 msec with two levels of UPRF, i.e. 300 187 and 3000 Hz practiced in two sessions (denoted as "UPRF 300Hz" and 188 "UPRF 3000Hz", respectively). The ultrasound spatial peak pressure applied 189 to the scalp was measured as 809.2 kPa (shown in Figure 2B -C, spatial- The EEG was sampled at 5 kHz and filtered using a bandpass filter with the 220 lower cut-off frequency at 1 Hz and the higher cut-off frequency at 45 Hz.
The pre-stimulus period was set as 400 msec before the trigger signal, and Figure 3A , D, G, Figure 4A and Figure 6 ). For EEG-231 based source modeling and imaging, the boundary element method (BEM) 232 (Hämäläinen and Sarvas, 1989; He et al., 1987) head model for each human 233 subject was established using OpenMEEG (Gramfort et al., 2010) , which 234 consisted of three layers, i.e. scalp, skull and brain with relative conductivities 235 of 1, 0.0125 and 1, respectively. The minimum norm imaging (MNI) was used 236 to solve the inverse problem, thus reconstructing the cortical source activity.
The source activity was imaged using the MNI for the duration of sonication. second null hypothesis is that the UPRF change will have no effect on the 253 MRCP source amplitude. The Kruskal-Wallis rank sum test was performed 254 to examine this hypothesis. Next, paired Wilcoxon test was further employed 255 to assess whether the increased UPRF will lead to a stronger 256 neuromodulation effect. For both statistical tests above, we performed 
The multi-channel EEG butterfly plots in Figures The panels of (C), (F) and (I) show more detailed views of the brain activities specifically at the primary 296 motor cortex (M1) in responses to the three ultrasound sessions, respectively. The ESI illustrated 297 reconstructed current source densities. The green patches in these ESI panels represent the seed 298 areas for further extracting the MRCP source profiles. Different color scale bars are used to allow 299 better presentation of the localized motor source at the cortical brain. L: left, R: right, A: anterior, P: 300 posterior. 301
The green patches overlaid on top of the ESI results in Figures 3C, F and I 302 were used to indicate the seed area of the cortical region of interest in our 303 study, i.e. primary leg motor area in left brain hemisphere. We extracted the 304 MRCP source activity from the identified area of 3.4 cm 2 confined in the 305 reconstructed source area. The resulted MRCP source profiles were 306 generated for subsequent analyses. Figure 4A presents the profiles for 307 comparisons directly among the three ultrasound conditions. In the source 308 domain, typical MRCP features were reconstructed and indicated with 309 horizontal arrows. The readiness potential (RP), also known as 310 Bereitschaftspotential, priors at the onset of movement (from -400 to -24 311 msec in Sham US and UPRF 300Hz; from from -400 to -20 msec in UPRF 312 3000Hz) and is involved in the movement preparation (Dremstrup et al., 313 2013) . According to the definition, it is more accurate to denote this MRCP 314 component as "late RP" given its neighboring timing to the movement onset.
Immediately following this late RP, the motor potential (MP) reflecting the 316 movement execution was reconstructed within a much short time period of 317 36-38 msec (from -24 to 12 msec in Sham US; from -24 to 14 msec in UPRF 318 300Hz; from -20 to 18 msec in UPRF 3000 Hz). Lastly, the MRCP source 319 profile reconstructed the third component, movement-monitoring potential 320 (MMP, from 12 to 178 msec in Sham US; from 14 to 362 msec in UPRF 321 300Hz; from 18 to 378 msec in UPRF 3000Hz), which controlled the 322 movement performance (Shakeel et al., 2015) . Based on the timing of with 25% and 75% quantiles (lower and upper hinges). Statistics by one-tail non-parametric paired 352
Wilcoxon rank sum test for examining the effect UPRF increase. *p < 0.05. 353
To further interpret the effect of UPRF in modulating the MRCP, a non-354 parametric analysis of variance (ANOVA) was performed using Kruskal-
Wallis rank sum test ( Figure 5A ). For this test, the Sham US condition can 356 be considered as a type of tFUS condition with UPRF of 0 Hz. As a result, 357 we found that the UPRF did play a significant role (Kruskal-Wallis chi-358 squared = 7.24, p < 0.05) in changing the MSPA of the human subjects.
However, the variance of observations in the condition of UPRF 3000Hz is 360 observed to be larger than the other two conditions. To further probe into a 361 more specific effect of the UPRF, the non-parametric paired Wilcoxon test 362 was further used ( Figure 5B ). Significantly higher MSPAs (V-statistic = 21, p 363 < 0.05) were observed by dosing the higher UPRF, i.e. 3000 Hz.
The MRCP magnitude was correlated with the elbow-flexion movement 365 property, such as the force and its speed (Siemionow et al., 2000) . To rule Figure 4A ) measurements, needs to be further investigated. As illustrated in 410 Figure 4A , the MRCP was initiated during the movement planning phase, i.e. 411 the RP, prior to the actual physical movement. In fact, the RP is raised as 412 early as 1.5 sec before the onset of movement (Shakeel et al., 2015) , which 413 may be useful to provide much earlier trigger signal for tFUS 414 neuromodulation, thus assisting the movement planning and preparation.
Since the MRCP can also be evoked by motor imagination (Shakeel et al., Amyotrophic Lateral Sclerosis (ALS) (Gu et al., 2009) , it would be valuable 424 to have a non-invasive neuroimaging tool, such as ESI, to map and quantify 425 the MRCP source at specific brain circuits with high spatiotemporal 426 resolution, thus informing the non-invasive neuromodulation for guidance 427 and feedback (Yu et al., 2020) . Electrophysiological source imaging (ESI) 428 has been pursued to localize and image brain electrical sources from 429 noninvasive scalp recorded EEG/MEG, and demonstrated to provide greatly 430 enhanced spatial resolution than the raw EEG/MEG in many applications 431 (He & Ding, 2013; He et al, 2018; Sohrabour et al, 2020) . The EEG-based 432 ESI (He and Ding, 2013; He et al., 2018) has demonstrated its unique and 433 significant role for effectively identifying epileptogenic brain sources 434 (Sohrabpour et al., 2020) and enhancing the subjects' BCI performances 435 (Edelman et al., 2019) . Although fMRI has been harnessed to monitor and 436 assess the neuromodulatory effects of tFUS on animals models (Folloni et 437 al., 2019a; Verhagen et al., 2019; Yang et al., 2018; Yoo et al., 2011) and on 438 humans (Lee et al., 2016b) , the method does not directly measure the neural 439 activities and the strong static magnetic field may confoundingly alter the 440 cortical excitability (Nakagawa and Nakazawa, 2018; Oliviero et al., 2011) .
In addition, besides the substantial concerns of ultrasound device 442 compatibility with the magnetic field, the fMRI imaging pulse sequences may 443 inevitably induce ancillary brain activations, e.g. auditory responses. Hence, 444 a natural setting for monitoring the tFUS modulating human brain with high 445 spatiotemporal resolutions, like the ESI is desirable.
Low intensity tFUS neuromodulation is deemed as generally safe without 447 inducing serious adverse effects on humans upon careful control of the 448 ultrasound intensities (ISPPA: 11.56-17.12 W/cm 2 ) (Legon et al., 2020) .
Although our study administered less ultrasound intensities than those 450 applied in (Legon et al., 2020) and even much less than the FDA's guideline 451 (ISPPA ≤ 190 W/cm 2 ) (FDA, 2008), we were also cautious about the tFUS 452 safety on the subjects during the experiment sessions. We surveyed the 453 subjects with a brief questionnaire for report of symptoms, such as headache, 454 neck pain, dental pain, nausea, dizziness, anxiety, abnormal muscle Figure 5A ).
Due to the time limit in our experiment protocol, we were unable to test 463 extensive UPRF conditions. However, as the UPRF is highly correlated with 464 the ultrasound spatial-peak temporal-average intensity (ISPTA), by increasing 465 this frequency, the total acoustic energy deposited onto the targeted brain 466 area is correspondingly increased. It is reasonable to infer that the increased 467 ultrasound energy in a high UPRF condition leads to increased excitatory 468 effects at the human primary motor cortex. Future research efforts will adjust 469 UPP for different UPRF levels to maintain the total ultrasound energy as a 470 constant during the fixed sonication period to tease out whether UPRF 471 frequency encoding plays a role in the modulation effects.
Inevitably, we observed inter-subject differences in response to the tFUS 473 neuromodulation (shown in Figure 4B -C and Figure 5B ). Such differences 474 may be attributed to many factors. One of the crucial factors is the inter- (Mueller et al., 2017; Webb et al., 2018) . 