Inclusion Criteria:

• - Aged between 18 - 69 years.

• - Received a diagnosis of MS (any type of MS) at least 12 months prior to baseline assessment.

• - Report cognitive problems, as determined by a cut-off score of 55 or lower on the oral SDMT.

• - Ability to give informed consent.

• - Able to commit to regular attendance in clinic, for up to 4 times a week for 4 weeks and follow up appointment eight weeks after the end of trial procedures.

Exclusion Criteria:

• - Diagnosed with depression or scores ≥15 on the Patient Health Questionnaire-9.

• - Medical history of, or self-reported, seizures.

• - Neurological conditions (in addition to MS), e.g., brain neoplasm, cerebrovascular events, epilepsy, prior brain injury or brain surgery.

• - Contraindications to MRI scanning (identified by standard MRI safety screening questionnaire).

• - Contraindications to TMS, including hairstyles or piercings that would impair magnetic transmission which cannot be altered to ensure effective intervention.

• - Frequent panic attacks which are likely to prevent regular attendance or participation in MRI/TMS procedures.

• - Prior TMS intervention.

• - Pregnancy.

• - MS relapse within the preceding 6 weeks.

• - Significant mobility problems if they are likely to preclude regular attendance in clinic, for up to 4 times a week for 4 weeks.

• - Involved with any other clinical trials involving medical procedures, interventions or treatment.

The primary objective is to assess the feasibility of the trial procedures, in terms of their acceptability and tolerability for pwMS who have cognitive impairment. For this aim, the completion of the intervention schedule will be measured (e.g., attending all sessions per the protocol, considering any missed appointments and reasons for non-attendance where possible) including the end of intervention assessments, as well as the 8-week follow up to ascertain participant willingness to complete the full study. Participants will be randomly allocated to one of four groups (Group 1: 4 administrations of intermittent theta burst stimulation (iTBS) over 1 week; Group 2: 8 administrations of iTBS over 2 weeks; Group 3: 16 administrations of iTBS over 4 weeks; Group 4: 8 administrations of sham iTBS over 2 weeks). Participants will not be aware whether they have been allocated to receive active or sham iTBS administration. Intervention

• - Active iTBS: Active connectivity-guided iTBS will be administered to the left dorsolateral prefrontal cortex (DLPFC).

The administration comprises bursts of 3 pulses at 50Hz with a power of 80% motor threshold, at a burst frequency of 5 Hz (i.e., every 200ms) for 2 seconds, repeated every 10 seconds for a total of 190 seconds (600 pulses). Blocks are repeated a total of 3 times, with 5 minutes rest intervals between blocks. (Duration and frequency: 30 min, 4 times a week for up to 4 weeks depending on group). Sham iTBS: The sham iTBS administration is performed under the same conditions and with an identical protocol and equipment to the full administration, except that it uses a commercially available sham iTBS coil designed for use in double-blind trials. This sham coil looks like the real coil and connects to the iTBS unit but delivers only a very weak and shallow stimulation thus simulating the sounds made by the real iTBS coil. At baseline, End of Intervention (EOI), and 8-week follow up, outcome measures will be completed to evaluate cognition, mood and fatigue. Participants will also undergo MRI scans at baseline and EOI. The purpose of the MRI is to allow identification of the exact location over which the iTBS intervention will be applied, and it will allow measurement of brain function before iTBS intervention (or sham). The MRI scan will include:

• - High resolution T1-weighted structural brain image for image co-registration, - Resting-state functional MRI (rs-fMRI) for connectivity-guided neuronavigation, - Fluid attenuated inversion recovery (FLAIR) - Diffusion tensor imaging (DTI) acquisitions to quantification spatial mapping of macro- and mircrostructural white matter injury, - Arterial Spin Labelling (ASL) perfusion imaging to map cerebral blood flow.

• - Task related functional MRI - N-Back task.

The investigators have developed a questionnaire to explore tolerability and acceptability of the procedures, and participants will also be invited to discuss their experience of participating in the trial at interview 8 weeks post-intervention. Finally, at the end of the study, the investigators aim to host a post-participation workshop at the beginning of month 28, following collection and analysis of main outcomes. Depending on covid-safe recommendations from the government and university, this may be via video call or at a venue. All participants will be invited to discuss whether the experience of participation (varying from 1-week to 4-weeks) can inform which of intervention regime investigators should take forward into a subsequent pilot trial, to expand on the preliminary data analysis from the qualitative interviews. Investigators will explore the magnitude and nature of the effect on cognition that would be needed to be achieved to give a meaningful change to them personally, such that the iTBS interventions of different durations would be warranted. For example, participants may feel that only a major improvement in day-to-day cognition would justify a 4-week intervention, whereas others may feel that any benefit would justify this. These issues will be explored to inform future trial design.

Arms

Active Comparator: Group 1

iTBS intervention lasting 30 minutes, given 4 days a week, for 1 week

Active Comparator: Group 2

iTBS intervention lasting 30 minutes, given 4 days a week, for 2 weeks

Active Comparator: Group 3

iTBS intervention lasting 30 minutes, given 4 days a week, for 4 weeks

Sham Comparator: Group 4

Sham iTBS intervention lasting 30 minutes, given 4 days a week, for 2 weeks.

Interventions

Other: - Intermittent theta burst stimulation (iTBS)

The localisation of the left dorsolateral prefrontal cortex (DLPFC) target will be identified using effective connectivity of the left caudate to identify the maximally-connected locus in the left DLFPC. Following this the iTBS will be administered to the target coordinates identified using the neuronavigation software available with the system. Connectivity-guided iTBS is then administered using a 70mm Double Air Film Coil (Magstim, Whitland, Dyfed, UK), connected to a Magstim Super Rapid-2 Plus-1 stimulator. The administration comprises bursts of 3 pulses at 50Hz with a power of 80% motor threshold at a burst frequency of 5 Hz (i.e., every 200ms) for 2 seconds, repeated every 10 seconds for a total of 190 seconds (600 pulses). Blocks are repeated a total of 3 times, with 5-minute rest intervals between blocks. During left DLPFC stimulation, the TBS coil is held by a support tangentially to the skull, with the axis of the coil angled approximately 90 degrees from the midsagittal axis.

Other: - Sham Intermittent theta burst stimulation (iTBS)

The sham iTBS administration is performed under the same conditions and with an identical protocol and equipment to the full administration, except that it uses a commercially available sham iTBS coil designed for use in double-blind trials. This sham coil looks like the real coil and connects to the iTBS unit but delivers only a very weak and shallow stimulation thus simulating the sounds made by the real iTBS coil.