Inclusion Criteria:  Subject eligibility is determined according to the following criteria prior to entry into the study:  In the opinion of the Investigator, the subject is capable of understanding and complying with protocol requirements. The subject signs and dates a written Informed Consent Form (ICF) and any required privacy authorization prior to the initiation of any study procedures. The subject is a healthy adult male or female. The subject is aged 18 to 55 years, inclusive at the time of consent. A female subject weighs at least 45 kg and a male subject weighs at least 50 kg. The subject has a body mass index (BMI) between 18.0 and 32.0 kg/m2 inclusive at Screening. A male subject who is non-sterilized and sexually active with a female partner of childbearing potential agrees to use highly effective contraception from the time of signing the ICF throughout the duration of the study and for 90 days (~5 half-lives) have elapsed since the last dose of study drug. Examples of highly effective contraception can be found in Appendix 1. A female subject of childbearing potential who is sexually active with a non-sterilized male partner agrees to routinely use highly effective contraception from the time of signing the ICF throughout the duration of the study and for 90 days have elapsed since the last dose of study drug. Examples of highly effective contraception can be found in Appendix 1. The subject has a negative urine/blood result for drugs of abuse (defined as any illicit drug use) at Screening or on Day -1.  Exclusion Criteria:  Any subject who meets any of the following criteria will not qualify for entry into the study:  The subject has received any investigational compound within 30 days or five half-lives (whichever is greater) prior to the first dose of study drug. The subject is an immediate family member, study site employee, or is in a dependent relationship with a study site employee who is involved in the conduct of the study (e.g., spouse, parent, child, sibling) or makes consent under duress. The subject has any clinically significant illness, such as cardiovascular, neurologic, pulmonary, hepatic, renal, metabolic, gastrointestinal, neurologic, immunologic, endocrine, or psychiatric disease or disorder, current infection with coronavirus disease 2019 (COVID-19), or other abnormality that may affect safety, increase the risk for seizure or lower the seizure threshold, or potentially confound the study results. It is the responsibility of the Investigator to assess the clinical significance of a subject's condition; however, consultation with the Biosion Medical Monitor may be warranted. The subject has a known hypersensitivity to any component of the formulation of BSI-045B. The subject has a history of drug abuse (defined as any illicit drug use) or a history of alcohol abuse within 1 year prior to Screening or is unwilling to agree to abstain from alcohol and drugs throughout the study. The subject has taken any prohibited concomitant medications (Section 5.5). The subject had a major elective surgical procedure within 8 weeks prior to Day 1. The subject is pregnant or lactating or intends to become pregnant or donate ova before, during, or within 90 days (~ 5 half-lives) since the last dose of study drug. If male, the subject intends to donate sperm during the course of this study or within 90 days (~ 5 half-lives) since the last dose of study drug The subject has had previous episodes of seizures or convulsions (lifetime) including absence seizure and febrile convulsion. The subject or any immediate family member has a history of epilepsy (including febrile convulsions). The subject has a history of neurologic abnormalities including abnormal electroencephalography, brain injury including traumatic injury, perinatal cerebropathy, postnatal brain damage, blood-brain barrier abnormality, and cavernous angioma. The subject has a history of cerebral arteriosclerosis. The subject has a history of cancer. Subjects with basal cell carcinoma, localized squamous cell carcinoma of the skin, or carcinoma in situ of the cervix may be included in the study if they have completed curative treatment at least 12 months before the first visit. Subjects with other malignant tumors may be included if they have completed curative treatment at least 5 years before the first visit (Day 1). The subject has a positive test result for hepatitis B surface antigen (HbsAg), anti- hepatitis C virus (HCV), or a known history of human immunodeficiency virus (HIV) infection at Screening. The subject has poor peripheral venous access. The subject has donated or lost ≥450 mL of his or her blood (including plasmapheresis) or had a transfusion of any blood product within 90 days prior to Day 1. The subject has an abnormal (clinically significant) electrocardiogram (ECG) at Screening or on Day -1. Entry of any subject with an abnormal (not clinically significant) ECG must be approved and documented by signature of the Principal Investigator or medically qualified Sub-Investigator. In the case of a corrected QT interval (Fridericia) (QTcF) >450 ms or >470 ms (HVs or AD patients with bundle branch block) or PR interval outside the range of 115 to 220 ms, assessment may be repeated once for eligibility determination at Screening and/or on Day -1. The subject has a supine systolic blood pressure <90 or >144 mm Hg or a supine diastolic blood pressure <50 or >94 mm Hg. If out of range, assessment may be repeated once for eligibility determination at Screening and/or on Day -1. The subject has a resting heart rate <40 or >90 bpm (not on ECGs) and considered clinically significant by the Investigator. If out of range, the assessment may be repeated once for eligibility determination at Screening and/or on Day -1. The subject has abnormal laboratory values at Screening that suggest a clinically significant underlying disease, or the subject has the following laboratory abnormalities: alanine aminotransferase (ALT) and/or aspartate aminotransferase (AST) >1.5 times the upper limit of normal unless otherwise agreed to by the Sponsor and Principal Investigator.  In addition to the general criteria above, AD patients in Part B must meet the following inclusion criteria to enter the study:  The patient has a diagnosis of AD (according to the criteria established by Hanifin et al, 2001 and Rajka et al, 1989). The EASI score is ≥15 at Screening. The score on the Investigator's Global Assessment is ≥3 at Screening. The score on the SCORing Atopic Dermatitis instrument is ≥20 at Screening. The total body surface area affected by AD is ≥10% as assessed by the EASI at Screening. The patient has an inadequate response to topical medications, or topical treatment is medically inadvisable.  In addition to the general criteria above, AD patients in Part B must not meet any of the following exclusion criteria:  The patient has another dermatologic condition that might confound a diagnosis of AD or a treatment assessment. The patient has a history of anaphylaxis following biologic therapy. The patient has a history of clinically significant infections within 4 weeks prior to Day -1. The patient has a diagnosis of helminthic parasitic infection within 6 months prior to Screening. The patient has received any marketed or investigational biologic agent within 5 half-lives prior to Screening. The patient has received treatment with immunosuppressive or immunomodulatory drugs without adequate washout, or has received phototherapy for AD within 4 weeks prior to Day 1. For drugs, an adequate washout period is 5 half-lives (e.g., 10 weeks for dupilumab). The patient has initiated treatment with topical corticosteroids (TCS) or topical calcineurin inhibitors within 1 week prior to Day -1. If rescue medications are deemed warranted by the PI class IV TCS may be used as rescue medication after Day -1 (see Table 13). The patient has initiated treatment with prescription moisturizers or moisturizers containing additives such as ceramide, hyaluronic acid, urea, or filaggrin degradation products during the Screening period (patients may continue to use stable doses of such moisturizers if initiated before the Screening visit, but should not change to a different product during the study). The patient plans to use any other prohibited medication or undergo any prohibited procedure during the study. Oral antibiotics are permitted. Bleach baths are not permitted. The patient has received any investigational compound within 30 days or 5 half-lives (whichever is greater) days prior to Day 1. The subject has a risk of suicide per the Columbia-Suicide Severity Rating Scale (a score of 4 or above on ideation or any suicidal behavior) or according to the Investigator's clinical judgment, has made a suicide attempt in the previous 6 months, or has a history of deliberate self-harm in the past 6 months. A subject with a lower score may be enrolled in the study. The patient has any clinically relevant abnormal finding.